introduction to heat transfer.pdf

7/28/2019 Introduction to Heat Transfer.pdf

1/15

ChapterChapter 11

Dr.Dr. WaelWael M.ElM.El--MaghlanyMaghlany


2/15

Heat TransferHeat Transfer Heat transfer is the study of mechanisms by bodiesHeat transfer is the study of mechanisms by bodies

exchange energy. The goal of this study is the predictionexchange energy. The goal of this study is the prediction

of rates and efficiencies of the process.of rates and efficiencies of the process.

Note: Heat transfer is distinct from thermo since itNote: Heat transfer is distinct from thermo since it

concentrates on the nonconcentrates on the non--equilibrium state, while thermoequilibrium state, while thermo

concentrates on systems in equilibrium.concentrates on systems in equilibrium.

ExampleExample: Consider tossing a freshly forged steal ball into: Consider tossing a freshly forged steal ball into

a tank of water.a tank of water.

Thermo would help us determine what the final state of the steelThermo would help us determine what the final state of the steelball/water system would be.ball/water system would be.

Heat Transfer will tell us how it got there and how fast.Heat Transfer will tell us how it got there and how fast.


3/15

Realize that: HeatRealize that: HeatEnergy. However, the word heat isEnergy. However, the word heat is

reserved for discussing processes or potentials for energyreserved for discussing processes or potentials for energy

exchange.exchange.

There areThere are 33 modes of heat transfer:modes of heat transfer:

ConductionConduction: ener exchan e throu h a solid bod or across: ener exchan e throu h a solid bod or across

bodies at the point of contact.bodies at the point of contact.

RadiationRadiation: energy exchange through electromagnetic radiation: energy exchange through electromagnetic radiation

and absorption.and absorption.

ConvectionConvection: energy conveyance by the bulk motion of a fluid: energy conveyance by the bulk motion of a fluid

accompanied by conduction between the fluid and the bodies itaccompanied by conduction between the fluid and the bodies it

comes in contact with.comes in contact with.


4/15

11.Conduction.Conduction The basic concept in heat conduction isThe basic concept in heat conduction is Fouriers LawFouriers Law::

When two differing temperatures occur on opposing sides of aWhen two differing temperatures occur on opposing sides of a

material, the rate of heat transfer through the material ismaterial, the rate of heat transfer through the material isdirectly proportional to the surface area and temperaturedirectly proportional to the surface area and temperature

difference but inversely proportional to the thickness.difference but inversely proportional to the thickness.

Mathematicall :Mathematicall :

x

TAq

(m)thicknessx

K)orC(TTdifferenceetemperaturT

)(mareaA

W)or(J/secfluxheatorratetransferheatq

oo

2

2

=

1

T2

T1

A

x

q


5/15

The constant of proportionality is called theThe constant of proportionality is called the thermalthermal

conductivityconductivity, k (W/m K), so that:, k (W/m K), so that:

dx

dTkA

x

TkAq =

=

T1

T2

qT

Where the negative sign is necessary if q is positive when flowingWhere the negative sign is necessary if q is positive when flowing

in the positive x direction, butin the positive x direction, but dTdT//dxdx


6/15

Thermal ConductivityThermal Conductivity Thermal conductivity depends strongly upon theThermal conductivity depends strongly upon the

material and usually also varies temperature.material and usually also varies temperature.

For fluids (gasses and liquids) conduction occurs throughFor fluids (gasses and liquids) conduction occurs through

the random motion of the fluid particles.the random motion of the fluid particles.

two gasses at different temperatures.two gasses at different temperatures.

Hot GasTH

Cold GasTC

boundary


7/15

Particles crossing the boundary carry with them energyParticles crossing the boundary carry with them energy

in proportion to the gas temperature.in proportion to the gas temperature.

As a result of this random motion, energy is transfer fromAs a result of this random motion, energy is transfer fromside of the partition to the otherside of the partition to the other -- this is conduction.this is conduction.

It also ollows that as tem erature increases, there isIt also ollows that as tem erature increases, there is

more random motion, and thus the conduction ratemore random motion, and thus the conduction rateincreases.increases.

This is particularly true for gasses.This is particularly true for gasses.

For liquids,For liquids, the situation is complicated by thethe situation is complicated by theintermolecular forces, and this rule is not generally true.intermolecular forces, and this rule is not generally true.


8/15

For solids, there are two mechanisms of heat transfer:For solids, there are two mechanisms of heat transfer:

the migration of free electrons and crystal latticethe migration of free electrons and crystal lattice

vibration.vibration. The migration of free elections is similar to theThe migration of free elections is similar to the

conduction by random particle motion in gasses.conduction by random particle motion in gasses.

Since the number of free elections is proportional to theSince the number of free elections is proportional to theelectrical conductance of the material, better electricalelectrical conductance of the material, better electrical

conductors are better heat conductors.conductors are better heat conductors.

