conduction 1 dimension 08

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One Dimensional, Steady state Conduction

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Page 1: Conduction 1 Dimension 08

One Dimensional,

Steady state Conduction

Page 2: Conduction 1 Dimension 08

The Conduction Rate Equation

x

TkAQx

T1

T2

T(x)

x

Qx

Thermal

Conductivity

Gradient Temperature

Surface Area

Page 3: Conduction 1 Dimension 08
Page 4: Conduction 1 Dimension 08
Page 5: Conduction 1 Dimension 08

Range of thermal conductivity for various states of matter at normal

temperatures and pressure

Page 6: Conduction 1 Dimension 08

Temperature dependence

of the thermal conductivity

of selected solid

Page 7: Conduction 1 Dimension 08

Temperature

dependence of the

thermal conductivity of

selected gases at

normal pressure

Page 8: Conduction 1 Dimension 08

Temperature dependence

of the thermal conductivity

of selected nonmetallic

liquids under saturated

condition

Page 9: Conduction 1 Dimension 08

Thermal Conductivity Measurement Apparatus

Page 10: Conduction 1 Dimension 08
Page 11: Conduction 1 Dimension 08
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Page 13: Conduction 1 Dimension 08

Heat Diffusion Equation

t

T

k

c

k

q

z

T

y

T

x

T p2

2

2

2

2

2

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Page 17: Conduction 1 Dimension 08

The plane wall

For one dimensional conduction in a plane wall,

temperature is a function of the x coordinate only and

heat transferred exclusively in this direction.

For one dimensional, steady state conduction in

plane wall with no heat generation , the heat flux is a

constant, independent of x.

Page 18: Conduction 1 Dimension 08

Thermal Resistance

kA

L

Q

TTR

x

ss

condt

2,1,

,

Thermal resistance for conduction

hAQ

TTR s

convt

1,

Thermal resistance for convection

Page 19: Conduction 1 Dimension 08
Page 20: Conduction 1 Dimension 08

The Composite Wall

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Example

A leading manufacturer of household appliances is proposing a self

cleaning oven design that involves use of a composite window

separating the oven cavity from the room air. The composite is to

consist of two high temperature plastics (A and B) of thicknesses

LA = 2LB and thermal conductivities kA = 0.15 W/M and kB = 0.08

W/m.K, During the self cleaning process, the oven wall and air

temperatures Tw and Ta are 400 °C while the room air temperature

T is 25 °C. The inside convection and radiation heat transfer

coefficient hi and hr as well as the outside convection coefficient

ho are each approximately 25 W/m2 K. What is the minimum

window thickness, L = LA +LB, needed to ensure a temperature is

50 °C or less at the outer surface of the window?

This temperature must not be exceeded for safety reasons,

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Find the heat transfer per unit area through the

composite wall sketched. Assume one dimensional heat

flow

Page 27: Conduction 1 Dimension 08

The cylinder

Lk

rrR condt

2

)ln( 12,

Thermal resistance for conduction (cylinder)

rLhR convt

2

1,

Thermal resistance for convection (cylinder)

Page 28: Conduction 1 Dimension 08

The cylinder

Page 29: Conduction 1 Dimension 08