Lecture Series 2Radiation Heat Transfer

Lecture OutlineI. Importance of Radiation in SENA EquipmentII. Radiation Fundamentals III. Radiation Heat Transfer EquationsIV. Bus Bar Example ProblemV. Practical Design Notes/Reference MaterialVI. Final Questions

Why Is Radiation Important In SENA Design?16 of 29 TCs exceeded UL limits--the max rise was 74.8C After paint, 2 of 29 TCs exceeded UL limits--the max rise was 66.1C One TC dropped by 10C and 16 other TCs dropped about 6CWhy?

Radiation Heat Transfer: The transfer of heat by thermal radiation. Thermal radiation is a specific range of electromagnetic waves (or photons) which occur solely due to temperature. Unlike conduction and convection, radiation does not require a medium to take place, therefore it can occur in a vacuum.FundamentalsElectromagnetic Wave Spectrum: Thermal Radiation Range: 0.1 to 100 micrometers wavelength (3x1015 to 3x1012 Hz) Only a portion of thermal radiation is in the visible range

FundamentalsPlancks Distribution: Spectral Blackbody Emissive Power1. Plancks Law (derived from the 2nd Law of Thermodynamics) describes the maximum amount of radiant energy that can be emitted at a given temperature and wavelength (Blackbody).2. As the temperature increases, more radiation appears at shorter wavelengths3. Below 800K (527C) all the radiation is in the infrared range and invisible to the eye (all SENA products)4. Solar radiation is at 5800K which peaks in the visible light range

Chart1

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0.00250207010.01237825020.04942864860.48245792192.909470816

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11.052663399213.09356424415.217997646519.668894192424.3285052188

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4.51313151635.19189636685.88585018487.30961259378.7695649866

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3.69128389394.22620496274.77167184835.88741234227.0281075161

3.34893985013.82603731674.31198842855.30468498936.3182693561

3.0445380473.47131219353.90555422164.79155328095.6951225415

2.77327114423.15610091933.54525782894.3383920385.1463750942

2.53100488182.8753358013.22505014153.93707374154.6617021948

2.31417707072.62467455552.93977105313.58071201154.2323982124

2.1197122862.40038730522.68500639483.2634526063.8510956639

1.94494986312.1992622882.45696957762.98030256253.5115372924

1.78758311292.01852707042.25240345192.72699005093.2083904756

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1.40107566551.57621371111.75327905792.11189106632.4749616793

1.29566505141.4560031091.61802705981.94599239392.2778528849

1.19988155751.3469387631.49547487411.79598145632.0999008846

1.11270129831.2478148621.3842292881.66007730991.9389239548

1.03322353761.15757346711.28307064181.53672619911.7930235037

0.96065430651.07528439421.19092879341.42456925091.6605430511

0.89429238811.00012808051.1068627221.32241520821.5400337404

0.83351730380.93138096031.03004317811.22921735241.4302252525

Ts = 50 degree C

75

100

150

200

Wave Length (mm)

Spectral Emissive Power (W/m2-mm)

Sheet1

Ts = 50 degree CT = 50 CT = 50 CT = 50 CT = 50 CT = 50 C

T(C)=5075100150200250

T(K)=323.15348.15373.15423.15473.15523.15

LamdaEbEbEbEbEbEb

100.00000000040.00000000670.0000006370.00002316460.0004238418

20.00250207010.01237825020.04942864860.48245792192.90947081612.4452681323

30.55088562991.59944113514.025766655718.386812235160.9192785597160.5373574375

45.345434513411.88969412323.759895604874.2411787915182.3688059695377.378440536

516.234948176630.778507527553.56214396133.3335129917273.8987535695490.7383053006

628.799785605849.09367185477.9336961214166.8601679536304.5844363402496.3877318763

738.512861676760.873672056990.5339904049174.23826061292.6767708856446.3513926194

843.843423033765.51104098892.8273747806165.1065706293260.8725150293378.9608949968

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1818.220509059422.158985722326.334256469835.271781638544.830291562154.8636753961

