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Engr FRANCIS M MULIMBAYAN
BSAE
INSTRUCTOR 4
ENSC 15
Fundamentals of Heat Transfer
Department of Engineering Science
University of the Philippines
Los BanosCollege, Los Banos, Philippines
Heat Transfer by
Convection
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Convection
o occurs between a solid surface and a moving fluid
o combination of heat diffusion (conduction) and bulk motion ofmolecules (advection)
o dominant form of heat transfer in fluids
o requires presence of material medium
o enhanced heat transfer due to fluid motion
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Introduction
Convective Heat Transfer
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Types of Convection
o Forced Convection
o occurs when fluid motion is
induced by an external meanssuch as pump or fan
o Natural Convection
o
brought by buoyancy forces dueto density differences caused bytemperature variations in thefluid
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Introduction
Convective Heat Transfer
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Classification of Fluid Flowso Viscous vs. Inviscid Flow
o Viscous flow the effect of viscosity is significant
o
Inviscid flow flow with zero viscosityo Internal vs. External Flow
o Internal flow through tubes or ducts in which the fluid is completelybounded by solid surface
o External flow of unbound fluid over a surface
o Open-channel flow though tubes or ducts or channels in which fluidis not completely bounded by the solid surface
o Laminar vs. Turbulent Flow
o Laminar highly ordered fluid motion
o Turbulent disordered fluid motion
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Introduction
Convective Heat Transfer
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Physical Mechanism of Convectiono Convection strongly depends on the following:
o fluid properties (, k, , and )o fluid velocityo geometry of the exposed surface
o type of fluid flow
o Newtons Law of Cooling
=
The crux of the convection problem is to find the heat transfer coefficient forthe situation at hand.
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Introduction
Convective Heat Transfer
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Nusselt Number
=
where: = heat transfer coefficient, W/m2-K = characteristic length, m = thermal conductivity, W/m-K
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Dimensionless Parameters
Convective Heat Transfer
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Reynolds Number
=
=
where:
= density, kg/m3 = free stream velocity, m/s = characteristic length, m
= dynamic viscosity, kg/m-s = kinematic viscosity, m2/s =
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Dimensionless Parameters
Convective Heat Transfer
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Prandtl Number
=
=
where: = kinematic viscosity, m2/s =
= thermal diffusivity, m2/s =
= dynamic viscosity, kg/m-s
= specific heat, J/kg-K = thermal conductivity, W/m-K
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Dimensionless Parameters
Convective Heat Transfer
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Grashof Number
=
where:
= gravitational acceleration (9.81 m/s2) = characteristic length, m = kinematic viscosity, m2/s
= surface temperature, = fluid temperature far from the surface, = coefficient of volume expansion
=
ideal gases
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Dimensionless Parameters
Convective Heat Transfer
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Rayleigh Number, Ra =
Correlation of Datao a convenient and relatively simple relation for the correlation of
experimental data is to assume an equation of the form:
=
o where C, m and n depend on the surface geometry and the flowcondition.
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Dimensionless Parameters
Convective Heat Transfer
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Nature of Convection Problems
Convective Heat Transfer
Convection
Natural Forced
External
Flow overFlat Plates
Flow overspheres
Flow acrosscylinders
Internal
Constant or constant
Turbulentor Laminar
flow
Developingor fully-
developed
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Natural Convectiono Brought by buoyancy forces due to density differences caused by
temperature variations in the fluid
Applicationso Found in equipment that are designed to operate without the
use of any fluid mover
Mean Film Temperature,o Temperature at which all fluid properties in natural convection
are evaluated
=
2
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Natural Convection
Convective Heat Transfer
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Nusselt Equations (See Table 9-1)
o depends on the geometry and orientation of the surface ,variation of temperature on the surface and thermo-physical
properties of the fluid.
=
= ,
Convective Heat Transfer Coefficient =
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Natural Convection
Convective Heat Transfer
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Natural Convection
Convective Heat Transfer
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Natural Convection
Convective Heat Transfer
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Natural Convection
Convective Heat Transfer
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Natural Convection
Convective Heat Transfer
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Natural Convection
Convective Heat Transfer
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Sample Problems
1. The outside diameter of a horizontal steel pipe is 4.6 cm.The pipe is located in a room where the ambient
temperature is 20C. The exterior surface temperature ofthe pipe is 40C. Determine the heat transfer rate from thepipe per unit length of the pipe.
