Appendix I

A Brief History of ThermalEngineering of ElectronicSystems

Electronic microminiaturization is affecting nearly every facet of our lives. Oneof the critical challenges to maintaining the past rate of miniaturization is inelectronic packaging, and more specifically, thermal engineering . To put this inperspective, at the periphery of the sun the surface temperature is about 6000°C, representing a heat flux of 107 W/m 2

• Current microchips generate a heat fluxof about 105 W/m 2 which must be cooled to around only 125° C. The applica­tion of advanced thermal engineering techniques requires a blending of the engi­neering disciplines of heat transfer, fluid dynamics, mathematics, and to a lesserextent, electronic theory. How did we get to this point, and what can we expectin the future?

The Egyptians had learned some physiology and surgery techniques as earlyas 3000 B.C. Using principles of evaporation (two-phase heat transfer), con­vection cooling, and heat radiation, they chilled their drinking water onrooftops at night. They also developed a system for measuring property lines,geometry, and a form of mathematics . The Chinese cut and stored ice for sum­mer usage staring about 1000 B.C. They also had a system of mathematics,writing, chemistry, and astronomy. During the 6th century B.C., the abacusoriginated in China, and was the fundamental instrument for performing calcu­lations until the 1500s.

Geometry studies progressed in ancient Greece . Thales (640?-546? B.C.),one of the Seven Wise Men of ancient Greece, used geometry to predict a solareclipse. He also experimented with static electricity. The Greek mathematicianPythagorus (580?-500? B.C.) formulated the Pythagorean Theorem, although itsprinciples were known earlier. Pythagorus was probably killed in a politicaluprising because he organized the Brotherhood of Aristocrats. The brotherhoodfinally disbanded about 400 B.C. Euclid (300?-? B.C.) published The Elements,

545

546 App. I A Brief History of Thermal Engineering of Electronic Systems

a 13-volume set of books about geometry, algebra, and number theory. Studentsused The Elements as textbooks until the late l800s.

About 200 B.C. the Indians passed on a numbering system to the Arabs .Around this time, Archimedes (287?-2l2 B.C.) was asked to find a method fordetecting a fake royal crown. He realized that since gold is one of the mostdense substances, mixing another metal with it would make a fraudulent crownlighter than an authentic crown. The problem became how to measure the den­sity of an irregularly shaped object. It is said that Archimedes discovered theprinciple while taking a bath. When he realized that his arms and legs seemedlighter in the bath, he ran down the streets of Syracuse, wearing only a towel,yelling "Eureka! Eureka!". Archimedes' principle says that when an object issubmerged, the loss of weight equals the weight of the fluid displaced by theobject. Known as specific gravity, this is the ratio between the weight of thefluid and the weight of the object. Archimedes was the greatest scientist of hisday and was respected in all of the civilized world. He originated processes thatforeshadowed the invention of integral calculus 1800 years later. When theRomans conquered Syracuse, Sicily in 212 B.C., a Roman soldier, mistakingArchimedes for an old beggar, ran a sword through him.

Although the Romans conquered many civil engineering problems, they con­tributed little to the advancement of mathematics as a science. After the fall ofthe Roman Empire in A.D. 476 there were no new European developments forhundreds of years. These were the Dark Ages. European scholars had turned totheology. By the 600s the Mayans had a much better understanding of theirnumbering system than the Europeans had of theirs. During the 700s, the Arabs,who had taken over much of the old Roman Empire, studied the writings of theancient Greeks. They combined those writings with the Indian decimal system.Between 813 and 833, AI-Khowarizmi, a professor in the Baghdad school ofMathematics, organized and improved the writings of Hindu and Arab scholars.When traders introduced translations of the ancient Greek books and new Arabideas into Europe during the A.D. WOOs, the Europeans organized them to agreewith their own religious views. To question the interpreted writings of theancient Greeks was punishable by death . The head of the Franciscan Orderjailed Roger Bacon (1214-1294), an English monk and one of the founders ofpresent day science, for "suspect innovations" in his work.

Progress in the sciences began again in the l400s, the European Renaissance.Leonardo Da Vinci (1452-1519) studied the sciences as an engineer, geologist,astronomer, and botanist. Among his many accomplishments was a canal sys­tem with locks that is still used. His sketches provided insight into the turbulentflow of liquids . In 1585, Galileo Galilei (1564-1642) invented the hydrostaticbalance. This device is still used to find the specific gravity of objects by weigh­ing them in water. Later in 1593, Galileo invented the thermoscope. The appa­ratus, similar to a thermometer, consisted of an inverted tube of water in a bowl.

App. I A Brief History of Thermal Engineering of Electronic Systems 547

It had no degree scale, and measured only temperature differences, not temper­ature. Galileo spent his last years confined to his villa by the Inquisition . Hewrote about his theories of motion, acceleration , and gravity. His work providedthe basis for Sir Isaac Newton' s laws of motion.

At about the same time Galileo was experimenting with fluids, Will iamGilbert (1540-1603), physician to Queen Elizabeth I, began to experiment withstatic electricity. He used the words electrum and electrica in his reports.

A contemporary of Galileo ' s, Sanctorius, introduced the first scale for thethermoscope in 1611. The low point temperature was when covered by snow.The high point was when a candle was held underneath. This scale had 110 unitsand was the first actual thermometer. The measurements were inaccuratebecause atmospheric pressure altered the readings. A more accurate thermome­ter using alcohol was invented in 1641.

John Napier (1550-1617), a Scotsman, published the famous Mirifici Loga­rthmorum Canonis Descriptio in 1614. His logarithms converted the lengthyprocedures of multiplication and division to the faster processes of addition andsubtraction. He also invented so-called "bones" or "rods" for multiplying anddividing, and for extracting square and cube roots. He published many formu­las used in spherical trigonometry.

Blaise Pascal ' s (1623-1662) father taught his son only the subjects hethought a son should know, mostly ancient dead languages. By the age of 12Blaise had taught himself geometry, and at the age of 16 published a book titledThe Geometry of Conics. His father relented and allowed the boy to studyphysics and mathematics when the famous philosopher and mathematician Rene("I think, therefore I am") Descartes (1596-1650) took an interest. At the ageof 19, noting his father ' s long hours spent calculating as a tax collector, he builtthe first calculating machine. His mechanical device added and subtracted byturning small wheels. The idea didn't catch on with the hand-calculating clerksin France for reasons of job security, so Blaise turned his attention to the studyof fluid pressure. Pascal' s Law says that the change of pressure at any point ina confined fluid is transmitted undiminished in all directions to all points withinthe fluid. Later, along with the French mathematician Pierre De Fermat(1601-1665), Pascal invented the theories of probability and statistics, andexplained their uses in card games and gambling .

In 1643, the Italian mathematician Evangelista Torricelli (1608-1647) pro­posed that atmospheric pressure determines the height of a fluid in an invertedtube over a container of the fluid. Torricelli was Galileo ' s successor at the Flo­rentine Academy. This theory led to the development of the barometer. As courtmathematician and philosopher to Grand Duke Ferdinand II of Tuscany, Torri­celli proved what is now known as Torricelli ' s theorem. This theorem says thatthe velocity of a liquid through an opening equals the velocity of a free-fallingbody from the surface of the liquid to the opening .

548 App. I A Brief History of Thermal Engineering of Electronic Systems

The problem of a thermometer responding to atmospheric pressure changeswas solved in 1644 when Grand Duke Ferdinand III of Tuscany (1608-1657)introduced the sealed thermometer, To further the experimentation and manu­facture of accurate thermometers, the Academia de Cimento in Florence wasestablished in 1657. The Florentines filled these thermometers with red winebecause it expands faster than liquid metal.

Robert Boyle (1627-1691), an Irish chemist, studied the changes in volumeof a gas as he varied the pressure. The result was Boyle's Law: P = constant/V.This shows that at a given temperature and volume, all gases will exert the samepressure, and became the general gas law: 9ft = PVInT. He also studied the boil­ing and freezing of liquids at reduced pressures.

The English astronomer Edmund Halley (1656-1742) predicted the return ofthe comet of 1682, studied compass needle deviations, and mapped the stars.Robert Hooke (1635-1703) stated Hooke's Law of proportional stress and defor­mation and discovered plant cells. Sir Christopher Wren (1632-1723), the Eng­lish architect and mathematician, redesigned all or part of 55 out of 87 churchesthat were destroyed in the Great Fire of London in 1666. One day in 1684 thesethree men were discussing the law of force that guided the planets around thesun. They could not solve the problem, so Halley traveled to Cambridge to con­fer with Sir Isaac Newton (1642-1727). Newton displayed the complete proofof the law of gravity that he had discovered 17 years earlier along with calcu­lus, and the laws of color and light. He had made these discoveries during an18-month period from 1665 to 1667. Newton disliked the negative criticism thataccompanies new scientific discoveries so he concealed his work.

In 1671, the German mathematician Gottfried Wilhelm von Leibniz(1646-1716) constructed a stepped-wheel device for multiplying by means ofrepeated additions. Scientists used his device in limited numbers. Leibniz didnot attempt to popularize his invention. He believed that a man should justaccept his lot in life, not try to change things, and make the best of it. The quote"This is the best of all possible worlds" is attributed to Leibniz. He also sharesthe credit for inventing calculus with Sir Isaac Newton.

Daniel Bernoulli (1700-1782), whose father and uncle were also famousSwiss mathematicians and physicists, discovered the relationship between fluidvelocity, density, pressure, and height. Bernoulli's Law, published in Hydrody­namica in 1738, explains that as the speed of a fluid increases, the pressure ofthe fluid decreases. In this work Bernoulli also explained his kinetic theory ofgaseous pressure in a container . Bernoulli collaborated with Leonhard Euler atthe St. Petersburg Academy of Sciences.

The German physicist Gabriel Daniel Fahrenheit (1686-1736) made the ther­mometer more accurate in 1714 by using mercury instead of alcohol, and devel­oped the temperature scale named in his honor. The Swedish astronomer Anders

App. I A Brief History of Thermal Engineering of Electronic Systems 549

Celsius (1701-1744) made a great impact on thermometers. Two years beforehis death he chose a fixed water freezing point, a water boiling point, and thedivision of the interval into 100 equal graduations (centigrade). Celsius origi­nally called the ice point 100 and the boiling point zero.

Charles Francois Du Fay (1698-1739), King Louis XV's Superintendent ofGardens , found that a static electricity charge can be deposited on any object.In 1733 he wrote about two different types of electricity: vitreous and resinous.Benjamin Franklin (1706-1790), Minister and frequent visitor to France,became interested in electricity about 1746. He called Du Fay's electricities pos­itive and negative. He conducted his famous kite experiment in 1752 and provedthat lightning is electricity. Franklin continued to experiment with electricityeven though he was knocked unconscious several times.

Leonhard Euler (1707-1783) became famous for his wide range of work inmathematics. Most of his work in number theory, probability, geometry,acoustics, mechanics, algebra, optics, finance , calculus, statistics, and algebrawas accomplished after he went blind in 1766. In the period between 1726 and1800, Euler's 866 books and articles represented one-third of all the research onmathematics, theoretical physics , and engineering mechanics. A Swiss societystarted to publish his work in 1909. After 50 years and 47 volumes they werestill not finished.

The Scottish scientist William Cullen discovered the principles of artificialrefrigeration in 1748 at the University of Glasgow. While experimenting withethyl ether, he evaporated it into a partial vacuum. This event was the dawn ofvapor cooling.

In 1760, a Scottish physician, Joseph Black (1728-1799), demonstrated thatheat does not have weight and devised the theory of latent heat. Another Scot­tish inventor, James Watt (1736-1819), patented an improved steam engine in1769. Watt used steam coils to heat his office in 1784. His inventions includethe engine governor, a throttle valve, and a type of double-acting engine. He per­formed research in chemistry and metallurgy and retired as a wealthy man in1800. The Watt equals one volt driving one ampere . About this time, the Frenchscientist Charles Augustan De Coulomb (1736-1806) formulated Coulomb'sLaw. This says that the force between two electric or magnetic charges variesinversely as the square of the distance between them. The Coulomb is equal tothe quantity of energy in 6.242 X 1018 electrons. Alessandro Volta (1745-1827),an Italian physicist, invented the electric battery. The volt is named in LordVolta 's honor.

Count Rumford (1753-1814) was born Benjamin Thompson, in Massachu­setts. Loyal to the crown during the American Revolution, Thompson moved toLondon in 1776. Thompson was knighted in 1784, and became a count of theHoly Roman Empire in 1791. In 1797 he designed an experiment to prove that

550 App. I A Brief History of Thermal Engineering of Electronic Systems

heat was not a fluid-like substance . He concluded that heat is not a fluid, but aform of mechanical motion. His research led to improvements in heating andcooking equipment.

Although it had been written about since 1670, the French Revolutioncaused the adoption of the metric system in 1799. A group of 12 mathemati­cians and scientists met with French King Louis XVI to discuss the adoptionproposal. Signing of the order was delayed because the King tried to escapeFrance and the murderous peasants . King Louis finally signed the proclamationfrom his jail cell.

In 1811, Amadeo Avogadro (1776-1856) suggested that: at any temperatureand pressure, the number of molecules per unit volume is the same for all gases.This became known as the Avogadro number (6.022 X 1023 atoms per mole).Interestingly, Avogadro himself had no idea what this number might be. He wasalso the first to distinguish between molecules and atoms.

Nicolas Leonard Sadi Camot (1796-1832) originated the field of thermody­namics. This French engineer and physicist worked to improve the efficiency ofthe steam engine. His conclusions apply to all devices that convert heat intowork. He found that the efficiency of a reversible engine depends on the tem­peratures between which it works. The French mathematician Joseph Fourier(1768-1830), like Leonhard Euler, was trained as a priest. Fourier did not takehis vows and turned to mathematics . In 1799 he accompanied Napoleon's armyin the conquest of Egypt. There he studied archaeology, the pyramids, and thesphinx. In 1822 he became famous for his mathematical treatment of the theoryof heat. He established the partial differential equations governing heat diffu­sion and solved them by using an infinite series of trigonometric functions ,known now as the Fourier series.

One of the first to work in the new field of electricity was Heinrich Geissler(1814-1879). Geissler removed the air from glass tubes and found that theyglowed with colors when an electrical current was passed through them. ThomasEdison (1847-1931) found that by inserting a small metal plate into the tube hecould cause current to flow from the filament to the plate. This was called theEdison Effect. Edison patented the device and called it the Thermionic Tube.

William Thomson (1824-1907) was knighted and became Lord Kelvin afterlaying the Atlantic Cable in 1866. Later, he described absolute zero as the tem­perature of a reservoir to which a Carnot engine would reject no heat. He laterdeveloped the absolute temperature scale, graduated in degrees Kelvin. Thisscale does not rely on a thermoelectric property of a substance so there is noproblem of deciding which thermoelectric property or substance to use. In termsof the Celsius thermometer, absolute zero is defined as -273.15°C. Absolutezero is often considered the point at which all random molecular motion stops.Although this is not a true definition , it is very close.

App. I A Brief History of Thermal Engineering of Electronic Systems 551

In 1804, the French inventor Joseph Jacquard (1752-1834) demonstrated hisloom for Napoleon. The loom used punched cards to weave complex textile pat­terns. Mobs of silkworkers, angry at the automation of their craft , destroyedlooms all over Europe. The Engli sh mathematician Charles Babbage(1792-1871 ) built the first true computer. Babbage also invented the speedome­ter and the cow-catcher. In 1822, incensed by the inaccurate mathematical tablesof his time, he constructed a system of cogs and gears called the "DifferenceEngine." The engine could rapidly and accurately calculate long lists of func­tions. Only one was built. After further experimentation he conceived of themore complex "Analytical Engine." He produced thousands of drawings for thisprogrammable device , which had data storage, logic circuits, memory, and dataretrieval. None were built . His ally, Augusta Ada Byron, counte ss of Lovelace ,daughter of the English poet Lord Byron (1788-1824), wrote a program to cal­culate Bernoulli numbers. She envi sioned punch card data entry similar toJoseph Jacquard's loom. The device would have been as large as a football fieldand would have required a power supply of six steam locomotive s to overcomethe gear friction during calculations.

