cfda_7_heatxfer.ppt

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Fluent Inc. 7/24/2013G1

Fluids ReviewTRN-1998-004

Heat Transfer


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Outline

Introduction

Modes of heat transfer

Typical design problems

Coupling of fluid flow and heat transfer Conduction

Convection

Radiation


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Introduction

Heat transfer is the study of thermal energy (heat) flows

Heat always flows from hot to cold

Examples are ubiquitous:

heat flows in the body home heating/cooling systems

refrigerators, ovens, other appliances

automobiles, power plants, the sun, etc.


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Typical Design Problems

To determine:

overall heat transfer coefficient - e.g., for a car radiator

highest (or lowest) temperature in a system - e.g., in a gas turbine

temperature distribution (related to thermal stress) - e.g., in the walls of a

spacecraft

temperature response in time dependent heating/cooling problems - e.g.,

how long does it take to cool down a case of soda?


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Heat Transfer and Fluid Flow

As a fluid moves, it carries heat with it -- this is called convection

Thus, heat transfer can be tightly coupled to the fluid flow solution

Additionally:

The rate of heat transfer is a strong function of fluid velocity Fluid properties may be strong functions of temperature (e.g., air)


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Conduction Heat Transfer

Conduction is the transfer of heat by molecular interaction

In a gas, molecular velocity depends on temperature

hot, energetic molecules collide with neighbors, increasing their speed

In solids, the molecules and the lattice structure vibrate


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Boundary Conditions

Heat transfer boundary conditions generally come in three types:

T = 300K

specified temperature

Dirichlet condition

q = 20 W/m2

specified heat flux

Neumann condition

q = h(Tamb-Tbody)

external heat transfer

coefficient

Robin condition

Tbody


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Conduction Example

Compute the heat transfer through the wall of a home:

shingles

k=0.15 W/m2-K

sheathing

k=0.15 W/m2

-K

fiberglas insulation

k=0.004 W/m2-K

2x6 stud

k=0.15 W/m2-K

sheetrock

k=0.4 W/m2-K

Tout = 20F Tout = 68

F

Although slight, you

can see the thermal

bridging effect

through the studs


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Heat Transfer Coefficient

h is not a constant, but h = h(T)

Three types of convection:

Natural convection

fluid moves due to buoyancy

Forced convection

flow is induced by external means

Boiling convection

body is hot enough to boil liquid

3

1

4

1

, ThTh

consth

2Th

Typical values ofh:

4 - 4,000 W/m2-K

80 - 75,000

300 - 900,000

Thot Tcold

Thot

Tcold

Tcold

Thot


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Looking in more detail...

Just as there is a viscous boundary layer in the velocity distribution,

there is also a thermal boundary layer

t

wT

UT ,

y

)(yT

velocity boundarylayer edge

thermal boundary

layer edge


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Nusselt Number

Equate the heat conducted from the wall to the same heat transfer in

convective terms:

Define dimensionless quantities:

Then rearrange to get:

)(

TTh

y

Tk wf

L

yy

TT

TTT

w

w

Nu

f

w

w

k

hL

L

y

TT

TTNusselt number

dimensionless heat

transfer coefficient

conductivity

of the fluid


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Energy Equation

Generalize the heat conduction equation to include effect of fluid

motion:

Assumes incompressible fluid, no shear heating, constant properties,

negligible changes in kinetic and potential energy

Can now solve for temperature distribution in boundary layer

Then calculate husing Fouriers law:

qTkTt

Tc

2u

0

ywwy

T

TT

k

TT

qh

From calculatedtemperature

distribution


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Correlations for Heat Transfer Coefficient

As an alternative, can use correlations to obtain h

E.g., heat transfer from a flat plate in laminar flow:

where the Prandtl number is defined as:

Typical values are:

Pr = 0.01 for liquid metals

Pr = 0.7 for most gases

Pr = 6 for water at room temperature

333.05.0PrRe332.0Nu

xx

k

cPr

ydiffusivitthermal

ydiffusivitmomentum


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Convection Examples

Developing flow in a pipe (constant wall temperature)

T wT T wT T wT

T

wT

x

bulk fluid temperature

heat flux from wall

T

wT


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Convection Examples

Natural convection (from a heated vertical plate)

u

T

Tw

gravity

As the fluid is warmed by the plate,

its density decreases and a buoyant

force arises which induces flow inthe vertical direction. The force is

equal to:

,T

)(T

g)(

The dimensionless group thatgoverns natural convection is the

Rayleigh number:

3Ra

TLg


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Radiation Heat Transfer

Thermal radiation is emission of energy as electromagnetic waves

Intensity depends on body temperature and surface characteristics

Important mode of heat transfer at high temperatures

Can also be important in natural convection problems Examples:

toaster, grill, broiler

fireplace

sunshine


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Black Body Radiation

A black body:

is a model of a perfect radiator

absorbs all energy that reaches it; reflects nothing

therefore = 1, = = 0

The energy emitted by a black body is the theoretical maximum:

This is Stefan-Boltzmann law; s is the Stefan-Boltzmann constant(5.6697e-8 W/m2-K4)

4Tq s


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Real Bodies

Real bodies will emit less radiation than a black body:

Example: radiation from a small body to its surroundings

both the body and its surroundings emit thermal radiation

the net heat transfer will be from the hotter to the colder

4Tq s

emissivity (between 0 and 1)

)( 44 TTAQ wnet s

T

q

wTA

wqnetQ


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When is radiation important?

Radiation exchange is significant in high temperature problems: e.g.,

combustion

Radiation properties can be strong functions of chemical composition,

especially CO2, H2O

Radiation heat exchange is difficult solve (except for simple

configurations)we must rely on computational methods


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Heat TransferSummary

Heat transfer is the study of thermal energy (heat) flows:

conduction

convection

radiation

The fluid flow and heat transfer problems can be tightly coupled

through the convection term in the energy equation

when properties (, ) are dependent on temperature

While analytical solutions exist for some simple problems, we must

rely on computational methods to solve most industrially relevant

applicationsCan I go back to

sleep now?

cfda_7_heatxfer.ppt

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