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Natural Convection
Convective Heat Transfer
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Sample Problems
2. A small holding tank in a chemical plant contains acorrosive liquid that is maintained at a temperature of
120F by means of an electrical heater. The heating elementconsists of a refractory disk 2 ft in diameter situated at thebottom of the tank. Estimate the power required, in Btu/hrto maintain the surface of the heating element at 160F. The
properties of the corrosive liquid at 140F are: = 4.8, = 0.023ft2/h, = 0.4Btu/h-ft-F and = 0.000125R-1.Use = 32.2ft/s2.
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Natural Convection
Convective Heat Transfer
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External Forced Convectiono Involves flow of unbound fluid over a surface.
Applications:o Used in mechanical and thermal design of many engineering systems
such as aircraft, automobiles, buildings, electronic components andturbine blades.
Flow over Flat plates
o Laminar: R e < 5 1 0
=
= 0.664//
o Turbulent: R e > 5 1 0
=
= 0.037. 871 /
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External Forced Convection
Convective Heat Transfer
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Flow across a single cylinder
Flow over spheres
= 2 0.4/
0.06/.
o The Nusselt equation above is valid
only if 0.71 380,3.5 7.6 10and 1.0
3.2.o All properties are evaluated at free
stream temperature except
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External Forced Convection
Convective Heat Transfer
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Sample Problems1. A small heater in the form of an electrically heated wire is
crossed back and forth in front of a fan which blows air over it ata mean velocity of 15 ft/s. The surface temperature of the wire
should not exceed 1300F. The air temperature is 60F. Theheater is to generate 3412.3 Btu/hr. Determine the length of acircular wire whose diameter is 1/32 inch.
2. The components of an electronic system are located in a 1.25-m-long horizontal duct whose cross-section is 18 cm x 18 cm. Thecomponents in the duct are not allowed to come into directcontact with cooling air, and thus are cooled by air at 28Cflowing over the duct with a velocity of 200 m/min. If the surfacetemperature of the duct is not to exceed 72C, determine thetotal power rating, in W of the electronic devices that can bemounted into the duct.
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External Forced Convection
Convective Heat Transfer
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Sample Problems3. The top surface of the passenger
car of a train moving at a velocity of70 km/h is 2.8 m wide and 8 m
long. The top surface is absorbingsolar radiation at a rate of 200W/m2, and the temperature of theambient air is 30C. Assuming theroof of the car to be perfectlyinsulated and the radiation heat
exchange with the surroundings tobe small relative to convection,determine the equilibriumtemperature of the top surface ofthe car.
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External Forced Convection
Convective Heat Transfer
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Internal Forced Convectiono Involves flow through a closed conduit that is sufficiently long to
effect the desired heat transfer
Applications:o Commonly used in heating and cooling applications
Different flow sectionso Pipes has circular cross-sections
o Ducts has non-circular cross-sections
o Tubes pipes with small diameter
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Internal Forced Convection
Convective Heat Transfer
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f
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Mean Velocity
o Velocity which remainsconstant for incompressible
flow when the crosssectional area of the tube isconstant
=
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Internal Forced Convection
Convective Heat Transfer
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Mean Temperature
o When a fluid is heated as itflows through a tube, the
temperature of the fluid atany cross-section changesfrom at the surface of thewall to some minimum atthe tube center.
o The temperature profile willchange whenever the fluid isheated or cooled.
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Internal Forced Convection
Convective Heat Transfer
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Bulk Mean Temperatureo Temperature where all fluid properties in internal flow are evaluated
= 2
o where:
= mean inlet temperature = mean outlet temperature
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Internal Forced Convection
Convective Heat Transfer
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C i H T f
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Velocity Profile
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Internal Forced Convection
Convective Heat Transfer
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C i H T f
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Velocity Profile
o Hydrodynamic entrance region
region from the tube inlet to the point at which the boundary layer
merges at the centerlineo Hydrodynamic entry length,
length of the hydrodynamic region
o Hydrodynamically developing flow
flow in the entrance regiono Hydrodynamically fully developed region
region beyond the entrance region in which the velocity profile isfully developed and remains unchanged
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Internal Forced Convection
Convective Heat Transfer
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C i H T f
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Temperature Profile
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Internal Forced Convection
Convective Heat Transfer
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C ti H t T f
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Temperature Profileo Thermal entrance region
region of flow over which the thermal boundary layer develops andreaches the tube center.
o Thermal entry length, length of thermal entrance region
o Thermally Developing Flow flow in the thermal entrance region where the temperature profile
developso Thermally fully-developed Region
region beyond the thermal entrance region in which the dimensionless
temperature profile expressed as
remains unchanged
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Internal Forced Convection
Convective Heat Transfer
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C ti H t T f
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Fully-developed Flow
o region in which the flow is both hydrodynamically andthermally developed and thus both the velocity and
dimensionless temperature profile remains unchanged. Entry Length
o distance from the tube entrance where the friction coefficientreaches within about 2% of the fully developed value.