In 1834 Jacob Perkin s, a Massachu setts inventor, patented a refrigeratoremploying a compressor and a closed-loop ammonia system. From 1843 to1850, James Prescott Joule (1818-1889) published a series of papers explain­ing his experiments to measure heat as an equal to mechanical energy. TheJoule, named in his honor, is equal to the energy expended moving a onecoulomb charge (6.242 X 1018 electron s) against one volt. A French engineer,Ferdinand Carre , developed the first heat absorption system between 1851 and1855. Later, Karle von Linde , a German engineer, introdu ced the first com­pression refrigeration system. Linde developed his ammonia refrigerant systembetween 1873 and 1875.

The science of hydrodynamic s was established in 1851 when the Britishphysicist and mathematician Sir George Stokes (1819-1903) described themovement of a sphere through a viscous fluid . The British system of units mea­sures kinematic viscosity in "Stokes." In 1883, Osborne Reynolds (1842-1912)published his paper on fluid turbulence. The dimensionless number ratio of iner­tial force to viscous force within the fluid stream is named in his honor. In 1871,the Englishman John Strutt, 3rd Baron of Rayleigh (1842-1919), explained whythe sky is blue. Lord Rayleigh made many contributions to the field of wavephenomena, and laid the foundation for the distribution of energy in blackbodyradiation. A dimensionless number ratio named in his honor represents the ratioof buoyant forces to viscous forces. The Grashof number is often multiplied bythe Prandtl number to arrive at the Rayleigh number. The ratio of the Grashofnumber and the Reynolds number suggests whether natural or forced convectiveforces are dominant.

552 App. I A Brief History of Thermal Engineering of Electronic Systems

In 1847 the German physiologist Hermann von Helmholtz (1821-1894), adirect descendant of William Penn, published a paper that consolidated allknown information about the conservation of energy . He supported his paperwith mathematical arguments. He was also the first to measure the speed ofnerve impulses.

A St. Louis bank clerk, William Burroughs (1885-1898), devised the firstcommercial calculating machine in 1885. He sold it in Chicago in substan­tial numbers.

An American engineer, Herman Hollerith (1860-1929), persuaded the U.S.Census Bureau to try punched card programming for the 1890 census . Soon,punched cards were being used in many offices . In 1896 Hollerith formed theTabulating Machine Company. Later, another firm absorbed Hollerith's com­pany to form the Computing-Tabulating-Recording Company, which evolved tobecome International Business Machines Corporat ion (IBM).

In 1904, John Fleming (1849-1945) built the Fleming Valve, a vacuum diodethat could detect radio signals. After several contributions to research in photome­try, Fleming was knighted in 1929. One year later, Lee De Forest a 33-year-oldAmerican inventor, patented the Audion Tube. It was the first amplifying triodevacuum tube. It was soon wedded with Marconi's wireless invention to produce ra­dio. Although De Forest had a technical Ph.D., it is said that he did not understandhow his device worked, and its discovery was an accident. Nevertheless, his dreamwas to bring his great joy (opera) into every home in America.

In 1906 the German inventor Hermann Nernst (1864-1941) discovered thethird law of thermodynamics. This 1920 Nobel prize law states that entropyapproaches zero as temperature approaches absolute zero. He sold his patentfor the Nernst lamp for one million marks, but an improved version of Edi­son's light bulb soon replaced Nernst's lamp. A New York farmhand, WillisCarrier, was fascinated by heat transfer during his studies at Cornell Univer­sity. One year after he graduated, he undertook the task of cooling a Brook­lyn printer' s office. His breakthrough accomplishment was to calculate andbalance the airflow against the cooling effect to reduce the humidity . This bal­ance further cooled the air. He built a very successful business. By 1930,movie theaters were advertising "Air-Conditioning" in larger letters than themovie title .

1913 saw the production of the first commercial refrigerator. The "Domelre"cost about $900 at a time when $11 was the average weekly wage.

Using the ideas of Charles Babbage, Dr. Vannevar Bush (1890-1974), whileDean of Engineering at the Massachusetts Institute of Technology (MIT), builtthe first large-scale electromechanical analog computer, the Differential Ana­lyzer, in 1925. In 1941 President Roosevelt appointed Dr. Bush to be the firstdirector of the Office of Scientific Research. His proposal for a similar office,for peacetime research , led to the formation of the National Science Foundation.

App. I A Brief History of Thermal Engineering of Electronic Systems 553

By the late 1920s pentode tubes had grown so large and powerful that cool­ing fans were placed around the devices. In 1935, I. E. Mouromtseff and H. N.Kozanowski published "Comparative Analysis of Water-Cooled Tubes as ClassB Audio Amplifiers." They used four gallons per minute of deionized water tocool an 11.3 kW tube. By 1942 liquid cooling was firmly established and wasrequired to cool such new and powerful devices as the Amplitron, the Mag­netron, and the Klystron tubes. During this time Mouromtseff devised a dimen­sionless number to evaluate cooling media, p0.8 kO.6 Cp 0.4/ I-L0.4. This has becomeknown as the Mouromtseff number.

The first large scale digital electromechanical computer, the Mark I, was de­signed by Dr. Howard Aiken (1900-1973) of Harvard University in 1937. IBMbuilt the computer in 1944. A year later, Grace Hopper, while troubleshooting themalfunctioning computer, found a moth lodged in a circuit. From that time on, acomputer malfunction was said to be a "bug." In February 1946, the first electron­ic digital computer was unveiled at the University of Pennsylvania in Philadelphia.John Mauchly (1907-1980) and J. Presper Eckert (1919-) built it for the sole pur­pose of calculating artillery ballistic tables. The Electronic Numerical Integratorand Calculator (ENIAC) made mistakes and required repairs about every sevenminutes. This milestone computer used air-conditioned hallways to cool its 18,000vacuum tubes, 500,000 soldered joints, and 30 tons of wiring. It is rumored that thelights of Philadelphia dimmed when the machine was turned on. At a cost $500,000(1946 dollars) it was the equivalent of today's hand-held calculator, and had aspeed of 500 additions and subtractions per second. ENIAC was nonprogrammableand had to be rewired for each new problem. In 1951 Mauchly and Eckert intro­duced the first commercially available computer, the UNIVAC I.

When Bell Labs developed the transistor in 1947, most scientists thought thatthe burden of cooling electronics would be eliminated. It was, but only for ashort time. Soon, the problem became worse. A 1949 article in PopularMechanics contained the bold statement "Someday, computers may weigh lessthan 1.5 tons." By the late 1950s powerful transistors and newly developed inte­grated circuits were in use. In 1958 J.S. Kilby invented the integrated circuit,which consists of multiple transistors on a single piece of silicon. While thesenew devices produced less total heat, there was now much less surface area todissipate that heat. Consequently, Watt density (heat generation/surface area)increased. Gordon Moore, co-founder of Intel Corporation, predicted that thenumber of transistors produced on a single silicon wafer will double every 18months. Moore 's Law has held true for more than 30 years.

By the 1960s engineers had devised indirect cooling using coldplates, andwere using dielectric fluids for direct immersion cooling. Airborne military sys­tems used coldplates with ethylene-glycol mixtures to cool their avionics. Uni­versities began to study direct immersion cooling as a way to avoid thereservoirs , piping, leak-proof connectors, and pumps mandated by indirect cool-

554 App. I A Brief History of Thermal Engineering of Electronic Systems

ing. In 1969 Dr. De Forest, father of radio , said "[Man will never reach themoon] regardless of all future scientific advances."

Although direct immers ion cooling was gaining use in closely controlledenvironments in the 1970s, direct immersion (pool-boiling) cooling for highpower assemblies was regarded with growing disfavor. Circuits had become sopowerful that some fluids would boil when in contact with these circuits . Engi­neers knew that the heat transfer coefficient increased dramatically during thisphase change, but actual systems suffered from thermal hysteresis at the criticalboiling temperature . Instead of the circuit maintaining the constant temperatureof the boiling fluid, ICs would sometimes exceed the boiling point by 50°Cbefore the fluid in contact with the IC would begin to boil. In 1977 KennethOlen, president and founder of Digital Equipment Corp, said "There is no rea­son for any individual to have a computer in their home."

Because of problems associated with direct immersion, system designers inthe early 1980's began to use ideas such as helium-cooled pistons, jet-impinge­ment, and heat pipes, for indirect cooling. These concepts were introduced innew supercomputers, most notably, the Thermal Control Module (TCM) in theIBM 3090. Because of the market pressure to develop even smaller systems,electronic companies began to provide large funds for research programs at uni­versities. Researchers began to understand the factors involved in reducing thethermal hysteresis in prior assemblies. In 1986, ETA Inc., developed a computerthat had its processors immersed in a bath of liquid nitrogen at -190°C.

Today, laptop computers use liquid heat sinks. Designers use ComputationalFluid Dynamics (CFD) to better understand convective cooling processes. Engi­neering specialists use lasers to cut microchannels into an IC's surface, andforce synthetic fluids costing over $300 per gallon through the microtunnels tocool the latest semiconductors. Prototype diamond substrates are now available.These substrates allow faster movement of electrons than either gallium arsenideor silicon. And, since they have a higher dielectric strength, diamonds can oper­ate at higher power levels. Also, diamonds have the highest thermal conductiv­ity (2000 Wlm K) of any material : Five times greater than pure copper, 17 timesgreater than silicon, and 40 times that of gallium arsenide.

Tomorrow, superconducting circuits may be standard catalog items. Minia­ture cryogenic systems will offer new challenges to designers . Automobiles willuse liquid cooling to improve module reliability in the severe underhood envi­ronments. "Smart" houses may have dedicated cooling for their computers.Magnetic and sonic refrigeration techniques may see commercial use. Twothings are certain: circuits will grow more powerful and smaller, and the ther­mal engineering specialists will be faced with more difficult challenges .

Appendix II

Properties

Air at Sea-Level Atmospheric Pressure

Temp. Density Coef. Specific Thermal Absolute Kinematic PrandtlExp. Heat Condo Viscosity Viscosity Number

(T) p 13 X 103Cp k IL X 106 V X 106 Pr

COF) COC) (kg/m ' ) (IlK) (J/kg K) (W/m K) (N s/rrr') (m 2/s)

32 0 1.293 3.664 1003.9 0.02417 17.17 13.28 0.713141 5 1.269 3.598 1004.3 0.02445 17.35 13.67 0.712750 10 1.242 3.533 1004.6 0.02480 17.58 14.16 0.712259 15 1.222 3.470 1004.9 0.02512 17.79 14.56 0.711868 20 1.202 3.412 1005.2 0.02544 18.00 14.98 0.711377 25 1.183 3.354 1005.4 0.02577 18.22 15.40 0.710886 30 1.164 3.298 1005.7 0.02614 18.46 15.86 0.710395 35 1.147 3.244 1006.0 0.02650 18.70 16.30 0.7098

104 40 1.129 3.193 1006.3 0.02684 18.92 16.76 0.7093113 45 1.111 3.142 1006.6 0.02726 19.19 17.27 0.7087122 50 1.093 3.094 1006.9 0.02761 19.42 17.77 0.7082131 55 1.079 3.048 1007.3 0.02801 19.68 18.24 0.7077140 60 1.061 3.003 1007.7 0.02837 19.91 18.77 0.7072149 65 1.047 2.957 1008.0 0.02876 20.16 19.26 0.7067158 70 1.030 2.914 1008.4 0.02912 20.39 19.80 0.7062167 75 1.013 2.875 1008.8 0.02945 20.60 20.34 0.7057176 80 1.001 2.834 1009.3 0.02979 20.82 20.80 0.7053185 85 0.986 2.795 1009.8 0.03012 21.02 21.32 0.7048194 90 0.972 2.755 1010.3 0.03045 21.23 21.84 0.7044203 95 0.959 2.718 1010.7 0.03073 21.41 22.33 0.7041212 100 0.947 2.683 1011.2 0.03101 21.58 22.79 0.7038

555

556 App. II Properties

Water at Sea-Level Atmospheric Pressure

Temp. Density Coef. Specific Thermal Absolute Kinematic PrandtlExp. Heat Condo Viscosity Viscosity Number

(T) p 13 X 103Cp k fL X 106 V X 106 Pr

(OF) (oq (kg/m') (IlK) (Jlkg K) (W/m K) (N s/m') (m2/s)

32 0 999.9 -D.068 4217.5 0.5580 1794 1.794 13.5641 5 1000 0.018 4202.7 0.5677 1530 1.530 11.3350 10 999.7 0.095 4192.4 0.5774 1296 1.296 9.41059 15 999.1 0.16 4185.8 0.5870 1136 1.137 8.10168 20 998.2 0.22 4181.7 0.5967 993 0.995 6.95977 25 997.1 0.26 4179.5 0.6064 880.6 0.883 6.06986 30 995.7 0.31 4178.6 0.6155 792.4 0.796 5.38095 35 994.1 0.35 4178.5 0.6243 719.8 0.724 4.818

104 40 992.2 0.39 4179.0 0.6325 658.0 0.663 4.348113 45 990.2 0.42 4179.9 0.6401 605.1 0.611 3.951122 50 988.1 0.45 4181.1 0.6472 555.1 0.562 3.586131 55 985.8 0.48 4182.6 0.6536 512.6 0.520 3.280140 60 983.5 0.51 4184.5 0.6594 470.0 0.478 2.983149 65 980.8 0.54 4186.8 0.6643 436.0 0.445 2.748158 70 978 0.57 4189.5 0.6686 402.0 0.411 2.519167 75 974.9 0.60 4192.9 0.6724 376.6 0.386 2.348176 80 971.7 0.63 4196.6 0.6753 350.0 0.361 2.175185 85 968.5 0.66 4201.0 0.6778 330.5 0.341 2.048194 90 965 0.69 4205.7 0.6797 311.0 0.322 1.924203 95 961.7 0.72 4210.6 0.6811 294.3 0.306 1.819212 100 958.4 0.75 4215.5 0.6822 277.5 0.290 1.715

App. II Properties 557

Perfluorocarbon FC-72 at Atmospheric Pressure (Boils at 56°C)

Temp . Density Coef. Specific Thermal Absolute Kinematic PrandtlExp . Heat Cond o Viscosity Viscosity Number

(T) p f3 X 103 < k fl. X 106 V X 106 Pr(OF) eC) (kg/m ' ) (IlK) (J/kg K) (W1m K) (N s/m2) (m2/s)

32 0 1740 1.601 1005.0 0.0600 1009.5 0.5802 16.9141 5 1727 1.611 1016.2 0.0595 932.4 0.5399 15.9350 10 1714 1.619 1025.6 0.0590 861.6 0.5027 14.9859 15 1701 1.626 1033.2 0.0585 799.5 0.4700 14.1268 20 1688 1.633 1039.8 0.0580 743.0 0.4402 13.3277 25 1675 1.640 1046.6 0.0575 693.8 0.4142 12.6386 30 1662 1.647 1053.5 0.0570 648.2 0.3900 11.9895 35 1649 1.654 1060.8 0.0565 610.1 0.3700 11.46

104 40 1636 1.662 1068.7 0.0560 574.3 0.3510 10.96113 45 1623 1.670 1077.5 0.0555 543.9 0.3351 10.56122 50 1610 1.680 1087.0 0.0550 514.8 0.3198 10.17131 55 1597 1.689 1096.5 0.0545 486 .0 0.3043 9.778

558 App. II Properties

Perfluorocarbon FC-77 at Atmospheric Pressure (Boils at 97°C)

Temp. Density Coef. Specific Thermal Absolute Kinematic PrandtlExp. Heat Condo Viscosity Viscosity Number

(T) p 13 X 103Cp k fL X 106 V X 106 Pr

COF) (0C) (kg/m' ) (l1K) (J/kg K) (W1m K) (N s/m') (m2/s)

32 0 1838 1.399 1005 0.0649 2356 1.282 36.4841 5 1826 1.407 1016 0.0646 2117 1.159 33.3050 10 1814 1.414 1025 0.0643 1905 1.052 30.3759 15 1802 1.421 1033 0.0640 1719 0.9539 27.7568 20 1789 1.429 1041 0.0637 1554 0.8686 25.4077 25 1777 1.436 1048 0.0634 1413 0.7592 23.3686 30 1765 1.443 1056 0.0631 1288 0.7298 21.5695 35 1753 1.451 1063 0.0628 1178 0.6720 19.94

104 40 1740 1.458 1071 0.0625 1083 0.6224 18.56113 45 1728 1.466 1079 0.0621 1001 0.5793 17.39122 50 1716 1.473 1087 0.0617 927.0 0.5402 16.33131 55 1704 1.481 1096 0.0613 862.4 0.5061 15.42140 60 1691 1.489 1105 0.0609 805.0 0.4761 14.61149 65 1679 1.497 1114 0.0604 753.2 0.4486 13.89158 70 1667 1.504 1123 0.0600 706.1 0.4236 13.22167 75 1655 1.512 1131 0.0595 662.3 0.4002 12.59176 80 1642 1.520 1140 0.0590 622.1 0.3789 12.02185 85 1630 1.527 1147 0.0585 584.0 0.3583 11.45194 90 1618 1.534 1154 0.0580 548.0 0.3387 10.90203 95 1605 1.541 1159 0.0575 513.2 0.3198 10.34

Data from Fluorinertlf Liquids Product Manual, 3M.

