Dr. Şaziye Balku 1

MECHANISMS OF HEAT TRANSFER

Dr. Şaziye Balku 2

• HEAT TRANSFER form of energy transfer due to temperature difference

• higher temperature lower temperature • stops when two mediums reach the same

temperature

BASIC MECHANISMS OF HEAT TRANSFER

1. CONDUCTION2. CONVECTION3. RADIATION

Dr. Şaziye Balku 3

CONDUCTION: Transfer of energy from more energetic particles of a substance to the adjacent

less energetic ones as a result of interaction between the particles

Mechanism of heat conduction

• In gases and liquids: due to collisions and diffusions of the molecules during their random motion

• In solids: combination of vibrations of the molecules in a lattice and the energy transport by free electrons.

Dr. Şaziye Balku 4

RATE OF CONDUCTION

1. Geometry of medium

2. Thickness

3. Material of the medium

4. Temperature difference

The rate of heat conduction through a plane layer is proportional to the temperature difference across the layer and the heat transfer area, but is inversely proportional to the thickness of the layer

Rate of heat conduction (area)(temperature difference)

Thickness

Dr. Şaziye Balku 5

x

TkA

x

TTkAQ cond

21

dx

dTkAQ cond

k: thermal conductivity of the material, measure of the ability of a material to conduct heat

Fourier’s Law of Heat Conduction

0x dxdT / : Temperature gradient

(Negative when temperature decreases with increasing x)

Heat is conducted in the direction of decreasing temperature. Heat transfer area A is always normal to the direction of heat transfer

Dr. Şaziye Balku 6

x

TkAQ cond

))(1(

))(3020()/(401/

m

CCmW

x

TkAQ cond

2/4010 mWq

For copper

Note that: the negative sign in Fourier’s law ensures that heat transfer in the positive x direction is a positive quantity

Dr. Şaziye Balku 7

THERMAL CONDUCTIVITY

The rate of heat transfer through a unit thickness of the material per unit area per unit temperature difference

Kinetic theory: thermal conductivity of gases is proportional to the square root of the absolute temperature and inversely proportional to the square root of the molar mass.

independent of pressure in a wide range

In liquids decreases with increasing temperature and also with increasing molar mass

In solids depends upon lattice vibrational waves and the free flow electrons

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The range of thermal conductivity of various materials at room

temperature• ability to conduct heat

• different for each material

At room temperature;

k= 0.608 W/m 0 C for water

k= 80.2 W/m 0 C for ironWhich one conducts heat better ?

The ones having low thermal conductivities are insulators

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The thermal conductivities of materials vary with temperatures

The thermal conductivities of certain solids exhibit dramatic increases at temperatures near absolute zero, when these solids become super conductors.

For example: Copper

T ( K) k (W/m. 0 C)

20 20 000

300 401

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THERMAL DIFFUSIVITY

Thermal diffusivity is a material property which represents how fast heat diffuses through a material.

The ratio of heat conducted through a material to the heat stored per unit volume

PC

k

storedheat

conductedheat

High k or low CP large thermal diffusivity

The larger the thermal diffusivity, the faster the propagation of heat into the medium. A small value of thermal diffusivity means that heat is mostly absorbed by the material and a small amount of heat will be conducted further.

Thermal diffusivity

Specific heatPC

Dr. Şaziye Balku 11

CONVECTIONHeat transfer between a solid surface and the adjacent fluid that is in motion and it involves the combined effects of conduction and fluid motion

Heat is first transferred from hot block to the adjacent layer of air by conduction and then carried away from the surface by convection

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If the fluid is forced to flow over the surface by external means such as a fan, pump or the wind, heat is transferred by forced convection whereas if the fluid is caused by buoyancy forces that are induced by density differences due to the variation of temperature in fluid it is called natural or free convection

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NEWTON’S LAW OF COOLING Rate of convection heat transfer temperature difference

)(

TThAQ SSconv

T

T

A

h

S

S

Convection heat transfer coefficient in W/m2.0 C

Surface area through which convection heat transfer takes place

Surface temperature

Temperature of the fluid sufficiently far from the surface

h is not a property of the fluid, experimentally determined, depends on

- surface geometry

- nature of fluid motion

- Properties of fluid

- Bulk fluid velocity

Note: Fluid temperature at the surface equals the surface temperature of the solid

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RADIATIONEnergy emitted by matter in the form of electromagnetic waves(or photons) as a result of the changes in the electronic configurations of the atoms or moleculesAll bodies at a temperature above absolute zero emit thermal radiation

• Does not require an intervening medium• Fastest (at the speed of light)• Possible also in vacuum

•Example: energy of sun reaching the earth•Thermal radiation: form of radiation emitted by bodies because of their temperature •different from other forms of electromagnetic radiation; X-rays, gamma rays, microwaves, and television waves that are not related with temperature

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STEFAN-BOLTZMANN LAWThe maximum rate of radiation that can be emitted from a surface at an absolute temperature is;

Stefan-Boltzman constant

=5.67×10-8 W/m2.K4

Black body: an idealized surface that emits radiation at this maximum rate

Black body radiation: radiation emitted by blackbodies

Real surfaces emit less radiation

1

10 For real bodies

For black bodies

Emissivity of the surface

4max, SSemit TAQ

4SSemit TAQ

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Radiation heat transfer between a surface and the surfaces around it

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)( 44surrSSrad TTAQ

)(

TTAhQ SScombinedtotal

Combined heat transfer coefficient includes effects of both convection and radiation in such an example and conduction heat transfer may be neglected.

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Although there are three mechanisms of heat transfer, a medium may involve only two of them simultaneously

Heat transfer through a vacuum is by radiation only

Solids: conduction and radiation

Fluids:

conduction and radiation (no motion)

convection and radiation (in motion)

conduction and convection (no radiation)

Dr. Şaziye Balku 19

HEAT TRANSFER BETWEEN TWO PLATES

radcondtotal QQQ

radtotal QQ

condtotal QQ

condtotal QQ