Laminar: = 0.05 = 0.05 =
Turbulent: 10
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Internal Forced Convection
Convective Heat Transfer
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General Thermal Analysis
o In the absence of work, the conservation of energy equation forsteady flow of a fluid in a tube can be expressed as:
=
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Internal Forced Convection
Convective Heat Transfer
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Convective Heat Transfer
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The thermal conditions at the surface can usually beapproximated with reasonable accuracy to be:
o
Constant surface temperature (constant ) Realized when a phase change process such as boiling and
condensation occurs at the outer surface of the tube
o Constant surface heat flux (constant ) Realized when the tube is subjected to uniform radiation or electric
resistance heating
=
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Internal Forced Convection
Convective Heat Transfer
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Convective Heat Transfer
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Constant
= =
=
ln
=
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Internal Forced Convection
Convective Heat Transfer
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Convective Heat Transfer
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Constant
= =
=
= , = ,
, =
, =
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Internal Forced Convection
Convective Heat Transfer
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Convective Heat Transfer
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Pumping Power Requirement
o Volume flow rate: =
o Friction Factor, For fully-developed laminar flow (or at least hydrodynamically
fully-developed) in tubes - Use Table 8-1.
For turbulent flow in tubes: = 0.790 ln Re 1.64 10 < R e < 1 0
o Pressure Drop,
=
2
=
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Internal Forced Convection
Convective Heat Transfer
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Convective Heat Transfer
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Internal Forced Convection
Convective Heat Transfer
Internal Forced Convection
Laminar Flow
Developing
flow
Use Equation 1
(constant Ts)
Fully-
developed flow
Table 8-1
(constant Ts and
qs)
Turbulent Flow
Developing
flow
See Note 1
(constant Ts and
qs)
Fully-
developed flow
Use Equation 2
(constant Ts and
qs)
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Convective Heat Transfer
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For developing, laminar flow in entrance region for circulartube assuming constant Ts
Equation 1: Nu = 3.66 . D/L
+. D/L /
For fully-developed turbulent flow in smooth tubes
Equation 2: Nu = 0.023Re/Pr
= 0.4 for heating ( > )
= 0.3 for cooling < Note 1: For developing, turbulent flow in smooth tubes, use
Equation 2.
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Internal Forced Convection
Convective Heat Transfer
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Convective Heat Transfer
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Internal Forced Convection
Convective Heat Transfer
Heat Transfer Coefficient
o can be computed once theNusselt value is known,
=
Convective Heat Transfer
o Constant = o Constant = , = ,
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Sample Problems
1. Water is to be heated from 10C to 80C as it flows througha 4-cm-internal-diameter, 18-m-long tube. The tube is
equipped with an electric resistance heater, which providesuniform heating throughout the surface of the tube. Theouter surface of the heater is well-insulated, so that insteady operation all the heat generated in the heater istransferred to the water in the tube. If the system is to
provide hot water at a rate of 2.4 L/min, determine thepower rating of the resistance heater and estimate the innersurface temperature of the pipe at the exit. Also, computethe pressure drop in the tube.
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Internal Forced Convection
Convective Heat Transfer
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Convective Heat Transfer
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Sample Problems
2. An air heater for an industrial application consists of an insulated, concentrictube annulus, for which air flows through a thin-walled inner tube. Saturatedsteam flows through the outer annulus, and condensation of the steammaintains a uniform temperature Ts on the tube surface. Consider conditionsfor which atmospheric air enters a 50-mm diameter tube at a temperature of15C and a flow rate of = 0.03 kg/s, while saturated steam at 2.5 bars
condenses on the outer surface of the tube.
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Internal Forced Convection
Convective Heat Transfer
If the length of the annulus is = 5m what is theoutlet temperature and heat gain of air? What isthe mass rate at which condensate leaves theannulus? Also, determine the LMTD, pressure
drop and the power requirement of the pump toovercome this pressure drop. From thethermodynamic property table, at = 2.5 bars,the saturation temperature and the latent heat offusion are 127.43C and 2181.55 J/kg, respectively