App. II Properties 559

Thennophysical Properties of Nonferrous Metals at 20 ce

Materials Density Coef. Specific ThermalExp. Heat Condo

p a X 106 cp k(kg/m' ) (IlK) (J/kg K) (W/m K)

Aluminum (1100) 2,713 23.6 921 222Aluminum (2014) 2,796 23.0 921 192Aluminum (2024) 2,768 23.2 921 189Aluminum (5052) 2685 23.8 921 139Aluminum (6061) 2,713 23.4 963 180Aluminum (7075) 2,796 23.6 963 121Aluminum (356) 2,685 21.4 935 159Beryllium 1,855 11.5 1,884 151Brass (C36000) 8,498 20.5 380 116Bronze (C22000) 8,802 18.4 377 189Copper (C11000) 8,913 17.6 383 391Copper (C12200) 8,941 17.6 385 339Copper (C22000) 8,802 18.4 377 189Copper (Alloy MF 202) 8,862 17.0 382 150Glass Seal (Alloy Ni 50) 8,332 8.46 482 10.4Gold 19,321 14.2 129 313Inconel (625) 8,442 12.8 410 9.82Kovar 8,343 4.30 16.0Lead 11,349 29.3 130 33.9Magnesium (AZ 31B-F) 1,772 25.2 1026 76.2Monel (400) 8,830 13.9 427 21.8Nickel (270) 8,885 13.5 461 91.0NILO (Alloy 42) 8,138 4.86 482 10.4Palladium 12,013 11.7 244 76.2Platinum 21,452 8.82 129 72.7Silver 10,494 19.6 234 419Solder (Sn60Pb40) 8,500 24.5 176 51.0Tantalum 16,608 6.48 151 54.5Tin 7,307 23.4 227 67.0Titanium 4,510 9.54 531 17.5Titanium (Ti-6AI-4V) 4,429 9.36 574 7.27Zinc (SAE 925) 6,699 27.4 417 109

560 App. II Properties

Thennophysical Properties of Ferrous Metals at 200e

Materials Density Coef. Specific ThermalExp. Heat Condo

p a X 106Cp k

(kg/m' ) (11K) (J/kg K) (W/m K)

Carbon steel (AISI 1010) 7,830 6.60 434 64.0Carbon steel (AISI 1042) 7,840 6.50 460 50.0Cast iron (ASTM A-48) 7,197 10.8 544 50.2Cast iron (ASTM A-220) 7,363 13.5 544 51.1Cast steels (carbon & alloy) 7,834 14.7 440 46.7Stainless steel (4130) 7,833 13.5 456 43.3Stainless steel (17-4 PH) 7,778 10.8 461 18.0Stainless steel (304) 8,027 17.3 477 16.3Stainless steel (316) 2,685 16.0 468 16.3Stainless steel (440) 7,750 10.1 461 24.2

App. II Properties 561

Thennophysical Properties of Plastic at 200e

Materials Density Coe£. Specific ThermalExp. Heat Cond o

p a X 106Cp k

(kg/m ' ) (11K) (J/kg K) (W/m K)

ABS (acrylonitrilebutadiene styrene) 1,058 72.0 1,466 2.70Acetal 1,415 82.8 1,465 3.01Acrylic 1,178 81.0 1,466 2.49

Alkyd 2,206 36.0 9.87Cellulose acetate 1,257 121 1,508 3.01Epoxy (cast) 1,148 59.4 1,884 4.15Epoxy (IC molding) 1,820 17.0 984 4.00Fluorocarbon (PTFE) 2,196 90.9 1,047 2.91Polyamide (nylon type 6) 1,247 89.1 1,675 2.08Phenolic 1,387 37.4 1,570 1.74Polycarbonate 1,203 67.5 1,256 2.39Polybutylene terephthalate(PBT) 1,307 72.0 1,905 1.90Polyester 1,287 85.5 1,780 2.29Polyimide 1,427 47.7 1,214 8.05Polyamide-imide 1,397 36.0 2.94Polyetherimide 1,277 54.0 1,090 2.2Polyetheretherketone 1,317 40.5 2.95Polyetherketone 103Polystyrene 1,039 72.9 1,361 1.54Polyethylene 933 225 2,261 3.95Polypropylene 903 86.4 1,884 2.22Polyvinyl Chloride (PVC) 1,447 54.0 1,050 1.77

562 App. II Properties

Thermophysical Properties of Ceramics at 20°C

Materials Density Coe£. Specific ThermalExp. Heat Condo

p IX X 106Cp k

(kg/m ') (11K) (J/kg K) (W/m K)

Aluminum oxide 3,982 5.67 879 30.0Aluminum nitride 3,200 4.40 711 200Beryllium oxide 2,900 7.00 1030 300Boron nitride (cubic) 2,200 3.80 709 1,300Diamond (film) 3,500 2.00 510 1,200Fused quartz 2,200 0.50 745 1.60Glass (die attach) 2,900 50.0Silicon 2,300 4.20 664 83.7Silicon nitride 3,300 2.00 624 21.0

Author Index

Abramovich,G. N., 208Addoms, J. N., 483Aihara, T., 389Aiken, H., 553Altoz, F. E., 116AI-Arabi, M., 378, 381Annund, W. J. D., 210Antonetti, V. M., 125Archimedes, 546Arnold, J. N., 376Austin, L. R., 209Avogadro, A., 550Ayyaswamy, P. S., 375, 376Babbage, c, 551, 552Bacon, R., 546Baines, W. D., 211Bardowicks, H., 307Bar-Cohen, A., 117, 120,257,352Berdahl, P., 434Berenson, P. J., 465Bergles, A. E., 446Bernath, L., 464Bernoulli, D., 158, 161, 167-172, 174-177, 197,

548,551Bernstein, M. 304, 318Bilitzky, A., 383, 414Black,J., 243,406,407,410-412,417,421 ,549Blasius, H., 188, 189,289Boelter, L. M. K., 281, 282, 284, 285Bohn, M. S., 288Bonilla, C. F., 462Boussinesq, J., 12,337,342Boyle, R., 548Bromley, L. A., 449, 466Brown, A. I., 348, 366Brunt, D., 434

Burroughs, W., 552Bush, V., 552Byron, Lord, 551Carnavos, T. C., 287Carnot, N. L. S., 550Carri, F., 551Carrier, W., 552Carrothers, P. J. G., 211Catton, I., 374-376Celsius, A., 414, 433, 549, 550Chao, B. T., 450Chen, M. M., 485, 487Chilton, T. H., 281, 282, 284, 285, 481Choi, H., 481Chu, H. H. S., 344, 346-348, 377Chun, K. R., 481, 485, 486Churchill, S. W., 291, 304, 318, 344, 346-348,

377,379,400,401Cichelli, M. T., 462Clapeyron, 446Clark, J. A., 466Clausius, 446Colburn, A. P., 256, 281, 282, 284, 285, 290,

295,481Cole, R., 447Coleman, H. W., 214Collier, J. G., 454Cooper, M. G., 119Coulomb, C. A., 549, 551Courchesne, J., 307Crawford, M. E., 286, 291, 296Cullen, W., 549Da Vinci, L., 546Daile Donne, M., 215Daniels, D. J., 466Danielson, R. D., 456

563

564 Author Index

Darcy, H., 179De Fermat , P., 547De Forest, L., 552, 554Delany, N. K., 307Descartes, 547DeWitt, D. P., 516Dhir, V. K., 461Dipprey, D. F., 310Dirichlet, 101Dittus, F. W., 281, 282, 284, 285Donaldson, E., 380Drew, T. B., 451Dropkin, D., 372Du Fay, C. F., 549Eckert, E. R. G., 257, 345, 553Ede, A. J., 378Edison, T. A., 550, 552Edwards, D. K., 267, 271, 272, 277, 278, 365Eichhorn, R., 467Elenbaas, M., 257, 349-351, 355, 356, 358-360,

386,387,389Elizabeth I, Queen, 547Ellion , M. E., 464Emery, A. P., 374Euclid,545Euler, L., 156, 158, 165, 167, 177,548-550Eustis, 447Fahrenheit, G. D., 548Fanning, 179,281,288Ferdinand III, 548Ferdinand II, 547Fleming, J., 552Florschuetz, L. W., 450Fourier, J. B. J., 51, 257, 258, 550Franklin , B., 549Frederking, T. H. K., 466Fromberg, R., 434Galileo, G., 546, 547Gebhart, B., 341Geissler, H., 550, 552Gibson, A. H., 197Giedt, W. H., 302Gilbert, W., 547Gilliland, E. R., 480Globe, S., 372Gnielinski, V., 282, 285, 315Graham, R. W., 448Gregg, J. L., 378Halley, E., 548Hamilton, J. B., 202

Hansen, M., 189Harper, C. A., 414Harris, C. H., 201, 203Hatfield, D. W., 365Hendricks, R. C., 448Herbert, M. V., 210Hetsroni, G., 446, 447, 456Hilpert, R., 302, 344, 347, 348, 360, 364, 366Ho, C. Y., 492Hollands, K. G. T., 373, 375Hollerith, H., 552Hooke, R., 548Hopper, G., 553Hottel, H. C., 425Howard, 425, 553Howell, J. R., 423, 425Imai, K., 207Incropera, F. P., 516IdeI' chik, I. E., 202, 203, 206Ito, H., 204, 206, 207Jackson, T. W., 345Jacob, M., 306, 308, 309, 320, 323, 329, 330,

372,551Jacquard, J., 551Joule, J. P., 136,551Kays, W. M., 286, 291, 296Kelvin, Lord, 399, 550Kern, D. Q., 112, 114Khamis, M., 378Khowarizmi, 546Kilby, J. S., 553Klimenko, V. V., 471Kovalev , S. A., 465Kozanowski, H. N., 553Kraus, A. D., 112, 114, 117, 120,257Kreith, F., 288Kutateladze, S. S., 461Lanville, A., 307LeFevre, E. 1., 378Leidenfrost, 452, 453, 464, 465Lewis, G. W., 258, 260, 480Lienhard, J. H., 382, 461, 465, 467, 485London, A. L., 286, 548, 549Louis XVI, King, 550Lovelace , Countess of, 551MacGregor, R. K., 374Madison, R. D., 206Mahrenholtz, 0 ., 307Marco, S. M., 348, 366Martin, H., 331-333, 335, 336

Author Index 565

Martin , J. G., 425Mauchly, J., 553McAdams, W. H., 364, 366, 376, 377McEligot, D. M., 270Meyer , L., 215Mikic, B. B., 125Mills, A. F., 189, 214, 267, 323, 325, 326, 328,

362,421 ,466Moin, P., 13Moody, L. F., 212, 281Moore, G., 553Mueller, c, 451Muriel, M. J. B., 425Nakai, S., 303Napier, 1., 547Napoleon, 551Nernst , H., 552Nikuradse, J., 212, 364Nukiyama, S., 451Nusselt , E. W. H., 192,241,249,250,253-261,

263 , 266-268, 270-273, 275-279,281-287, 290-292, 296, 302, 303, 305,306, 308-310, 313-316, 318, 319,325-328, 332 , 333, 335-340, 343, 344,347, 348, 350-352, 355, 356, 358-360,362 , 364, 365, 367-369, 372-374, 376,379, 382, 383, 387 , 388, 390 , 444,453-455,459,460, 471, 472, 476-479,481,484-486

Obasaju, E. D., 307Okazaki , T., 303Oosthuizen, P. H., 380, 381Ozisik, M. N., 56Owe, H. J., 291Parke r, J. R., 206Pascal, B., 547Penn, W., 552Perkins , J., 551Petukhov, B. S., 475Pinker , R. A., 210Plank, M., 402, 403, 407Plesset, M. S., 450Pohlhausen, E., 289, 290PrandtI, L., 12, 184, 194,246,249,250,253,

254, 256, 258-260, 264-269, 278, 280,289, 290, 294, 295, 301, 309, 325, 327,337,390,400,444,454,551

Pythagorus, 545Quarmby, A., 302Rai, M. M., 13

Ramsey, J. W., 319, 325, 327Rayleigh , 3rd Baron of, 116,257,258,260,337,

343, 344, 346-349, 359, 360, 362, 364,367-369, 371, 373-375, 377, 382, 400,401,465,509,512,551

Reynolds, 0., 13, 175, 179-186, 189, 191, 192,194, 195, 210 , 212 , 215 , 225 , 226 ,228-231,235,247,248,250,253-256,258-260, 263, 265-268, 271-273, 277 ,280-282, 284, 292 , 294-304, 306, 307,309 , 311 , 313-316, 323 , 325-328,335-337, 339, 343, 390, 448, 467, 470,472,475,477,481 ,485,486,496,55 1

Rich, B. R., 362Rohsenow, W. M., 350 , 352 , 446 , 447 , 454,

455,481,485Roosevelt , F. D., 552Rumford, Count, 549Sabersky, R. H., 310Sadasivan, P., 485Sanctorius, 547Schl ichting, H., 215, 292Schmidt , E., 51, 258, 260, 261, 289, 480Schne ider, P. 1., 57Seader , J. D., 209Seban, R. A., 481, 485, 486Seto, W. W., 534Shah, R. K., 286Sherwood, T. K., 260, 261, 480Shlykov, Y. L., 120Sieder, E. N., 281, 282, 284, 285Siegel, R., 425Soren sen, N. E., 307Sparrow, E. M., 310, 319, 325, 327, 378, 389Squire , H. B., 301Steinberg, D. S., 366Stokes , G., 13, 15, 177,551Strutt , J., 260, 551Sukhatme, S. P., 303Sunderland, 1. E., 389Swear ingen, T. W., 270Sylvester, N. D., 212Tate , G. E., 281, 282, 284, 285Taylor, R. P., 12, 66Thale s,545Thomp son, B., 549Thomson, W., 550Torricelli, E., 161,547Vemuri , S. B., 389Vennard, J. K., 198

