Chapter 2
Heat Conduction Equation
292
Heat is generated in a large plane wall whose one side is insulated while the other side is maintained
at a specified temperature. The mathematical formulation, the variation of temperature in the wall, and the
temperature of the insulated surface are to be determined for steady onedimensional heat transfer.
Assumptions
1
Heat transfer is steady since there is no indication of any change with time.
2
Heat transfer
is onedimensional since the wall is large relative to its thickness, and there is thermal symmetry about the
center plane.
3
Thermal conductivity is constant.
4
Heat generation varies with location in the
x
direction.
Properties
The thermal conductivity is given to be
k
= 30 W/m
⋅
°C.
Analysis
(
a
) Noting that heat transfer is steady and onedimensional
in
x
direction, the mathematical formulation of this problem can be
expressed as
T
2
=30°C
x
k
g
Insulated
L
dT
dx
gx
k
2
2
0
+=
&
()
where
and
= 8
×
10
&&
./
gg
e
xL
=
−
0
05
&
g
0
6
W/m
3
and
dT
dx
0
0
=
(insulated surface at
x
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '10
 Dr.DanielArenas
 Thermodynamics, Mass, Heat, Heat Transfer, 0 k, 0 l, 0.5 L

Click to edit the document details