1916.043356658919.36062857122.857821957330.294879558838.196865550646.4519972011

2014.144135866616.951826645619.897563056526.126477292832.707583825239.5546512573

2112.490834275914.878859541417.373792861322.62351156328.142965462433.8650834703

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239.801345954911.553806616113.372088471417.167150820521.125269563225.2048851886

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Sheet1

Ts = 50 degree C

75

100

150

200

Wave Length (mm)

Spectral Emissive Power (W/m2-mm)

Sheet2

Sheet3

FundamentalsStefan-Boltzmann Law:Eblackbody -- the total emissive power or heat flux(W/m2)n -- the index of refraction (=1 vacuum,~1 gases, =1.5 for glass) -- the Stefan-Boltzmann Constant (5.67x10-8 W/m2 K4)Tsurf -- the surface temperature of black body (Kelvin)Important Notes:All objects above 0 Kelvin emit thermal radiation The amount of energy emitted is based on temperature (K) to the 4th power At higher and higher temperatures, radiation heat transfer becomes more and more significant and can be the dominant form of heat transfer.

FundamentalsAll real surfaces absorb and emit less heat flux than a blackbody.Def: Total emissivity is the ratio of emissive power of the surface to that of a blackbody (note: surface property only)--% of the maximum amount of emitted heat flux.0 1, depends on the surface conditions (roughness, finish, plating, oxidation, paint, etc.)Three types: directional, spectral (wavelength), or total (all)Important Notes:For hand calculations or CFD, use the total emissivity!For IR Thermography one must use the spectral emissivity in the IR range of the IR camera Total emissivity Normal emissivity (except for highly polished surfaces)

FundamentalsMeasured total emissivity of common SENA materials.

Sheet1

MATERIALSTOTAL EMISSIVITY

Silver Flash Cu0.03

Tin Plated Cu0.06

Matte Tin Cu0.22

Blackened Matte Tin Cu0.53

Glastic0.8

Painted Steel0.87

Grey Painted Steel0.86

White Painted Steel0.88

Galvanized Steel0.06

Alkaline Matte Tin plating Al0.08

Acid Matte tin plating Al0.08

Bright acid tin plating Al0.06

Painted Al0.82

Sheet2

Sheet3

Irradiation: Total amount of radiation that is incident on a surface (G--W/m2) For most engineering problems, surfaces are opaque ( = 0). Def: Absorptivity () = ratio of absorbed radiation to incident radiation. (note: depends on surface and nature of incident radiation)Three types: directional, spectral (wavelength), or total (all)Absorptivity table values are typically described by the irradiation (ex. solar absorptivity, low temperature absorptivity, etc.)Fundamentals

when the surface emittance and the irradiation lie in different wavelength ranges.FundamentalsIn engineering, we assume = Kirchhoffs Law: blackbody -- = Graybody Assumption extends Kirchhoffs Law to real surfacesImportant Notes:Solar heating! Gsolar is concentrated between 0.2 and 3 microns where as the emitted radiation range of SENA equipment is 2 ESENA 100 microns

Other Radiation Terms

Intensity = amount of energy that departs a surface (information about directional distribution)Radiosity = total amount of energy that departs a surface (reflected + emitted).Directional = depends on directionHemispherical = all directionsDiffuse = independent of directionNormal = perpendicular to surfaceSpectral = wavelength dependentMonochromatic = one wavelengthTotal = all wavelengths, all directionsFundamentals

Qrad is the net heat transferred between the surface and the surroundings or surface 1 to surface 2 in wattshrad is the radiation heat transfer coefficient and has the units (W/m2-K). f1-2 is the view factor from surface 1 to surface 2 (unitless). is the emissivity of the surface (unitless). is the Stefan-Boltzmann Constant = 5.67x10-8 W/m2 K4Radiation Heat Transfer EquationsRadiation Heat Transfer in terms of a heat transfer coefficient

Radiation Heat Transfer EquationsAsL = 20t = .25W = 2QradQconvTs=105C=378KT=50C=323KSteady-stateAdiabatic at the endsNegligible q at top and botCu matl negligible temp gradient through thickness