566 Author Index

Volta, A., 549von Karman, T., 300von Leibniz, G. W., 548von Linde, K., 551Ward Smith, A. 1., 206Watt, J., 5, 6, 72, 242, 338,505,522, 528, 549,

553Whitaker, S., 305White, F. M., 215, 292, 397, 407, 411,412, 432,

542Wills, M., 310, 313, 314, 316Wong, H. Y., 425

Wong, P. T. Y., 465Wren, c., 548Yamagata, K., 454Yardi, N. R., 303Yovanovich, M. M., 125Yuge, T., 378Zigrang, D. 1., 212Zografos, A. I., 389Zuber, N., 449, 461, 463, 464Zukauskas, A. A., 302, 319, 322, 323, 325-327,

329,330Zwick, S. A., 450

Subject Index

Absolute ,asperity angle, 119, 121, 122deviation , 472pressure, 161scale, 538terms, 142zero, 431, 438, 552

Absolute temperature , 244, 398, 399, 402-404,434,490,491,520,521 ,550

Absolute viscosity, 133, 134, 181, 251, 252,268,272,282,294,443,454,458

Absorptance, 419, 435, 496energy, 399, 406, 431,440heat, 132,242,348,405,406,440,441 ,444,

490,496,551radiation, 3, 397, 398,407,419,433solar energy, 407, 410, 429, 431-433sound, 519, 525

Acceleration , 142, 144, 146, 147, 155components , 143, 147, 151-156, 169fluid, 140, 142-148,208,297gravitational, 158, 168, 223, 254, 339, 362,

454level, 524, 525streamline, 150, 156, 157, 159, 171two-dimensiona l, 166, 167

Acoustics, 518, 529, 537, 538, 540-542, 549Acoustic

doublet, 535impedance, 529, 532intensity, 528, 531power, 522, 525, 537, 542pressure, 527, 528, 531-533, 535, 536, 543resistance, 529unit, 538, 540, 541wave, 520, 524, 526-532,542

Adhesive, 22, 24-27, 33, 36Adiabatic, 59, 101, 257, 351, 526Air, 16,94,216,219,220,230,242, 348, 357,

519,520,526-530ambient, 16, 40, 48, 93-95, 109, 248,

324-328,353,518bulk modulus, 132convection, 90, 131, 262density , 132,219,220,528film, 95, 96flow, 16, 17, 184,216,219,221 ,223-227,

245,255,306,323,552head loss, 229, 230inlet, 227, 235interface, 116, 120-124, 136, 137,480mass, 242particles, 519, 527, 528, 530pressure, 131,520,528,529,538properties , 248, 313, 314, 356, 357, 520space, 22, 438, 530, 532speed of sound in, 520temperature , 93-95, 96, 248, 324-328, 345,

348, 353, 507, 521, 524unstable 218

Air-cooled, 3, 221, 263, 312, 438Algebra, 65, 253, 396,428,434, 546,549Altitude, 131, 132, 142,220Alumina, 120, 122Aluminum, 23, 36, 46, 71, 108, 120,410

bracket, 33, 35, 76, 90core, 46emittance , 399, 407, 410heat sink, 23, 92,102,105, 120,417heat spreader, 45interface, 120, 122, 124wall, 71

567

568 Subject Index

American, 259, 549, 552American Revolution, 549Amplitude, 99, 194,531 ,535,536,538,542,

544Analog, 552Analogic, 51Analogy, 250, 281, 292, 293, 295, 310Analysis, 152,224,382,461 ,465,466,517,553

acoustic, 526, 541conduction, 57, 59, 89, 128convection, 382dimensional, 250, 253-255, 461finite element, 9, II, 13, 15, 382finite difference, 11, 12,63finite volume, 11, 12fluid flow, 131, 148, 165, 174, 259, 260,

280, 288, 289thermal, 16, 17,51,57,249,517turbulence, 12whole-field, 12

Analytic solution, 52Anechoic chamber, 536Angular, 301, 302Annular, 102, 105, 106, 108,425,469Apparent, 23, 116, 117, 120, 121, 123, 194,260,

337Approximate, 65, 69, 149, 156, 291, 434, 468,

492,534Arabs, 546Area, 2, 6, 107, 115-117, 125,288,294,515

cross-sectional, 3, 102, 123, 148, 163,224,230,271 ,288,467

surface, 2, 6, 48, 92, 105, 115, 125, 278,304,325,349,389,398,414,508,535,553

unit, 22, 99, 179, 191, 193,237,251,270,293,294,402,448,492,528

Arrangement, 316, 318, 323, 326, 328, 535Array, 16,64,105, 149,312,319,534,535

finned, 102, 108, 115, 129,389,414,417jet, 331, 332, 333pin-fin, 316, 318-320, 322, 323, 326,

328-330, 389, 390plate, 352, 353, 381, 382, 383, 414, 417printed circuit board, 351, 353

Aspect, 206, 302,374-376,542Asperities, 117-123,212, 309,310Asymmetric, 351-353 , 382Atmosphere, 222, 232, 233, 262, 434, 451, 455,

456,458,490

pressure, 131, 142,220,221 ,439,441 ,520,528,529,538,547,548

radiation and, 429, 433, 434standard, 179,223,439,520,528

Atomic, 3, 22, 23Automotive, 211, 456Average, 293, 386,387, 406, 420, 528, 542, 552

density, 90, 92directional, 408, 419flow, 148,330,469,531friction coefficient, 185, 186, 191,214,246,

248,249,295gap, 119heat transfer coefficient, 259, 272-274 , 278,

279,291,303,318,335,336,383,466,485- 487

heat flux, 429Nusselt number, 250, 259, 261, 268, 277,

282, 287, 291, 296, 302, 303, 305, 306,308, 309, 318, 325-328, 332, 333, 335,336, 364, 367, 369, 376, 382

pressure, 140, 524properties, 149, 491, 527roughness, 121, 122,225Sherwood number, 261sound pressure level, 524, 525Stanton number, 262temperature, 64, 87, 94-96 , 125, 269, 270,

277-279 ,293,332, 366,368-371 ,386,387,507

time, 12, 192, 194velocity, 179, 182,284,438

Avogadro number, 550Axial, 11, 13, 60, 61, 116,216, 218, 221, 267,

534,535Azimuth, 408, 419Baffle, 534, 535Balance, 79, 81, 178,275,434,446,478,546,

552energy, 48, 65, 74, 75,84, 86, 90,101,405,

406,419,421,475Band,397,524,525,539-542Bar, 117, 120,257,350,352,474Barometer, 547Base,

area, 107, 115heat flow, 112heat sink, 319, 323, 324, 382, 384, 389, 390,

417logarithmic, 521, 523, 524

Subject Index 569

Bathtub drain vortex, 170Beam, 535Bel, 521Bend, 172,204-206,224,233,268Bernoulli,

constant, 158equation, 158, 161, 167, 169-172, 174-177,

197,551numbers, 551terms, 168

Bernoulli's law, 548Bessel functions, 105, 110, Ill , 113, 534Binaural,543Biot number, 86, 96, 129, 255, 256Blackbody, 398, 399, 402-407 , 419, 430, 431,

433,434Blackbody radiation, 260, 402, 403, 407, 419,

431,551Blade, 219, 519Body, 13,406,438,519

falling, 161,547fluid, 145,237,262,296,297force, 341, 342heated, 445,461 ,465shape factor, 4solid, 256

Boiling, 237, 437, 439, 441, 444, 445, 450-453 ,458,459,466-468,470,478,479,516

film, 452, 464-466flow, 444,466,467,468,471,496liquid, 101,516,548nucleate, 446, 448, 450-452, 454, 455, 459,

460,463,464,468,471 ,476,496point, 137,442,456,458,461,496,549pool, 444, 450, 451, 453, 454, 460,

464-466,554saturated, 445spontaneous, 161subcooled, 444, 445transition, 452viscosity, 268

Boundaries, 45, 89, 101, 148, 156, 172, 295,330, 353

Boundary conditions, 15, 100, 102, 189acoustic, 527, 530conduction, 39, 44, 47, 52, 55-57, 64, 75,

77, 128, 129convection, WI , 102,289phase change, WI , 102,491-493radiation, WI

transient, 84, 89, 96Boundary layer, 187, 188, 191,257,296,297,

301,349displacement, 185, 186,215,247-249,292,

311flow, 260, 361, 374thermal, 185, 241, 245-249, 263, 265, 274,

288-290,362thickness, 185, 186, 189,215,245,246,248,

249,290,292,302,311 ,362velocity, 184-186,203,245,246,248,249

Boussinesqapproximation, 342concept, 12number, 337

Bracket, 33, 35, 36, 73, 74, 76, 90, 91Branch, 207, 208Breakdown, 23British, 181,260,551Btu (British Thermal Unit), 5, 21, 22, 49, 402,

403Bubble Reynolds number, 448Bubbles, 15, 139, 161, 437, 439, 444-452,

459-46 3,468,469,471 ,478,496Buckingham 7T, 250, 252, 254, 442, 443Bulk, I, 8, 132, 180, 273-275 , 302,438,445,

464,466,520,526Bulk temperature, 245, 268-270, 282, 284, 285Buoyancy, 254, 258,374,551

force, 339-342, 361, 362, 371, 376, 437,443,444,446,448,466

Burnout, 453Calculus, 546, 548, 549Calorie, 241Capacitance, 70, 74, 75, 85, 86, 89, 92, 94-96,

129Capacity, 241, 242, 288, 492Capillarity, 137Carbon, 410, 457Carbon dioxide, 397Card, 45, 225, 547, 551, 552Carnot engine, 550Case, 5, 243, 335, 338,396,412,499,505

temperature, 511, 514Casting, 212, 309Catalog, 554Cavitation, 15, 161Celsius, 414, 433, 550Center, 59,159,160,221,330,374,411 ,525

frequency, 530, 541

570 Subject Index

Center (cont.)line, 44, 45, 47, 48, 60, 61,424of curvature, 141, 169, 170, 171of tube or cylinder, 38, 60, 61, 176-178,

265,268,297,469to center, 210, 214, 225,310,312,316,323,

390,474Central Processing Unit (CPU), 16, 276, 306,

307,309,333,335,336Centrifugal, 216, 218-221CFD, see Computational Fluid DynamicsChange, 7, 9-11, 84, 89, 220, 273, 342, 343,

397,422,525,527,528,530,554momentum, 469, 470, 475, 478phase, 15, 102, 135, 237, 437-439, 441,

444,470,490,491 ,496,554pressure, 132, 144,207,208,216,237,520,

547,548rate of, 6, 86temperature, 27, 87, 142,243,256,437,438volume, 132, 243, 548

Channel, 181, 208, 212, 309-314, 316, 349,353,358,359,382-387,389,414,417

flow, 184, 207, 215, 224-226, 257, 277,311,314,355,356

Characteristic, 216, 221, 223, 243, 252, 254,298,445,462,529,534

dimension, 181, 191, 253, 332, 335, 336,355, 356, 378, 382, 386-388, 463, 509,512

length, 263, 314, 315, 364,446,448,449,459-461 ,471 ,476,478

Chassis, 16,33,36,45,51,71,218,221-223,236-238, 263, 312, 338, 349, 396, 412,429

Chilton-Colburnanalogy, 281correlation, 282, 284,285factor, 481

Chimney, 258Chinese, 545Chip, 5, 124,276-279,307,309,312,333,338,

413,499Churn, 469Circuit, 26, 46, 472, 482, 516, 539, 553, 554

board , 45, 222-225, 309, 311-313, 349,351,353,366,499,506

Circular, 16, 60, 102, 103, 106, 153, 273-275,285,337,425,530,532,533

duct, 212, 273-275, 281, 285, 315

heat source, 125, 126, 128Circular tube, 274, 275, 281, 315Classical thermodynamics, 6Clausius-Clapeyron relation, 446Clean, 464, 483Closed system, 7Coefficient, 75, 461, 481, 536

mass transfer, 261, 479-481drag, 191,298,301,304,305,307,448friction, 179, 186,248-250,261,281 ,288,

290,295,296,309,310heat transfer, see heat transfer coefficientinterlace, 116, 119, 120,454,457,459,460loss, 195, 197, 198,200-208,210,211 ,223,

229,230,232-235,238momentum, 195,292thermal expansion, 243, 254, 339, 458skin friction, 185, 191, 246, 256surface tension, 136, 137,441

Collector, 547Combination, 1,7, 10, 120, 133, 161,382,389,

439,516liquid/surface, 454, 456, 457

Combine, 81-83, 105, 176, 177,251,259,294,492,540

Combined, 90, 219, 223, 231, 253, 499, 518,538,546

head loss, 227, 229, 231, 235, 236heat transfer, 15,39, 128,499,501,506,516resistance, 70, 82, 515

Commercial, 13,407,410,552,554Compact, 204Complex , 5, 6, 10, II, 36, 56, 241, 275, 496,

527,529,551flow, 201, 204, 262, 270, 280, 296, 316,

331,389geometries , 12,51,52,57,289,305,376,

423,435sound, 541, 542

Component, 71, 76, 143, 151, 155, 169,221 ,225,242,305,309,310,429,438

acceleration, 152-155, 169active, 23, 45, 51, 71height, 310, 314, 315directional, 10, 11temperature, 73, 74, 76, 116velocity, 10, 11, 151, 169, 176, 177, 188,

189, 192, 259, 280, 361Composite, 36, 37, 39,46,71 ,501 ,502Compressibility, 10, 15, 131, 132, 156,280

Subject Index 571

Computational Fluid Dynamics (CFD), 9-11,13,554

Computer, 9-13 , 85, 129, 150, 165, 338, 382,493,522,536,553,554

Computer program, 423, 435Concentrate, 52Concentric cylinders and tubes, 60, 376, 412,

421,425Condensate, 483, 486-488, 496Condensation, 437, 439, 442-444, 483-487,

489,496,527,528,531-533Conditioned, 553Conduct, 21, 102, 108Conductance, 79, 102, 104, 116, 117, 12~123,

128,301-303,488,489,492Conduction, 2, 3, 21, 76, 116, 241, 245, 337,

374,434,465,503complex, 51, 53, 57, 60, 61, 65-67electrical, 22, 23heat, 1,28,29,32,33 ,38,42,51,57,61,68,

84,97, 123,128,257,263,489,501,502simple, 32, 33, 38, 39, 42, 48thermal, 22, 24, 32, 74, 507transient, 68, 74, 84-86, 89, 129

Conduction equation, 32, 33, 38, 53, 57, 61,245,257,491

Conductivity, 256, 292, 294, 335, 366, 367, 369,382

thermal, 3, 21-24, 27, 49, 59,119,120,122,268

Cone, 380, 381Conical, 197-199,203Conjugate, 15Conservation, 15,64,289,421,516,517,552

of energy equation, 251, 253, 258of energy law, 7of mass, 10, 12, 187

Constant, 57, 132, 133, 168, 188,220,274,429,454,461,463,520,527,528,530

Stefan-Boltzmann, 3, 102, 398, 402, 404,411

numerical, 54, 71, 76, 98, 101, 135, 146,147, 180, 194, 260, 265, 267, 270, 275,276,289,301,349,448,483,494,542

of integration, 44, 47Construction, 223Contact, 5, 24, 116, 117, 119-124, 133,456Contact resistance, 6, 16, 102, 108, 115, 116,

