One Dimensional,

Steady state Conduction

The Conduction Rate Equation

x

TkAQx

T1

T2

T(x)

x

Qx

Thermal

Conductivity

Gradient Temperature

Surface Area

Range of thermal conductivity for various states of matter at normal

temperatures and pressure

Temperature dependence

of the thermal conductivity

of selected solid

Temperature

dependence of the

thermal conductivity of

selected gases at

normal pressure

Temperature dependence

of the thermal conductivity

of selected nonmetallic

liquids under saturated

condition

Thermal Conductivity Measurement Apparatus

Heat Diffusion Equation

t

T

k

c

k

q

z

T

y

T

x

T p2

2

2

2

2

2

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.

Thermal Resistance

kA

L

Q

TTR

x

ss

condt

2,1,

,

Thermal resistance for conduction

hAQ

TTR s

convt

1,

Thermal resistance for convection

The Composite Wall

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,

Find the heat transfer per unit area through the

composite wall sketched. Assume one dimensional heat

flow

The cylinder

Lk

rrR condt

2

)ln( 12,

Thermal resistance for conduction (cylinder)

rLhR convt

2

1,

Thermal resistance for convection (cylinder)

The cylinder