Chart2

7.81014874124.75790670443.721.97498014140.5386309477

8.17230203434.97852882553.942.06655913510.5636070368

8.5485338245.2077275024.132.16169820840.5895540568

8.93914008435.44568303994.282.26047220520.6164924196

9.34441678925.69257574514.422.36295596970.6444425372

10.4237340766.35009087394.692.63588677780.7188782121

11.60121607277.06740749264.912.9336408460.8000838671

12.88148737337.84734288265.093.25738761160.8883784395

15.76889626069.60633910135.363.98753698541.0875100869

19.122957487911.649617785.574.83569039921.3188246543

Rad,Painted E=.87

Rad,Black Matte Tin E=.53

Free Conv

Rad,Matte Tin E=.22

Rad,Tin-plated E=.06

Bus Bar Surface Temperature (C)

Heat Transfer Coefficicient (W/m2K)

Sheet1

TsurfHconvHrad,E=.06Hrad,E=.22Hrad,E=.53Hrad,E=.87

853.720.541.974.767.81

953.940.562.074.988.17

1054.130.592.165.218.55

1154.280.622.265.458.94

1254.420.642.365.699.34

1504.690.722.646.3510.42

1754.910.802.937.0711.60

2005.090.893.267.8512.88

2505.361.093.999.6115.77

3005.571.324.8411.6519.12

3505.731.585.8114.0022.98

4005.861.896.9216.6827.38

5006.072.629.6023.1237.95

6006.223.5312.9331.1451.12

7006.344.6316.9940.9367.19

8006.435.9621.8752.6886.47

9006.517.5327.6266.55109.24

10006.599.3734.3482.73135.80

Sheet1

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

Rad,Painted E=.87

Rad,Black Matte Tin E=.53

Free Conv

Rad,Matte Tin E=.22

Rad,Tin-plated E=.06

Bus Bar Surface Temperature (C)

Heat Transfer Coefficicient (W/m2K)

Sheet2

Sheet3

Ts=105C=378KT=50C=323KAsL=20t=.25W=2Radiation Heat Transfer Current Ampacity Improvement QradQconvSteady-stateAdiabatic at the endsNegligible q at top and botCu matl negligible temp gradient through thicknessCu@105C = 2.31x10-8 -m55% increase in current capacity over tin coating

Method of Solving A Solar Radiation Application2. Use on-line calculator to determine solar irradiation on a surface3. Determine the solar absorbtivity of the surface 4. Multiply the solar absorptivity by the solar irradiation to obtain the total heat flux absorbed on each surface1. Determine the equipment orientation and location5. Include heat flux in the energy balance equation or as a heat load in your thermal analysis softwareOne surface of enclosure

Practical Radiation Considerations For Design2. For all indoor SENA equipment the radiation is in the infrared range and invisible to the eye.

3. For engineering calculations or CFD, use the total emissivity!6. How well a hot object can see a cool surface that it is radiating to, will determine how much heat will be radiated!4. To increase radiative heat transfer and reduce temperature use dull, painted, or oxidized type surfaces rather than polished or shiny surfaces.7. For forced convection applications radiation effects are usually minimal.8. For natural convection in vented enclosures radiation CAN be significant.9. For natural convection in non-vented enclosures, radiation is very critical!5. For outdoor SENA equipment solar loading is important ( ) . Small values of the ratio of / ( less than 1) are required for external enclosure surfaces (the surface absorbs less than emits).1. All SENA products emit thermal radiation!

Radiation Reference Material1. Introduction To Heat Transfer, F. P. Incropera, and D. P. DeWitt, 2nd ed., John Wiley & Sons, Inc., 19902. Radiative Heat Transfer, M. F. Modest, McGraw-Hill, Inc., 19933. Handbook of Heat Transfer, W. Rohsenow, J. Hartnett, Y. Cho, 3rd ed., McGraw-Hill, 19984. Heat Transfer, J. Holman, 3rd ed., McGraw-Hill, 19975. Radiation Heat Transfer, E. Sparrow, R. Cess, Augmented Edition, Hemisphere Publishing, 19786. Thermal Radiation Heat Transfer, R. Siegel, J. Howell, Augmented ed., Hemisphere Publishing, 19817. Heat Transfer & Fluid Flow Data Book I, Genium Publishing Corp.8. Heat Transfer & Fluid Flow Data Book II, Genium Publishing Corp.9. http://www.tak2000.com/tc/prop2.htm10. http://www.electro-optical.com/bb_rad/emissivity/matlemisivty.htm

Questions?