119, 123, 129Continuity, 167, 169, 197

Continuity equation, 163, 164, 171 , 187, 188Contraction, 201, 203, 204, 227, 229-231, 243Control, 75, 216, 288, 300,431 ,451 ,453,518,

531,542,554Control surface, 8, 516Control volume, 7-9, 15,77,87Convection, 67, 77, 336, 339, 401, 434, 503,

506forced, 10,49 , 131,222,252,253,262,263,

273, 274, 276, 280, 285-289, 292, 296,304, 305, 309, 316, 330, 337, 338, 340,343,438,466-468,518

heat transfer, 39, 89, 109, 241, 252, 262,442,479,480,505,506,509,512

natural, I, 10, 22, 49, 90, 105, 109, 237,242, 245, 253, 254, 257, 258, 260, 262,268, 336, 337, 339-341, 343, 345, 348,349, 361, 366, 371, 376, 378, 38~382,389,451,496,509-513

Convective heat transfer coefficient, 6, 49, 92,93, 98, 115, 253

Convective mass transfer coefficient, 261Convergence, IIConversion, 132,261 ,410Cool, 3, 85, 137,225 ,323,331 ,333,335,337,

364,397,438,439,443,516,553,554Coolant, 1,2,162,173,222,341 ,456,474

fluid, 2, 209, 212, 309, 316media, 1, 2, 85, 86, 304

Cooling, 16, 27, 131, 133, 269, 331, 336, 348,464,482,490,506,552

air, 3, 221, 263, 312, 438conduction, 413convection,48,309,349,390,518,545,554liquid, 39, 242, 438, 553, 554radiation, 396, 397, 414

Coordinate, 10, 11, 28, 29, 32, 33, 66, 75, 76,152

Copper, 5, 6, 22, 23, 45, 124,276, 277,410,457,474,475,477,554

Correlation, 280, 286, 319, 322, 327, 390,509-513

Addoms,483AI-Arabi-EI-Rafaee, 381Al-Arabi-Khamis , 378Arnold,376Ayyaswamy-Catton, 375, 376Brown-Marco, 348Brunt, 434Catton, 374

572 Subject Index

Correlation (cont.)Chen, 487Chilton-Colburn, 282, 284, 285Chun and Seban, 481, 485Churchill, 379, 400, 401Churchill-Chu, 344, 346-348 , 377Collier, 454Dipprey-Sabersky, 310Dittus-Boelter, 281, 282, 284, 285Edwards, 267, 277, 278Elenbass, 351Globe-Dropkin, 372Gnielinski, 282, 285, 315Hatfield-Edwards, 365Hilpert, 344, 347, 348, 360, 364Hollands, 373, 375Jacob, 308, 309, 329, 330Klimenko, 471, 472Kovalev, 465LeFevre-Ede, 378Lienhard-Eichhorn, 467MacGregor-Emery, 374McAdams, 376Mills, 323, 325, 326, 328Nakai-Okazaki, 303Petukhov, 475, 477Rich-Mills, 362Rohsenow, 454, 455Shlykov, 120Sieder-Tate, 281, 282, 284, 285Sparrow-Ramsey, 319Swearingen-McEligot, 270Whitaker, 305Wills, 310, 313, 314, 316Zukauskas, 302, 319, 322, 323, 325-327,

329, 330Cover, 10, 375CPU, see Central Processing UnitCritical, 49, 162, 182, 253, 260, 349, 371, 375,

376,439,455,545,554heat flux, 448, 453, 460-464, 467,468,496radius, 48, 50Rayleigh number, 260, 371Reynolds number, 181, 191,292,296

Crossflow, 181, 186, 191,292,301,303,304,467,468

Cryogenic, 554Current, 13,23,46, 117,447,545,550,552Cylinder, 149, 175-177, 181, 376-378, 461,

465-468

conduction in, 32, 38, 46-49, 60, 61, 86convection on, 255, 274, 296-304, 318, 319,

325,327,341 ,366,376,378,389radiation on, 412, 421, 425

Cylindrical coordinate, 29, 32Damage, 1,221,538Darcy friction factor, 179Dark Ages, 546Decibel, 521, 535, 538, 542Density, 21, 140-142, 148, 158,220,268,339,

365, 443, 458, 461, 480, 526-529, 531,532

gas, 132,219,244,475,477,520,528,529liquid, 146, 160,237,243,475,477mass, 31, 134, 160,454,470,475,477,520,

526solid, 492, 546

Departure, 447, 448, 450, 496Design, 1,5,6,92,221,243,249,257,467,520Diameter, 60, 139,202,227,235,304,389,461,

487bubble, 449, 450, 476, 478hydraulic, 181-183, 225, 226, 263, 265,

267,314,315,332,481inner, 34, 39, 108, 288, 474outer, 39, 108,302

Diamond,5, 22, 23, 307, 554Diaphragm, 534, 542Dielectric, 22, 24-26 , 553, 554Difference, 12,52,66,70,95,237,337,342,

443,543equation, 63-65 , 67, 69pressure, 138, 142,341temperature, 58, 59, 69, 71, 85, 87, 89, 97,

ll2, ll5, ll6, 254, 257, 274, 275, 290,336,349,396,405,444,446,483,492,502, 514, 547

Differential, 54, 149, 151, 157, 165-168, 177,188,241,330,422,434,550,552

element, 140,408equation, 169, 189,495,526pressure, 209, 222temperature, 3, 22, 57-59, 69, 71, 85-89,

97, ll2, ll5, ll6, 242, 254, 257, 274,275,290,346,349,396,405,444,446,452,483,492,502,514,547

Diffuse, 402, 420, 421, 427, 428Diffusion, 12, 100, 101, 186,259-261,480,550Diffusivity, 31, 49, 97, 251, 254, 257, 259-261,

264,294,464,492

Subject Index 573

Dimension, 51, 102,252-254,340, 348, 349,446,461--463

characteristic, 181, 191,253,332,335,336,355, 356, 378, 382, 386-388, 463, 509,512

Dimensional, 148-151, 156-159, 165-167,252,260-262

one-, 3, 32, 33, 36, 51, 68, 101, 128, 148,149, 156-159, 161, 165, 167, 520, 526,530

three-,ll , 13, 16, 57, 63, 116, 148-150 ,156, 161, 204, 262, 300, 362, 378, 382,390,424,519,530

two-,ll, 13,36,51, 53, 57, 59, 63, 64, 77,149, 151, 165-167, 169, 171, 192,261 ,301

Dimensional analysis, 63, 250, 253-255, 461Dimensionless, 212,448,551

equation, 493form, 39,178,261group, 181,250-254,257-259,442,444number, 250, 551, 553parameter, 258, 260, 442, 461, 471, 476, 478stream function, 188

DIP, see Dual Inline PackageDirect, 12, 13,23,237,390,429,507,552-554Directional, 407, 408, 419, 420, 534Directivity index or gain, 535Dirichlet, 101Discharge, 220, 221Disk, 61, 539Displacement, 3, 134, 151 ,216,220,301,362,

405,519,526-528,531-533boundary layer, 185, 186, 215, 247-249,

292,311Dissipation, 6, 10, 12,48,90, 109, 111, 112,

156,340,389,510,513,536Dittus-Boelter correlation, 281, 282, 284, 285Double, 138,349,423,427,549,553Doublet, 535Drag, 133, 184, 195, 209, 212, 265, 288,

296-298,300,304-307,309Drag coefficient, 191,298,301 ,304,305,307,

448Drop, 170

pressure, 179,204 ,208,209,212,221,223,262,263,277,296,309,316,319,320,323,329,330,467,469,470,496

temperature, 86Droplet, 139,469,483

Dry, 482Dual Inline Package, 59, 216Duct, 133,212,216,218,274,285-287,309,

319,323,325-328Ducted,316Dynamic, 13, 15, 140, 156, 159, 177, 184, 195,

216Ear, 519, 537-543Eckert number, 257Eddy, 180,204,263Eddy heat conductivity, 292, 294Eddy viscosity, 12, 194, 195,292,294,337Edge, 56, 61, 180, 181, 191,215 ,257,268,292,

301,311 ,312,343,364,424Effectiveness, 15,21 ,48, 101, 103, 133,220,

223,260,316,348,349,363,433,527,528

emittance, 414, 417Efficiency, 103-106, 108-112, 133, 180, 216,

218,219,221 ,237,331 ,390,406,538,542, 550

fin, 6, 103-105 , 108-111, 115, 129, 324,387, 388

Egyptians, 545Elasticity, 21, 132,518,519,526,538,542Elbow, 268Electrical, 22, 23, 136,441 ,549,550Electroacoustic, 543Electromagnetic, 3,13,397,405,406,519ElectroMagnetic Interference, 209Electron, 21Electronic, 2,137,161 ,218,222,238,257,263,

349,366,431 ,482,553,554cooling, 12, 13, 15, 16, 27, 38, 129, 131,

135, 156,216,221 ,296,331,348,378,397, 406, 407, 420, 438, 456, 464--467,472,490,496,503,506,529

device or component, 1, 15, 221, 242, 396,429,434,518,520

packaging, 6, 100, 102, 116,518,545Electronicequipment, 1,21, 115, 148,209,241 ,

243,496,516,518,521,525,541,544Element, 76, 138, 139, 141, 159, 169, 170,254,

408finite, 9, 11-13, 15fluid, 1, 140, 142-144, 156, 178,342

EMI see ElectroMagnetic InterferenceEmissivity, 3, 396, 398, 399, 402--404, 406,

411,412,414,417,419,422,431--435,506

574 Subject Index

Emissivity (cont.)factor, 102, 405hemispheric~,408,410

directional, 407, 408Enclosure, 90, 243, 366, 371, 372, 374, 375,

399,412,417,427-429,438,439Energy, 2, 6, 8, 86, 89, 99, 293, 405, 419, 431,

438,440,479,518,528,531,551conservation, 7,10,251 ,253,258,289,421,

516,552heat, 5, 7, 21, 71, 180,242, 259, 280, 397,

406,411,441 ,448kinetic, 7, 8, 12, 21, 22, 216, 301potential, 7, 8, 136,441

Energy balance, 48,65,74,75,84,86,90, 101,405,406,419,421 ,475,478

Energy conservation equation, 289Energy density, 528, 531-533Engineering, 15, 148, 161, 259, 261, 280, 398,

411,419,453,467,499,546,549,552thermal, 9, 396, 545, 554

English, 142,222,342,546,548,551English system, 5, 22, 25, 26, 36, 42, 46, 50, 63,

73, 91-93, 95, 96, 105, 111, 122, 139,145, 147, 155, 161, 164, 174, 176, 183,184, 186, 200, 223, 226, 230, 232, 233,235,241- 243, 248, 272, 273, 277-279,284,285,306,307,309,313-315,324,326, 329, 336, 339, 347, 348, 356, 358,360,367,368,371,385,387,401 ,414,418,431 ,433,440,441,460,463,477,488,489,496,506,511

Enhancement, 13, 102, 310ENIAC, 553Enlargement, 199-201Enthalpy, 8, 11,251 ,274,437,494Entrance, 201-203, 223, 229, 230, 233, 265,

268,271,272,274,276,282,349effect, 182, 267, 277, 278

Entropy, 9,552Entry, 490, 551Environment,5,16,92,105,120,194,366,482,

505,510,513,520,522ambient, 4, 6, 101, 112,222,242,362,379,

429,499Epoxy, 33, 36, 124,411,432,505Equation, 11, 54, 81, 96, 142, 165, 185, 208,

289,389,446,493Bernoulli, 158-161 , 167, 169-172,

174-177, 197,238

conduction, 28, 32, 33, 38, 53, 57, 61, 245,257,491

empirical,6, 117,241,249,260,301energy balance, 12,48,86, 187,251,253,

258,260gener~, 28, 29,36,47,365,438heat transfer, 39, 257, 402Navier-Stokes, 13, 15, 177rate, 7, 9, 49, 517wave, 526,527,530

Equivalent, 181,214,304,521,524,534,553Error, 57,67, 69, 70,86,97,104,270,278,280,

282,538Ethylene, 553Euler equation, 156, 158, 165, 167, 177Eustis number, 447Evaporation, 437-439, 438,443,471,479, 481,

496,545Excess temperature, 444, 451, 454, 455Exchanger, 108, 288Expansion, 1,6, 12,51,66, 131-133, 197-200,

204,232-236,458,516,521abrupt, 197,232-235gradual, 198, 224, 233therm~, 133,242,243,251,254,339,343

Explicit, 11, 12, 75, 212Exponential, 88, 527Extend, 265, 323, 397,445Extended, 129,414,534Extended surface, 102, 256Falling, 161,481,487,547Fan, 1, 16, 17,90, 216, 218-220, 222, 223,

236-238,262,263,338,519Fanning friction coefficient, 179,281,288Fatigue, 15, 538FC, see F1uorinertFilament, 550, 552Film, 95, 96, 269, 345, 410, 445, 481, 483, 484,

486,487Film boiling, 452, 453, 464-466Film evaporation, 471Film thickness, 134, 485Fin, 102, 106, 107, 112-114, 248, 382-384,

386,414,417pin, 16, 103, 174,273,296,316,319,320,

322,323,325,327,389Fin efficiency, 6, 103-105, 108-111, 115, 129,

324,387,388Finite, 16,71 ,75, 102, 126-128, 149Finite difference, 11, 12, 15,52,63-67,69,70

Subject Index 575

Finite element, 9, 11-13, 15Finned, 105, 115, 288, 387, 388Fit, 237Fitting, 382Flat, 149, 218, 247, 291, 292, 296, 341, 343,

345,413,428,461 ,465,481,524plate, 13, 181 , 182, 184, 185, 191,245,248,

250, 263-265, 273, 289, 290, 302, 310,340, 348, 378, 390

surface, 107, 181, 185,214, 246, 288, 295,414,463,485

Florence, 548Flow, 15, 131, 184, 197,216,223, 235, 242,

262, 297, 301, 310, 330, 361, 378, 468,470

heat, 2, 3, 21, 32, 33, 36, 38,39,51,53,54,57-59 , 70, 72, 75, 81, 112, 114- 116,120, 255, 258, 268, 294, 382, 398, 492,502,514

laminar, 10, 13, 133, 177, 179, 180, 182,186, 191, 192,209, 212, 215, 250, 259,260, 263, 265-267, 269, 273, 274, 279,286,289-292,296,300,302,309,311 ,322,342,367,369,376,481 ,483

turbulent, 10-13, 133, 148, 177, 180-182,191 , 192, 194, 195,204,205,209,212,260, 263, 269, 280-282, 286-288, 292,295, 296, 302, 309, 315, 343, 344, 348,362,363,377,481,546

internal, 265, 269, 270, 273, 466, 467, 496external, 13,288,296,466,467

Flow rate, 2, 3, 162-164, 179,221 ,236,251,270-272,466,467,483

volumetric, 199,200,219,227,228,230Flow regime, 180Flowfield, 11, 12, 148, 149, 150, 151, 165,

167-175,204,364, 389FI<rCool, 137,443Fluctuating, 191, 192,526Fluid, 27, 132-135, 146, 221, 242, 257, 263,

268,343,362,547bulk temperature, 269, 270, 282density, 10, 181,298,339,342,365dynamics, 9. 13, 15. 131, 140. 142. 148,

