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Heat Transfer ME 3345

Introduction

Chapter 1

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Conduction

HEAT FLUX q

Where k is THERMAL CONDUCTIVITY (W/mK)

Two cases will be considered:

(1) Transient response, initial temperature T1 > T2, then heat conduction occursto spread the vibration (Thermal Energy) uniformly throughout solid so a new

temperature is reached at some time:

(2) Steady-state where T1 and T2 are a constant in time.

Gradient is therefore: and heat flux is:

Units of heat flux are W/m2 Units of heat conduction W/mK

For a rod of area A, the heat conducted is qA, units Watts = Joules/second

2

21 TT+

dx

dTkqx =

"

L

TT

dx

dT 12 =

L

TTkqx

12" =

1T

2T

L

time

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Convection

Forced Convection imposed flow of fluid

Natural Convection due to boyancy forces

Flat Plate:

BOUNDARY LAYER region over which temperature and the velocity change.

Convection Heat Transfer occurs through both random molecular motion & bulk

fluid motion within the boundary layer.

qCONV = hA(TS Tinfinity)

where h is the HEAT TRANSFER COEFFICIENT

NUSSELT # Nu = hL/k a dimensionless parameter

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Radiation - 1

Radiation is emitted by any material at a finite temperature,T, this includessolids, liquids, and gases.

Temperature T is above absolute zero -273oC or 0oKelvin

A Black Body is a perfect source of radiant emission.

Emissive Power PLANCKS LAW

is STEFAN-BOLTZMANN CONSTANT = 5.67x10-8 W/m2/K4

A real surface emits less energy by the amount

where is the EMISSIVITY of the real surface

4TEb =

4

TE=

10

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G IRRADIATION of a surface is sum of radiant energy

arriving at a surface from all sources.ABSORPTIVITY is fraction of irradiation that is adsorbed

GADS = G and E = T4

Conservation of energy yields:

qnett = GADS E

A GRAY surface has a emissivity that is independent ofdirection and wavelength.

Hence and GADS =

T

4

10

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Radiation Exchange - 1

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Nett qRAD = q/A = heat loss heat gain

qRAD = T4S G and because =

Then: qRAD =

(T4

s T4

sur)

If we include convection to gas then:

q = qCONV + qRAD= hA(Ts Tinfinity) + A(T

4s T

4sur)

Radiation Exchange - 2

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Modes of Heat Transfer

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Conservation of Energy 1st Law

Consider a control volume

The rate at which thermal and mechanical energy enters acontrol volume, plus the rate at which thermal energy isgenerated within the control volume, minus the rate at which

thermal energy and mechanical energy leave the controlvolume must equal the rate of increase of energy stored withinthe control volume.

i.e. If inflow of energy greater than outflow, difference must be

stored internally.

V

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Conservation of Energy over time t

The amount of thermal and mechanical energy that enters a control volume,

plus the amount of thermal energy that is generated within a control volume,

minus the amount of thermal and mechanical energy that leaves the control

volume must equal the increase in the amount of energy stored in the

control volume.

dtdEEEE stoutgin =+ &&&

is the volumetric energy generation rate

is the volumetric energy stored

Conservation of Energy:

gE&

stE&

t

dt

dEEEE stoutgin =+

V

gE&

stE&in

E& outE&

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Control Volume

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Surface Control Volume