Hello and welcome to Lecture Series 2 on Radiation Heat Transfer. Presenting today are Kevin Parker , John Richter, and Stuart Brogden. The purpose of these lectures are to equip engineers at each design center with the theoretical skills in the area of thermal management for improving future designs. The Thermal Management Team feels strongly that having a solid understanding of the physics involved is critical for effectively conducting thermal analysis.Here is the outline of what we plan to go over in this presentation.Lets begin with some fundamentals. Radiation heat transfer is defined as the transfer of heat due to thermal radiation. Thermal radiation is a specific type of electromagnetic wave which is emitted due to the temperature of the object surface. Radiation heat transfer is unique from conduction or convection because it does not require a transfer medium such as air for convection or a solid or fluid for conduction. This means that radiation heat transfer can occur in vacuum conditions. Radiation heat transfer is the sole means of heat transfer in space applications. I mentioned electromagnetic waves and here is a graph of the electromagnetic wave spectrum at different wavelengths. In the electromagnetic wave spectrum are X rays, ultraviolet waves, infrared waves, visible light, and microwaves. The yellow arrow marks the wavelength range of thermal radiation. Notice that the visible light range is only a small part of thermal radiation. The majority of thermal radiation is in the infrared range. Infrared radiation is not sensitive to color where as radiation in the visible light range is.Maxwell Planck was one of the pioneer scientists who investigated the phenomenon of radiation heat transfer in the early part of the 20th Century. From the Second Law of Thermodynamics, Planck derived what is called the Plancks Law. There are a few important points about thermal radiation that we can learn from Plancks Distribution. First this distribution describes the maximum amount of energy that can be emitted at a given temperature and wavelength. An object that can emit this amount of energy is referred to as a blackbody (perfect radiator). In reality, no object is a perfect radiator, but is some degree less than a blackbody. To describe how much energy an object can emit, we can compare it relative to a blackbody. We will discuss this in more detail when talking about emissivity. Secondly, notice in the top graph that as the temperature increases, the total amount of energy emitted increases and more and more energy appears at shorter wavelengths. The third point is that below 800K which is equal to 527 degrees Celsius, all the radiation is in the infrared range which is invisible to the eye. The bottom graph is a plot of the typical temperature range of our equipment. You can see that the wavelength of this radiation is completely in the infrared range. Since this is not in the visible light range, for the majority of situations color is not important for our equipment. But there is an exception. You can see from the top graph that solar radiation is at 5800K. This radiation peaks in the visible light range. When dealing with outdoor equipment, the color of the exterior surface will be significant in how much radiation will be absorbed from the sun.Now lets look closer at the relationship between the amount of energy radiated by an object and its temperature. This is described by the Stefan-Boltzmann Law. Eblackbody is the total emitted power or heat flux of a perfect radiator. n is the index of refraction of the medium in which the radiation is passing through. In most situations this value will be 1. Sigma is the Stefan-Boltzmann Constant which is equal to 5.67 x 10-8 W/m2K4. This is a proportionality constant. And Tsurf is the surface temperature of the blackbody. It is very important to note that this temperature must be absolute temperature. For SI units this is degrees Kelvin and in English Units this would be degrees Rankine.

There are some important items to note from this equation:All objects above 0 Kelvin emit thermal radiation. This means that radiation heat transfer will always occur in our thermal problems. But the important thing is for us to determine if this form of heat transfer is significant enough to take into account. Secondly, the amount of energy emitted is based on the surface temperature to the 4th power. In many situations, the internal temperature of an object is significantly different than the surface temperature. This means that the properties that govern radiation heat transfer are surface properties. The last thing to note is that at higher and higher temperatures, radiation heat transfer becomes more and more significant. In some of these high temperature situations, heat transfer can be the dominant form of heat transfer.