161, 181, 184, 195. 237, 245-247. 259,262,269,292,296,331,390,545,554

element, I, 140-144, 156, 178,342flow, 13, 15, 148, 149, 156, 177, 180, 181,

184, 192,265 ,291,292,296,305,316,330,337,344,361 ,363,382,390

friction, 191,237,256,261,475,477particle, 140, 142, 148, 151, 152, 184, 191,

192, 194,245,246,292,293,296,304,438

Fluorinert, 137, 182, 183,277,333,443,456,458,474,482,487,488

Flux, 51heat, 33, 57, 67, 77, 97, 98, 101, 102, 257,

262, 270, 274, 275, 277, 287, 343, 350,366,384,429,438,445,448,451,453,454,456,459-465,467,468,496,545

Foil, 123, 124,410Force, 11, 134, 140, 169,204,220-222,251,

441,530,548,554buoyancy, 339-342, 361, 362, 371, 376,

437,443,444,446,448,466drag, 209, 298inertial, 181,260,300,551shear, 133, 177, 191, 341, 342viscous, 181, 184,254,258,260, 263, 371,

374,551shear, 133, 177, 191,341 ,342

Forced,48, 184,212 ,221,245,258,471,542,551

Forced convection, 10,49, 131,222,252,253,262, 263, 273, 274, 276, 280, 285-289,292, 296, 304, 305, 309, 316, 330, 337,338,340,343,438,466-468,518

Form, 32, 57, 64, 136,298,349,439,441,445,451,483,526

Forward difference, 69Fourier,

law, 97, 241modulus, 257, 258number, 257

France, 547, 549, 550Free, 5, 219, 280, 288, 314, 330, 353, 520, 521,

526,532,547convection, 1,336,451 ,454electrons, I, 3, 22, 23jet, 163,331plate or surface, 215, 311, 359, 360stream, 181, 184, 185, 187, 189, 191,

245-247,289,290,296,297,303,306Freezing, 243, 244, 268, 437, 490, 492, 493,

496,548,549French Revolution, 550Freon, 137,443Frequency, 220, 397, 447, 448, 496, 519-521,

525,532-536,538,540-543

576 Subject Index

Friction, 133, 156, 161, 184-186,208,216,329,342,469

coefficient, 179, 185, 191, 246, 248, 250,256,261 ,281,288,295,296,309,310

Factor, 195,209 ,212,222,225,226,229,231,235,238 ,279,285,315,470,475,477

Fanning, 179,281,288Darcy, 179

Frictional, 133, 156,208,235,238,296,341 ,342

Fully-developed, 178Gamma, 397Gap, 119-121, 123,257,312,494,495Gas, 21, 22, 27, 131-133, 156,237,243,268,

269,280,306,397,441,515,516,548constant, 133, 244, 480molecules, 133,429,433,439

Gaussian, 97, 542General, 13,55,75, 131, 148, 150, 165, 170,

379,412,526,527,530equation, 28, 29, 32, 33, 36, 38, 47, 53, 365,

438,491gas law, 244, 548

Geometric, 102, 265, 325, 328, 383, 385-388,435

German, 184,258,259,261 ,548,551,552Glass, 9, 49, 405, 410, 422, 550Gradient, 135, 170, 179, 191, 297, 301, 341,

469,470,474-478temperature, 3, 21, 22, 33, 85, 86, 102,246,

257, 264, 265, 274, 290, 293, 382, 389,495,501

Graph,238Graphical, 51, 57, 58, 128, 135,243,534Grashof number, 254, 258, 260, 268, 337, 339,

343,367,368,376,379,444,551Gravitational, 299, 337, 342, 444, 469, 470,

475,478acceleration, 158, 168, 223, 362, 454constant, 299, 342, 454

Gravity, 140, 173,221,254,337,339,363,469,476,478,483,509,512,546-548

Grease, 120-124Greece, 545Ground, 120, 150,457Growth, 301, 444, 450Half, 35, 36, 194,300,316,535,538,540Hard, 116,410Hardness, 119, 120, 122Harmonic,529, 531, 532

Head, 142, 158, 161 ,237,296,542,546Head loss, 195, 197, 199-201,209,223-227,

229-236,238,279Hearing, 518, 538,539, 542, 543Heat, 5, 47, 71, 79, 86,93, 103, 117, 126,243,

264, 340, 348, 407, 488, 495, 549-551,553

energy, 7, 21, 242, 397, 406specific, 11,31 ,87,90, 113, 114, 133,241,

242,251,252,440,441 ,443,454,458,491,520

Heat conduction, 1,28,32,38,42,51 ,57,61,68,84,97, 123, 128,257,263,489,501

Heat exchanger, 108, 288Heat flow, 2, 3, 21, 32, 33, 36, 39, 51, 53, 54,

57-59 ,70,75,81 , 112, 114-116, 120,255, 258, 268, 294, 382, 398, 492, 502,514

Heat flux, 33, 57, 67, 77, 97, 98, 101, 102,257,262, 270, 274, 275, 277, 287, 343, 350,366,384,429,438,445,448,451,453,454,456,459-465,467,468,496,545

Heat sink, 3-6 , 16, 17,23,92, 101, 109, 116,120, 123, 276, 316, 323-329, 384, 385,387-389,417,418,492,499

Heat spreader, 45, 333, 335, 336, 456, 459, 460,463,505

Heat transfer, 15,22,53, 101, 114, 125,256,263, 288-290, 294, 295, 353, 374, 399,516

average coefficient, 87, 259, 272-274, 278,279, 291, 303, 318, 335, 336, 466,485-487

coefficient, 4, 6, 48, 49, 92, 93-95, 98, 108,109,115,116,121 ,122,132,133,172,241,245,249-251,253,255,258,261,262, 266, 268, 270, 280, 282, 286, 290,302, 305, 308-310, 313-316, 325-328,330, 337, 343, 349, 352, 355-362, 365,367- 371, 387-390, 401, 402, 438, 442,452,456, 459, 460, 471, 476-480, 483,489,490,496,505,506,509-513,554

conduction, 3, 21, 33, 76, 129convection, 2, 6, 21, 23, 37, 39, 49, 89, 92,

93, 98, 109, 115, 148, 237, 241, 249,252, 253, 262, 330, 390, 442, 479, 480,503,505,506,509,512

local coefficient, 265, 301, 484overall coefficient, 37, 39, 40, 42, 472, 474,

494,514,515

Subject Index 577

radiation, 3, 4, 23, 75, 396-398 , 402, 404,423, 434, 453, 465, 506, 510, 513,515

Height , 102, 112-114, 140-142, 160-163,212,225,309-311 ,319,366,386, 387

Helium, 554Helmholtz instability, 449Hemisphere, 408, 420, 537Hemispherical, 402, 403, 408, 410, 419-422,

535High power, 554High speed, 257, 438Hindu, 546Hollow, 32Homogeneous, 469,470, 526, 534Horizontal, 61, 141, 153, 199,373,378,381,

389,390,465,469,470,486-490cylinder, 366, 376, 377, 461, 466, 483plate, 361, 363, 364surlace, 364, 366-371,464,509,512

Hot, 1,2,246,397,405 ,452,466 ,467 ,503 ,515Hottel's rule, 425Hydraulic , 216, 265

diameter, 181-183,225,226,263,267,314,315, 332, 481

radius, 225, 226, 383, 386-388Hydrodynamic, 132, 185, 188,265,289,461Hydrostatic balance, 546Hyperbolic, 16, 106IBM, 552-554IC, see Integrated CircuitIce, 439-441,444,494,495, 545, 549Ideal, 140, 148, 156, 158, 161 , 169, 173, 174,

177,184,216,297,343Immersion, 84,131 ,148,181,451 ,520,553,

554Impedance, 222, 223, 237, 483, 529, 532,

534-536Impeller , 220, 221Impinge, 162Impingement, 131,221,310,330-332,554Implicit, 11, 12,75Indians, 546Induced, 15, 148,242,361 ,362,467Inertial, 175, 180, 181,260,300,551Infinite, 56, 85, 89, 135, 463, 480, 530, 534,

535,550dimension, 61, 96, 126, 139,201 ,229,230,

352,412,413,421,424,425,428,461,520

medium or substrate, 61, 126,305,399,463semi-, 61, 96

Infinite cylinder, 425Influence, 185, 237, 246, 280, 342, 364, 382,

454,461,518Infrared , 397,407,429,431Initial , 33, 64, 88, 243, 263, 450, 466, 491, 527,

530Inlet, 204, 221, 222, 224, 227, 229, 230, 235,

263,270,277, 335,349Inner, 48, 60, 102, 108,421,474Input, 84, 384, 441Inquisition, 547Inside, 139,205,243,281,288,316,396,412,

417,425,427,429,456,506,515,536Insulation, 48, 49, 57Insulator, 33, 505Integral, 45, 108, 168, 172,423,427,450,546Integrated circuit (IC), 537, 553, 554Integrating , 39, 47,89,167,168,170,191 ,194,

259,276,290,291,295,493,495Intensity, 407, 408, 419, 521-524, 528, 531,

532,535,536,538-541,543Intensity of radiation, 422Interlace , 6, 102, 115, 123, 124, 129, 184,241,

245,256,268,331,491-493thermal, 5, 108, 116, 119, 120

Interlace resistance , 116, 117Interfacial, 485Internal, 133, 180,243,287,468

energy, 7, 8, 86, 89, 97, 251, 431flow, 13,265,269,270,273,466,467,496heat, 31-33, 40, 46, 53, 64, 68, 84temperature, 85, 86, 444,501

Inviscid, 184Irradiation, 405, 419-422Irreversible, 9Irrotational, 168-170, 297Isentropic, 133Isotherm , 54Isothermal, 57, 85, 132, 256, 269, 274-276,

281,348,427,446plate, 290, 291, 349-353surlace, 59, 67, 247, 291, 362, 364

Isotropic , 526, 534Italian, 547, 549Iteration, 314Iterative, 12, 275Jacob correlation , 308, 309Jet, 137, 139, 161-165,333,443,540,554

578 Subject Index

Jet impingement, 131,330-332Joule, 136Junction, 1,4-6,46, 207,396,413,414,499Kelvin, 399Kinematic viscosity, 133, 134, 181, 251, 254,

260, 261, 264, 551Kinetic, 7, 8, 12, 21,22, 216, 280, 301,448,

519,528,531,548King, 549,550Klystron, 553Laminar, 180-182, 194, 273, 274, 277, 289,

291, 292, 296, 343, 348, 485, 486, 509,512

flow, 10, 133, 177, 179, 180, 182, 186, 191,192, 209, 212, 215, 250, 259, 260, 263,266, 267, 274, 279, 286, 289-292, 300,302, 309, 311, 322, 342, 367, 369, 376,481,483

external flow, 13, 288, 296, 466, 467internal flow, 265, 269, 270, 273, 466, 467,

496Laplace equation or transform, 31, 51, 57Large scale, 191, 195,292,552,553Latent, 437, 440, 441, 443, 444, 454, 461, 483,

485,488-490,492,549Lattice, 3, 23Law, 7-9 ,402,405,411 , 547,549,553

Boyle' s, 132, 244, 548conservation, 15,516,517Fourier' s, 21, 22, 25, 33, 57, 86, 97, 101,

116, 241,547Newton's, 140, 142, 143, 156, 157, 165,

166, 169, 170,304,342thermodynanrics,6-9,132,552

Lay, 118, 119Layer, 23, 71, 120, 268, 293, 309- 311, 373,

452,453,483,502thermal boundary, 185, 241, 245-249, 263,

265,274,288-290,362thickness, 185, 186, 189,215,245,246,248,

249,290,292,302,311 ,362velocity boundary, 184-186,203,245,246,

248, 249Lead, 5, 21, 57, 68, 124,296, 389Least, 63, 115, 220, 221, 456Length,191 , 229,231 ,233,397,404,407,408,

419,422characteristic, 263, 314, 315, 364, 446, 448,

449,459-461 ,471 ,476,478flow, 181, 235,296, 316

unit, 40, 42, 48, 179,210,298,474Lewis number, 258, 260, 480Life, 1, 15, 26, 243, 244, 548Liquid, 27, 133, 137, 161 , 237, 243, 268, 442,

443, 446, 452, 464, 466, 469, 470, 479,554

flow, 101, 220, 269,467,468immersion, 131, 520molecule, 438, 439phase, 437, 439,454surface, 136,441 ,444,445,451temperature, 450, 492

Liquid metal, 548Liquid-cooled, 39, 438Lobe, 535Log, 380,521-525,535Logarithm, 521, 523, 524, 538Logarithmic, 39, 521Logic, 551Longitudinal, 119, 318, 323, 519, 520, 526,

543fin, 102, 103, 105, 106, 112, 113, 287,414

Loop, 551Loss, 24, 86, 198, 216,269,479,538,543,546

coefficient, 195, 197, 198, 200-208, 210,211, 223,229, 230,232-235 , 238

head, 195, 197, 199-20 1, 209, 223-227 ,229-236, 238, 279

heat, 42, 86, 101 ,402minor, 195pressure, 131, 178, 195,204, 205,222, 223,

261Loud, 538,540Loudness,538-542Loudspeaker,524,525Low, 23, 102, 137, 165, 219, 327, 382, 396,

448,465,470,539,541-543,547power, 5pressure, 216, 218, 221, 238, 262, 439Reynolds number, 297, 301, 309, 316, 325thermal conductivity, 5, 6, 27, 265, 452velocity, 10, 17, 182,337,467,468

Lumped, 85, 86, 89,94-96,129Mach number, 131,257Major, 9, 51, 466Mark I, 553Mass, 10, 12, 136, 142, 143, 157, 167, 187, 193,

241,243,269,474,478,490,536density, 31, 134, 160,454,470,475,477,

520,526

Subject Index 579

flow,179, 220, 242, 251, 270, 271, 272, 466,467,481 ,483

unit, 8, 9, 339, 340, 437Mass transfer, 256, 258, 260, 261, 289, 337,

479~81

Mathematical, 256, 258, 259, 280, 550-552Matrix, 81, 510, 513Maximum, 108, 115, 162, 216, 218, 297, 302,

340,404,444,535,544heat, 49, 102, 112,352,353,357,452,461 ,

462,467temperature, 1, 5, 6, 23, 26, 45, 46, 48,

90-92,94,96,396,414,434velocity, 178,316,318,324,325,327,331,

448,449,460Mayan, 546Mean, 12, 117, 203, 212, 280, 286, 337, 472,

523,524,527,530,538temperature, 269, 270, 293velocity, 171, 173, 174,481

Mean value, 192, 193,429,525Mel, 541Melting, 101,437,451,491Melting and freezing, 490, 496Membrane, 530Memory, 551Mesh, 57, 63, 66, 67, 227Metric, 342,440,441 ,463,550Microminiaturization, 545Micron, 405, 408, 419Microphone, 525Microprocessor, 59, 85, 116, 120, 323,

411~13,456,459,460,462

temperature, 325-329Military (MIL), 26, 27, 243, 553Minimum, 49, 117,218,302, 353, 379, 453,

464,465Minor, 195,356,357,535Mist, 469, 471Mixed, 191, 195, 269, 338Mixed boundary layer, 260, 296, 348Mixing, I, 12, 16, 244, 266, 280, 293, 337,

546Mixing cup, 269Model, 6, 10, 15, 16,85,86,96,97, 116, 193,

280,467,469,503,515flow, 11-13e,12

Modified, 113, 177,257, 350, 386, 387, 447,485,488,489

Module, 59, 63, 456, 506, 507, 510, 511, 513,514,554

Modulus, 132,257,258,399,520,526Molar, 188Mole, 550Molecular, 11, 12,22, 133, 186,241 ,268,310,

