PROBLEM 4.80
KNOWN:
Plane composite wall with exposed surfaces maintained at fixed temperatures.
Material A
as temperaturedependent thermal conductivity.
h
FIND:
Heat flux through the wall (a) assuming a uniform thermal conductivity in material A
evaluated at the average temperature of the section, and considering the temperaturedependent
thermal conductivity of material A using (b) a finitedifference method of solution in IHT with a space
ncrement of 1 mm and (c) the finiteelement method of FEHT.
i
SCHEMATIC:
ASSUMPTIONS:
(1) Steadystate, onedimensional conduction, (2) No thermal contact resistance
etween the materials, and (3) No internal generation.
b
A
NALYSIS:
(a) From the thermal circuit in the above schematic, the heat flux is
12
A
B2
x
AB
B
TT
T
T
q
RR
R
−−
′′
==
+
(
1
,
2
)
a
nd the thermal resistances of the two sections are
(
3
,
4
)
AA
A
BB
RL
/
k
/
k
=
B
=
T
he thermal conductivity of material A is evaluated at the average temperature of the section
()
{ }
Ao
1
A
B
o
kk
1
T
T/
2
T
α
⎡
=+
+
−
⎣
⎤
⎦
(
5
)
S
ubstituting numerical values and solving the system of equations simultaneously in IHT, find
<
2
AB
x
T
563.2 K
q
52.64 kW / m
(b) The nodal arrangement for the finitedifference method of solution is shown in the schematic
below.
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 Spring '10
 LEE,J.S.
 Thermodynamics, Heat, Heat Transfer, Thermal conductivity, IHT, temperaturedependent thermal conductivity

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