The Stefan-Boltzmann Law applies to perfect or ideal surfaces (blackbodies). Now lets consider a real surface which is what we are interested in. As I mentioned before, all real surfaces absorb and emit less radiation than a blackbody. To quantify this difference, a parameter is introduced called the emissivity or emittance of the surface. Note that this a surface property. The Total emissivity is defined as the ratio of the emissive power of the surface to the emissive power of a blackbody. Another way to say this is that the emissivity is a percentage of the maximum amount of heat that could be emitted at that surface temperature. Emissivity is always a value between 0 and 1 and is dependent on the surface conditions of the object. A few examples of these conditions would be surface roughness, plating, oxidation, and paint. A good example of this would be a bus bar. A bus bar with silver plating will have a low emissivity, but if you paint that same bus bar, then the emissivity will increase drastically and also the radiation exchange of heat. Finally it must be noted that there are different types of emissivities. Directional emissivity is dependent on the direction in which the radiation is being emitted. Spectral emissivity is dependent on the wavelength of the radiation. And the total emissivity is independent of direction and wavelength. For your hand calculations, you will usually use the total emissivity. An interesting note if you are doing IR thermography, then you will need to use the spectral emissivity in the range of the IR camera. Finally, when looking up emissivity values, the tables will sometimes contain normal emissivities. The normal emissivity is approximately equal to the total emissivity for most surfaces except for highly polished ones.Since emissivity is an important parameter for radiation calculations, two years ago the Analytics Group sent many Schneider materials to a testing facility to measure their total emissivity. And here is a table of the results of those tests. Note that most of the platings have very low emissivities. Where as the paints have fairly high emissivity values. Also note that the paint values are all around the same emissivity. This means that white painted enclosures emit the same amount of radiation as black painted enclosures for inside applications. Another thing to note that some people fail to consider is that plastics usually have a high emissivity. Our Glastic material has an emissivity of 0.8. At this point we have looked at some of the fundamentals of radiation and considered how much radiation can leave or be emitted from a surface at a given temperature. Now lets look at the amount of radiation striking a surface. This type of radiation is referred to as irradiation. Irradiation is defined as the total amount of radiation that is incident on a surface. It is given the notation of G. The total amount of radiation energy hitting a surface can do one of three things at that surface. It can be transmitted. It can be reflected. Or it can be absorbed into the material. Three parameters describe these three conditions--the transmissivity (tau), the reflectivity (rho), and the absorptivity or absorptance (alpha). For most of our engineering problems, the surfaces are opaque which means that the transmissivity is zero. The absorptivity is an important surface parameter for radiation which is dependent on the surface conditions, similar to emissivity, but is also dependent on the nature of the irradiation. The most common type of irradiation is solar. The absorptivity is defined as the ratio of the absorbed radiation to the total irradiation on that surface. Like emissivity, there are three types--directional, spectral, and total. When looking for absorptivity values, note that you will need to look for values based on the type of irradiation that you are dealing with. What this means is that you will have to look up values for solar absorptivity when dealing with outside applications rather than a low temperature absorptivity. Weve considered the two radiation situations for an object. That is, the case where energy is radiated by the object which is defined by the emissivity and the case where energy is radiated to an object which is defined by the absorptivity. Now we need to bring these two situations together for a given object to quantify the total radiation heat transfer.

For the majority of our radiation problems we assume that the absorptivity is equal to the emissivity. This is called the Graybody Assumption. Kirchhoffs Law first proved this for a perfect radiator and it was found to be a good assumption for most engineering situations. But we need to note some important situations. The absorptivity cannot be assumed to be equal to the emissivity in the case where the irradiation is a different wavelength range than the emitted radiation. A common application of this is in the case of solar heating. The solar irradiation is between 0.2 and 3 microns where as the emitted radiation range of Schneider Electric equipment is between 2 and 100 microns.

At the bottom here is a table of absorptivities for common Schneider Electric materials. Notice how the paints vary with color. In outside enclosure design, an important parameter for an enclosure is the ratio of the solar absorptivity to the total emissivity. To keep an enclosure cool, this ratio should be less than 1.0. This just means that you want your enclosure to emit more radiation than it will absorb.That concludes our discussion of radiation fundamentals. Here is a list of terms and their definition that you might encounter when reading about radiation heat transfer.