441, 480, 550diffusivity of heat, 264, 294diffusivity of momentum, 264

Molecule, 22, 133, 136,402,438,441Momentum, 7, 10, 15, 16, 180, 186, 193-195,

197,264,280,292,476,478,485change, 342,469,470,475diffusivity, 259-261equation, 11, 12, 187-189,260

Monochromatic, 403Moody chart, 212, 281Motherboard, 16Mouromtseff number, 553Move, 22, 131, 133, 146, 151, 179, 180,221,

262,296,349,364,519fluid, 220, 238

Moving, 6, 133, 134, 148, 182, 184, 216, 238,245,260,262,439,551

Multidimensional, 51, 53, 57-59, 128Multiple, 267, 423, 514, 553Natural,48, 131, 184,438,527,537,551Natural convection , 254, 258, 336, 337, 339,

349,376,382flow, 257, 262, 340, 34 1, 343, 371, 378,

379,389,509,512Natural convection heat transfer coefficient, 109Near, 67, 216, 218, 243, 265, 268, 297, 302,

340,397,534Net, 209, 342, 399,422,423,448,479Network, 57, 63, 64, 70, 71, 499Newtonian, 2, 15, 135,403Neumann boundary, 101Nodal, 63-65, 71, 75, 76Node, 63-65 , 67, 74, 77, 81, 83, 84Noise, I, 218-220, 263, 286, 518, 521,

536-538,540-543Nonuniform, 171Non-Newtonian, 15, 135Normal, 91,119,153,159,169,187,193,195,

219,361,371,519,527,538,542convection, 331,466operation, 1,516

Noy,540Nozzle, 162-164,330-332,335

580 SUbject Index

Nucleate boiling, 446, 448, 450-452, 454, 463,464,466,468,496

dominates, 471, 476, 478Nusse1t number, 455, 459, 460

Nucleation,448, 454, 456Number, 36,58,64, 131,262,378,411 ,456,

480,494,502,532-534,540-543,553Biot, 86, 96, 129, 255, 256Elenbaas,257,349 ,350,355, 356,358-360,

386, 387, 389Grashof, 254, 258, 268, 337, 339, 343, 367,

368,376,379,444,551Jacob, 444, 494Nusse1t, 192, 241, 249, 250, 253-261, 263,

266-268, 270-273, 275-279 , 281-287,291, 292, 296, 302, 303, 305, 306,308-310, 313-316, 318, 319, 325-328,332, 333, 335-340, 343, 344, 347, 348,350-352, 355, 356, 358-360, 362, 364,365, 367, 369, 372-374, 376, 379, 382,383, 387, 388, 390, 444, 453-455, 459,460,471 ,472,476-479,481,484-486

Prandt1, 246, 249, 250, 253, 254, 256,258-260, 264-269, 278, 289, 290, 294,295,309,325,327,337,390,444,454,551

Rayleigh, 116, 257, 258, 260, 337, 343, 344,346-349, 359, 360, 362, 364, 367-369 ,371,373-375,377, 382,400,401 ,465,509,512,551

Reynolds, 13, 175, 179-182, 185, 186, 189,191, 192, 195,210,212,215,225,226,228-231, 235, 247, 248, 250, 253-256 ,258-260, 263, 265-268, 271-273, 277,280-282, 284, 292, 295-304, 306, 307,309, 311, 313-316, 323, 325-328 ,335-337, 339, 343, 390, 448, 467, 470,472,475,477,481 ,485,486,496,551

Numerical, 13, 15, 16,51, 52, 128,301, 517,553

Nusse1t number, 192, 241, 249, 250, 253-261,263, 266-268, 270-273, 275-279,281-285, 287, 290-292, 296, 302, 303,305, 306, 308-310 , 313-316, 318, 319,325-328, 332, 333, 335-340, 343, 344,347, 348, 350-352, 355, 356, 358-360,362, 364, 365, 367, 369, 372-374, 376,379,382,383,387,388,390,444,454,455,459,460,471 ,472,476-479,481 ,484-486

Octave, 525, 541, 542Octave band, 525, 541Offset, 60, 142One-third, 525, 541, 549Opaque, 396,419,422Open, 90, 146, 181,209,228,230,268,288,

330,385,387Optimization, 10, 112Optimum, 112-114,333,352,353,389Order of magnitude, 259Orientation, 16, 119,361,363,380,381,384,

389,509,512Outer, 38, 47-49, 60, 74, 102, 108, 396,421,

487Outlet, 39, 204, 209, 218, 221, 222, 263, 273Outside, 136, 139, 184, 187,205,297,390,441,

490,515,516Overall, 4, 71, 115, 116, 120, 122, 127, 133,

195,331,502,538,541Overall heat transfer coefficient, 37, 39, 40, 42,

472,474,494,514,515Parabolic, 16,44, 106, 178, 179,268,274Partial, 52, 152, 165, 167, 177, 188,434,452,

492,526,549,550Particle, 157,397,527-529,531-533

fluid, 140, 142, 148, 151, 152, 184, 191,192, 194,245,246, 292, 293, 296, 304,438

Particular, 148,259,285,330,492,541PCB, see Printed Circuit BoardPeak, 16,27 , 117, 120,462Peclet number, 259, 291Penetration, 15Pentode, 553Perceived, 540Perfect, 76, 132, 133, 257, 367, 369, 396, 399,

405,406Perforation, 207, 209-211, 224, 231, 232Periodic, 99, 464, 519, 544Phase, 10, 99, 101, 102, 131, 135,453,454,

492,535 ,541,543-544,554two-, 15, 16,466-472,474,475,477, 479,

496, 545Phase change, 15,237,437-439,441 ,444,490,

491,496Phon, 538Piece, 259, 553Pin, 273, 390Pin-fin, 16, 103, 174,296,316,319,320,322,

323,325 ,327,389

Subject Index 581

Pipe, 11,39,40, 149, 159, 181, 182, 197-201,204,212,238,310,376,451

Pitch, 541-543Plane, 141, 146, 151, 193, 194,294, 297,331 ,

466,514,521 ,534acoustic wave, 520, 524, 526-529surface, 67, 77, 107, 149

Plane wall, 32, 33, 38, 39, 43, 44, 46, 60, 67, 85,515

Plastic, 5, 39, 412Plate, 54, 73,102,133,180,209,249,307,330,

355-360,363,369,381,414,550flat, 13, 181, 182, 184, 185, 191 ,245 ,248,

250, 263-265, 273, 289, 290, 292, 296,302,310,340,341 ,345,348,378,390,413

horizontal, 361, 364isoflux, 291, 296, 350-353isothermal, 290, 291, 349-353parallel, 181 ,267,270,349,412perforated, 209, 211, 231, 232rough,214vertical, 257, 341, 343, 344, 349, 353

Point, 151, 158,216,222,237,280,397,454,527, 530, 535

alphanumerical, 7, 12, 63, 146-148, 153,155, 160, 161, 163, 164, 172-174, 185,246,296,301 ,303,428,439,452,453,460,461,491,528,534,550

boiling, 137, 442, 456, 458, 461, 496, 549,554

contact, 116, 117, 120-122grid or nodal, 12, 13,64,65initial or starting, 142, 185,245 ,246,297stagnation, 172-175, 296, 297, 301-303 ,

330,331time, 52, 66, 88, 148,453

Polar, 11, 151, 152Pool, 447, 554Pool boiling, 444, 450, 451, 453, 454, 460,

464-466Porosity, 179,209-211,228,230,232,259,438Potential, 7, 8, 32, 136, 159, 161 ,275,441,502,

514,519,528,531Potential flow, 297, 300Power, 5, 93, 95, 121 , 172, 216,256,263,338,

399,434,451 ,490,537,542,553component, 23, 33, 34, 36, 71, 92, 101, 108dissipation, 6, 510, 513emissive, 396, 402-404, 408, 422

maximum or full, 91, 94pumping, 179, 180,288sound, 521, 522, 525, 536, 541, 544

Prandtl number, 246, 249, 250, 253, 254, 256,258-260, 264-269, 278, 289, 290, 294,295, 309,325,327,337,390,444,454,551

Pressure, 5, 115, 139-141, 158, 174, 237, 280,300,434,461 ,474-478,526,550

absolute, 142, 161 ,244atmospheric, 131 , 142,220,221,439,441 ,

520,528,529,538,547,548constant, 27, 28, 144,243,252,443,520difference, 138, 142, 341drop, 179,204, 208, 209, 212, 221, 223,

262, 263, 277, 296, 309, 316, 319, 320,323,329,330,467,469,470,496

fluid, 160, 173, 187,209,216,221 ,261,296, 547

gage, 142, 173, 175sound, 521, 523-525, 527, 529, 532, 533,

540-542static, 159, 160, 208, 216, 218, 219, 222,

223, 527, 538total, 159,207,216,469

Pressure loss, 178, 195,204,205,222,223,261Primary, 1,4,22,118,131 ,175,193,250,253,

331,389Primary dimension, 252Principle, 421, 546Printed Circuit Board (PCB), 6,15,45,46,331,

351,353,411Probability, 280, 547, 549Process, 7,9,101 ,133,243,275,439,441 ,445,

483,492,496,526boiling, 444, 446freezing, 493transfer, 280,337,444,479,516

Profile, 57, 134, 171, 189, 195,265,266,268,274,281,330,342

rectangular, 105, 106, 112,414temperature, 275, 289, 340triangular, 106, 112-114

Propeller, 216Properties, 6, 21, 75, 131, 149, 192, 242,442,

466,488,492,516,527,538,545,550air, 248, 313, 314, 338, 345, 354, 356, 357,

385,399,482,508fluid, 28,148,156,181,187,188,241 ,257,

260,268,269,272,297,302,458

582 Subject Index

Properties (cont.)material, I I, 12,74, 120, 122, 133variation, 268, 269, 270, 272, 281, 467

Prototype, 554Public domain, 129Pulsating, 530, 534, 535Pump, I, 180, 220-222, 262,466Pumping power, 179, 180, 288Quality, 466, 470, 474, 475, 478, 541, 542Radial, 11,31 ,38, 39,46, 102, 169, 170, 174,

176, 274, 530-532Radiation, 1,3, 10, 15,49, 84, 90, 101, 116,

241,400,408,413,420,429,432,499,516,545

blackbody, 260, 398, 399, 402-405 , 407,419,430,431 ,433,434,551

graybody, 399heat transfer, 23, 75, 396-398, 402, 404,

423,434,453,465,506,510,513,515impedance, 534-536pattern, 534view factor, 16, 396, 422-424, 427, 428,

435,507Radius, 49,60,102,118,1 39,169,170,175,

461, 535bubble, 446, 450critical, 48, 50hydraulic, 225, 226, 383, 386-3 88

Random, 13, 133, 136, 191,441 ,542, 550Rankine, 399Rapid, 161Rate, 6,23, 135, 142, 237,262, 340,441,450,501

equation, 7, 9energy, 87, 257, 293, 398flow, 2, 3, 163, 164, 179, 199, 200, 219,

221, 227, 228, 230, 236, 251, 270-272,466,467,483

heat flow, 2, 3, 53, 57, 58, 70, 75, 398, 492,502

heat transfer, 4, 7, 21, 39, 42, 48, 53, 54, 58,59,89, 113-115, 184,245,257,261,276, 290, 293-295, 399, 438, 496, 503,506, 514

Rayleigh number, 116,257 ,258,260,337,343,344, 346- 349, 359, 360, 362, 364,367- 369, 371, 373-375, 377, 382, 400,401,465,509,512,551

Reaction, 534, 535Real, 48, 85, 104, 114, 116, 161, 194, 244,348,

411,421,435,492,527, 529,534

fluid, 156, 175, 177, 289,297,390flow, 149, 156, 170, 177, 184,297,390object, 405, 406, 419surface, 399, 407

Reciprocal, 6, 257Reciprocity, 428Rectangular, 31, 54, 61, 63,103,1 27, 206, 233,

234, 286, 287,424,530coordinate, 28duct, 309fin, 104, 114profile, 105, 106, 112,414

Rectilinear, 175Reflectance, 398, 405, 406, 420, 421, 427, 515Relative, 2, 86, 134, 140, 142, 177, 260, 399,

463,467,492,535,538Reliability, 1, 554Reliable, 28Renaissance, 546Resistance, 76, 89, 117, 177, 238,371,466,

469,470,475,478,493,503,516,529contact, 6,16,102,108,115,116,119,123,

124, 129flow, 221thermal, 4-6 , 9, 22, 23, 26, 27, 36, 39, 43,

45, 49, 65, 70-75 , 79, 86, 94, 95, 107,116, 121, 123, 125, 129,251, 255, 256,262,499, 502, 505, 506, 515

Resistance-Capacitance, 70Resistor, 49-51, 84Restriction, 252Reverberation, 521Reynolds analogy, 250, 292, 295Reynolds number, 13, 175, 179-182, 185, 186,

189, 191, 192, 195, 210,212,215,225,226, 228-231, 235, 247, 248, 250,253-256, 258-260, 263, 265-268,271-273 , 277, 280-282, 284, 292,295-304, 306, 307, 309, 311, 313-316,323, 325-328, 335-337, 339, 343, 390,448,467,470,472,475,477,481,485,486,496,551

Reynolds stress, 194Rocket, 522Romans, 546Room, 396, 520, 525, 528Root mean, 527Rotary, 220Rotating, 216, 220, 221, 374Rotational, 168, 221

Subject Index 583

Rough surfaces, 115, 309Roughness, 181, 195,267,287,291

RMS, 117, 119-122surface, 117, 156, 180,212,214,263,281,

282, 309, 310, 456Round-off, 184Safety, 90, 209, 221Sand, 309Sand grain, 212Satellite, 432Saturation, 438, 439, 447, 450, 464, 480, 483,

486,496Saturation temperature, 443-446, 479Scalar, 151,337Scale, 13,57 ,191 ,195, 197,292,467,521 ,538,

540,547,548,550,552,553Scatter, 433Schmidt number or method, 51, 258, 260, 261,

289,480Scottish, 549Screen, 209-211, 224, 345Second law, 9, 142, 143, 156, 157, 165, 166,

169,170,342Secondary, 150,204,331,374Segment, 13Semi, 12, 61, 96Semiconductor, 1,4-6, 10,45Separation, 184,204,297,300--302,314,315Series, 37, 56, 71,297,411,492,495,499,502,

503,527,542,544,551Fourier, 51, 550Taylor, 12, 66

Series and parallel, 36, 70, 219, 501, 502, 516Shape, 102, 110, Ill, 197,267,285,296,304,

307-309,330,366,403,530,534arbitrary, 382, 527factor, 4, 58-61, 63, 128velocity profile, 265, 268

Shear, 140, 161, 191,251 ,341 ,485Shear stress, 134, 135, 177, 179, 185, 194, 195,

246,294Sherwood number, 260, 261, 480Short, 10,26, 191,265,285,310,382,424,483,

490,541,553Shroud, 316SI,22, 186,222,279,284,285,508SI system, 142,223,241,348,518Silicon, 23, 25, 26, 124,505,506,553,554Silicone, 124,411,443Silver, 23, 411

Similarity, 188Simple, 1,59,71,86,89, 102, 107, 141, 148,

165, 172, 187,221,366,371,465,492correlation, 322, 509, 511geometries and shapes, 32, 52, 128, 129,

147,174,177,390,428source, 530, 535

Simultaneous, 167,204 ,253,255,499,506Single, 16,33, 114, 135, 170,232,251 , 310,

365,374-377,501,538cylinder, 302, 389jet, 330, 332phase, 467-470, 472point, 12,532

Sink, 5, 6, 16, 17, 23, 92, 101, 116, 276,323-328 , 384, 387, 388, 417, 418, 492,499