Lattice vibration is associate with vibrations of the atomsLattice vibration is associate with vibrations of the atomsand molecules bound in the structure of solids.and molecules bound in the structure of solids. BasicalyBasicaly,,

shake one side of a crystal and the other side moves inshake one side of a crystal and the other side moves in

response.response.


9/15

For lattice vibration, the thermal conductively is usuallyFor lattice vibration, the thermal conductively is usually

associated with the packing density of the crystal.associated with the packing density of the crystal.

MaterialMaterial k (W/m/k (W/m/ooK)K)

DiamondDiamond 10001000++

Typical values atTypical values at

300300ooK:K:

Copper (pure)Copper (pure) 385385

AluminumAluminum 237237

IronIron 8080

WaterWater 00..613613

OilOil 00..145145

AirAir 00..026026

Note that differentNote that differentreferences givereferences give

different valuesdifferent values -- thethe

experimentalexperimental

measurement of k ismeasurement of k is

very difficult!very difficult!


10/15

22..ConvectionConvection Consider cool air adjacent to a warm horizontal wall.Consider cool air adjacent to a warm horizontal wall.

Surface temperature =Ts

Air temperature = T

q

If the air remains at rest (like trapped between layers of clothes), theIf the air remains at rest (like trapped between layers of clothes), theproblem is simply one of conduction and the air is an effectiveproblem is simply one of conduction and the air is an effective

insulator.insulator.

If the air is in motion, however, the heat transfer rate increasesIf the air is in motion, however, the heat transfer rate increases

dramatically. Think wind chill factor!dramatically. Think wind chill factor!

The difference between the two cases has to do with the ability ofThe difference between the two cases has to do with the ability of

fluid to carry energy through motion.fluid to carry energy through motion.


11/15

In this situation, there are really two mechanisms atIn this situation, there are really two mechanisms at

play:play:

Near the wall surface (were velocity is low due to fluid viscosity),Near the wall surface (were velocity is low due to fluid viscosity),conduction heat transfer dominates.conduction heat transfer dominates.

Away from the wall, the bulk motion of the fluid carrying heatAway from the wall, the bulk motion of the fluid carrying heat

..

Thus, convective heat transfer is really a combined effectThus, convective heat transfer is really a combined effect

and, as a result, is rather difficult to analyze in detail.and, as a result, is rather difficult to analyze in detail.

However, experimentation has indicated that there is aHowever, experimentation has indicated that there is abasic relation governing this type of heat transfer.basic relation governing this type of heat transfer.


12/15

The basic concept which describes this convective heatThe basic concept which describes this convective heat

transfer istransfer is Newtons Law of CoolingNewtons Law of Cooling::

)(

= TThAqs

w

all!

t

he

f

rom

a

way

f

lux

h

eat

f

or

i

tive

po

s

Wo(J

rthq

Our study of convection will be ways to calculate values of h underOur study of convection will be ways to calculate values of h under

different flow conditions.different flow conditions.

K

)

/(W/m

econducta

film

ortc

o

effi

cie

tr

ansf

er

he

at

co

nvec

tiv

h)(ma

rea

A

o2

2


13/15

We should also differential between when the fluidWe should also differential between when the fluid

motion is forced, free or mixed:motion is forced, free or mixed:

Forced convectionForced convection is when an external source (like a fan) isis when an external source (like a fan) isresponsible for the fluid motion across the surface.responsible for the fluid motion across the surface.

Free (natural) convectionFree (natural) convection occurs when buoyancy effectsoccurs when buoyancy effects

fluid motion.fluid motion.

Mixed convectionMixed convection occurs when both forced and naturaloccurs when both forced and natural

convection are simultaneously present.convection are simultaneously present.

Finally, when phase changes occur (boiling orFinally, when phase changes occur (boiling orcondensation), the heat transfer is enhanced due to thecondensation), the heat transfer is enhanced due to the

high latent heats of these processes.high latent heats of these processes.


14/15

Typical value of h are:Typical value of h are:

ProcessProcess h (W/mh (W/m22//ooK)K)

Free ConvectionFree Convection

GasesGases 22--2525

Li uidsLi uids 5050--10001000

Forced ConvectionForced Convection

GasesGases 2525--250250

LiquidsLiquids 500500--2020,,000000

Phase ChangesPhase Changes

Boiling or condensationBoiling or condensation 25002500--100100,,000000


15/15

33..RadiationRadiation All bodies at a temperature above absolute zero emitAll bodies at a temperature above absolute zero emit

thermal energy as electromagnetic radiation.thermal energy as electromagnetic radiation.

The theoretical radiation from an idealized surface (aThe theoretical radiation from an idealized surface (a

black body) is give by the Stefanblack body) is give by the Stefan--Boltzmann Law:Boltzmann Law:

-

For real bodies, the total emitted radiation is less thanFor real bodies, the total emitted radiation is less than

the black body amount called the emissivity,the black body amount called the emissivity, , such that:, such that:

4

semis ATEq ==

4o28- K/W/m5.669x10 sbemis ATEq ==

1)0(emissivity

introduction to heat transfer.pdf

Documents