Sinusoidal, 520, 527Skin friction, 185, 191,246,256,300,301Sky, 260,434, 551Slope, 118, 120, 122, 144-147,243Slow, 10Slug, 5, 6, 144, 146, 160Slug flow, 469Solar, 407, 410, 429, 431-433, 545Solder, 124Solid, 2, 21, 23, 86, 96, 99, 101, 117, 132, 172,

243,256,297,437,439,491,492,494Solidification, 437, 492Sone, 538Sonic, 554Sound, 218, 518-520, 528, 531, 534, 535,

537-539,543Sound power, 521, 522, 525, 536, 541,544Sound pressure, 521, 523-525, 527, 529, 532,

533, 540-542Source, 4, 11, 74, 123-128, 221, 397, 434,

516, 519, 525, 528, 530, 532, 534, 537,543

Source strength, 535Space, 7,52,119,221 ,309,337,372,431 ,490,

525, 532Spacecraft, 4, 429Spacing, 27, 61, 117,318,323,358,385-387,

389center, 210, 214, 316, 390, 474plate, 270, 349, 350,352,353, 355-357

Species, 188,289,480Specific, 12,81, 112, 142, 160, 168, 173-175,

249, 310,368-371,460,521,532

584 Subject Index

Specific heat, 11,31,87,90,113,114,241,242,251,252,440,441,443,454,458,491,520

Spectral, 403, 407, 408, 410, 421distribution, 402, 404irradiation, 419, 420reflection, 420, 427

Speed, 133, 180, 182,220,221,257,397,402,438,460,519,532,548,552,553

Speed of sound, 520, 521, 524, 529Sphere, 32,42,46,60, 86, 181,297 , 304, 305,

366,378,396,399,461,466,530,534,551

Spherical, 42, 519, 530-532,534,535,547Spherical coordinate, 29, 32, 76Spine, 102, 103, 106Spiral, 287, 288Spread, 125,519,520,530Spreader,45,333 , 335, 336,456,459,460,463,

505Spreading, 123, 125Stability, 12,75 ,364,445,461,464Staggered, 316, 318-320, 322, 323, 326,

328-330,389Stagnation, 175Stagnation point, 172-174,296, 297, 301-303,

330, 331Stagnation pressure, 159Standing, 353, 529, 530Stanton number, 250, 256, 261, 262, 290, 310State, 6, 7, 9, 131, 148, 195,340,439,479,516,

526,544steady, 15, 16,22 ,31 ,32,38,60,64,66,67,

84-86 , 90, 91, 93-95, 109, 128, 153,265,431 ,482,511,513

Static, 140, 141, 146, 161,209, 519, 529, 545,547,549

pressure, 159, 160,208,216,218,219,222,223,527,538

Steady, 134, 148, 151, 166, 168, 187,221,544Steady state, 15, 16, 22, 31, 32, 33, 38, 60, 64,

66, 67, 84-86, 90, 91, 93-95, 109, 128,153,265,431 ,482,483,506,511 ,513

Stefan-Boltzmann, 3, 102,398,402,404,411Stokes, 13, 15, 177, 551Straight, 102, 204Strain, 132, 134, 135,337,538Stratified, 263Stream, 151, 181, 184, 188,208,212,245,247,

260,302,303,309,542,551

free, 185, 187, 189, 191,246,289,290,296,297, 306

Streamline, 148-151, 153, 155-160, 168-172,238, 362

Streamtube, 148, 149, 156, 159Stress, 13, 15, 133-135, 177, 179, 185, 194,

195,246,294,337,548String, 343,422,428Strip, 127Sublimation, 437, 439Submerged,330, 333, 546Substantial, 382, 414, 552Substrate, 126-128Superheated, 445, 446, 465Surface, 3, 61, 86, 102, 184,245,305,331 ,361 ,

410,421,435,453,479,496,510,534area, 2,4, 6,48, 87, 92, 104, 105, 107, 115,

116, 125, 136,278,279,290,304, 307,325- 328,349,364,389,398,399,414,441,508,511,535,536,553

flat, 107, 181, 185,214,246,288,295,414,463,485

heated, 101, 284, 343, 364, 365, 374,450-452,456,460,461,465,466

temperature, 2, 4, 44, 48, 59, 99, 101, 125,268-270, 272, 273, 275, 282, 289, 290,313, 314, 324-329, 338, 383, 414, 465,468,483,545

Surface tension, 15, 136-139, 161, 237, 251,437,441-444,446,454,458,462,467

Swedish, 548Swirl, IISwiss, 548, 549Switch,543Symmetrical, 45, 46, 296, 297, 350-353, 534System, 6-9, 46, 85, 89, 165, 222, 238, 280,

330-331,515,521,545,554cooling, 39, 173,216,221 ,482,490coordinate, 10, 11,28,29,32,66,75,76English, 5, 25, 26, 122, 145, 147, 155, 161,

164, 174, 176, 183, 184, 186, 200, 226,230, 232, 235, 241-243, 248, 272,277-279, 284, 307, 309, 314, 315, 326,329, 336, 339, 347, 348, 356, 358, 360,368,371,387,414,460,477,506,511,551

fluid, 166, 167, 260one-dimensional, 3, 33, 101two-dimensional, 53, 59, 63SI, 142,223,241,342,348,463,518,550sound,537,539,542

Subject Index 585

Taylor series, 12, 66TCM, see Thermal Control ModuleTee, 268Temperature, 21, 73, 83, 98, 142, 265, 343, 399,

408,434,439,445,451 ,479,496air, 93-95, 248, 324-328, 345, 348, 353,

507,521,524difference, 3, 22, 57-59 , 69, 71, 85-89, 97,

112, 115, 116, 242, 254, 257, 274, 275,290, 336, 349, 396, 405, 444, 446, 452,483,492,502,51 4,547

distribution, 42, 44, 47, 48, 54, 56, 57, 64,69,86, 261, 289

factor, 506fluid, 246, 268-270, 275, 277-279, 282,

302,335,356,357,386,387,469junction, 1,4-6,396,413,414maximum, 1,45,46,48,90,91, 92, 94,96operating, 1, 23,26,90potential, 275, 502, 514rise, 2, 3, 6, 22, 25-27, 32, 35, 36, 45, 46,

50,51, 59, 63, 89-91, 93-96, 122, 127,242, 243, 257, 270, 277- 279, 283-285,306,308,309,313,314,336,348,355,357, 358-360 , 367-371, 387, 388, 440,441,509,511 ,51 2,514

scale, 548, 550surface, 2, 4, 44, 48, 59, 99, 101, 125,

268-270, 272, 273, 275, 282, 289, 290,313, 314, 324-329, 338, 383, 413, 414,465,468,483,545

Test, 119, 129, 136, 254, 302, 310, 521, 536Thermal, 9, 43, 74, 89, 94, 242, 256, 275, 343,

352,441 ,496boundary layer, 185, 241, 245, 246, 248,

249, 263, 265, 274, 288- 290, 362conductance, 79, 116, 121-123conductivity, 3, 21-23 , 27, 49, 59,11 9,120,

122, 268contact, 115, 116, 124, 129diffusivity, 31, 49, 97, 251, 254, 257, 259,

264,464,492radiation, 421

Thermal Control Module, (TCM), 554Thermal resistance, 4, 6, 22, 23, 26, 27, 70, 75,

86, 121, 123, 125,499,502,51 6total, 5, 49, 71, 505, 506

Thermionic Tube, 550, 552Thennodynarrrics, 6-9 ,132, 258,550,552Thermoelectric, 550

Thermometer, 546-548, 550Thennoscope, 546, 547Three-dimensional, 13,57, 63, 116, 161,262,

362, 378, 382, 390,424,519,530flow, 16, 148-150, 156, 204,300,378problem, 11, 149

Threshold, 538, 539, 542, 543Timbre, 541, 542Time, 10, 11,98, 194,429,492,553

constant, 88, 91, 94, 95interval or step, 7, 9, 74, 75, 524

Tip, 102, 383Torricelli, 161,547Total, 89, 172, 216, 298, 300, 307, 403, 469,

511,513,514,523hemispherical emittance, 408rate, 53, 54, 58, 115, 290, 294, 502, 506thermal resistance, 5, 6, 49, 70, 71, 73, 505,

506Transfer, 193, 194, 220, 264, 411-413 , 422,

481,519Transferred, 3, 5, 21, 103, 399-402,423,444,

483,503,515,51 6,519Transformer, 90, 91Transient, 13, 15, 16, 68, 84-86, 89, 91, 96,

128,129,255,490,496Transient heat conduction, 257Transistor, 33, 34, 36, 92-94, 108, 553Transition, 203, 234-236, 453, 464

laminar to turbulent, 133, 181, 182, 191,215, 260, 273, 274, 280, 282, 291, 292,296,300,302,3 11,3 15,343

Transition boiling, 452Transrrrission, 22, 215, 264, 398, 405, 406, 422,

518Transport, 12, 180, 191 ,259,260, 397Transverse, 119,215, 259,260, 316, 318,323,

526Traveling, 17, 238, 397, 482, 527- 529Triangle, 287, 424, 428Triangular, 106, 112-114,286Tube, 38, 39, 48, 160, 173, 178, 179,233 ,263,

276, 280, 285, 287, 468, 474, 486-490 ,515

round, 177, 181,206,234,265,266,270,274, 275, 281, 288, 315, 469

vacuum, 378, 550, 552, 553wall, 265, 270, 274, 275, 282, 469

Tubular, 148Turbulence, 12, 13, 16, 195, 280,303

586 Subject Index

Turbulence (cont.)full, 181,260,263,323transition to, 181, 182, 191, 215, 273, 274,

291,292,296,311Turbulent exchange coefficient, 292Turbulent flow, 12, 13, 194, 195,263 ,281

larrrinarto, 10, 133, 180-182, 191,215,260,273,274, 280, 282, 291, 292, 296, 300,302,311 ,315,343

Turbulent rate of heat transfer, 293, 294Turbulent shearing stress, 337Turning, 439, 547Two-dimensional, 11, 13,36,51,53,57,59,63,

64,77,166,171 , 192,301flow, 149, 151, 165, 167, 169,261

Two-phase , 15, 16, 466-472, 474, 475, 477,479,496,545

Ultimate, 4, 101Ultraviolet, 397,429Unheated, 268Uniform, 86, 158, 274, 348, 534

heat flux, 287Units, 91, 136, 233, 273, 285, 302, 433,

440-442,482,488,489,521,538area, 22, 29, 99, 179, 191, 193,237,251,

270,293,294,402,448,492,528English system, 5, 25, 26, 122, 145, 147,

155, 161, 164, 174, 176, 183, 184, 186,200, 226, 230, 232, 235, 241-243, 248,272, 277-279, 284, 307, 309, 314, 315,326, 329, 336, 339, 347, 348, 356, 358,360,368, 371, 387,414,460,477,506,511

length, 40, 42, 48,179,210,298,474mass, 8, 9, 339, 340, 437SI system, 142,223 ,241 ,348,518time, 22, 179volume, 11,243,528,531,550

Unit surface conductance, 302, 489UNIVAC I, 553Universal, 133, 480Unsteady, 84, 469Vacuum, 3, 21, 117, 142,378,397,402,431,

549,552,553Vapor, 443,448,458,461,464-467,470,479,

482,483,486,492,496,549bubble, 161, 439, 445-447, 449, 450, 456,

460,469column, 445, 449, 451layer, 452, 453

phase, 437, 439,454pressure, 161,438,439,445,480water, 397, 434, 444

Vaporization,161,441,454,458,461,462,485Variable, 12, 49, 66, 84, 140, 142, 209, 220,

252-254, 257, 258, 269, 289, 396, 444,466

Varied, 241,285, 548Vector, 8, 53, 148, 150, 151,408,419Velocity, 10, 151, 174-177, 182, 192,228,316,

467,470,535boundary layer, 184-186, 203, 245, 246,

248,249fluid, 134, 163, 164, 184, 195, 197, 199,

245,260,265,284,298,340,343,548head,197,222,223,226,227,229-236,296particle, 528, 529, 531-533profile, 134, 171, 189, 195,265,268,274,

281,330,342Vena contracta, 201, 203Vertical, 140, 147, 153, 165, 173,297,364,368,

380,383,385,387,389,390,486,487cylinder or tube, 61, 341, 345, 366, 378,

468,489,490height, 141, 160, 161, 237, 349plate,257 ,340,341,343-345,349,353,378surface, 361, 366, 367, 369, 370, 371, 374,

464,466,485,509,512Vibration, 3, 21, 161,518,524,526, 534, 541,

542,544View, 4, 16, 52, 116, 148, 151, 396, 397,

422-424, 427, 428, 435, 507, 510, 513,541

Viscosity, 12, 140, 156, 177, 237, 269, 284,285,470

absolute, 133, 134, 181,251,252,268,272,282,294,443,454,458

eddy, 12, 194, 195,292 ,294,337kinematic, 133, 134, 181, 251, 254, 260,

261,264Viscous, 13, 133, 180, 181, 184, 186,220 ,254,

258, 260, 263, 268, 298, 300, 371, 374,551

Void, 116, 117, 119, 120Voltage, 84Volume, 12, 16, 74, 132, 220, 221, 243, 343,

450,548control, 7-9 , 15, 75, 77, 87flow, 219, 238, 316unit, 11, 528, 550

Subject Index 587

Vortex, 170,212,300,301,309Vorticity, 13, 168VVake, 221, 297, 300, 301, 316, 389VVml,37, 71, 108,201 , 215,263,270,282,311 ,

439,477,503,524chassis, 33, 36, 45, 51, 412friction, 161, 195, 203,204,469,470heated, 341, 374,444,446,450plane, 32, 33, 38, 39, 43, 44, 46, 60, 67, 85,

515surface, 105, 107, 186, 191,269,272,273,

331,341 ,349,444,446,515, 516VVater, 135, 137, 185, 216, 241-244, 330,

439,441 ,443,451 ,452,457,494,546,549

deionized, 199, 242,282,493,529,553vapor, 397, 434velocity head, 226, 227, 229-236

VVatt,5,6,72, 242,338,505,522,528 ,549,553VVave, 84, 260, 518, 527, 530, 532-534, 541,

543,544,551acoustic, 519-521, 524, 526, 528, 531

Wavelength, 397, 404-408, 419, 422, 449, 520,534,544

VVaviness, 119VVavy, 483, 485,486VVeber number, 467VVeight,90, 141, 156, 159,243,480,546,549

specific, 133, 142, 146, 160, 161, 173-175,460

VVet, 258, 460VVetted, 104, 182,456,480,481VVidth, 61, 112, 113,301, 332, 365, 414, 424,

461, 535,541 ,542plate or board, 231, 290, 314unit, 185, 247,481,485

VVire, 209-211, 227, 228, 230,292, 343, 451VVork, 7, 212, 251, 258, 267, 310, 441, 452,

538, 546-550Yield, 49,51 ,58,112,133,159,285,294,427,

451,462,521 ,535Zenith, 408, 419Z-axi s, 140, 147, 362Zuber constant, 461, 463

Author Biography

Ralph Remsburg is currently President of Electronic Packaging Associates, Inc.,a consulting firm with offices in Austin, Texas , and headquartered in Sarasota,Florida. Formerly, Mr. Remsburg had held engineering positions up to the direc­tor level, before becoming a consultant. Ford, Chrysler, Delco, Hghes, Loral,and Dell Computer are just a few of the companies that have used his services.Mr. Remsburg has 17 patents, five published papers, is a member of Mensa, andis listed in Who's Who. Mr. Remsburg can be contacted at remsburg@aol.com.

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