298
Finite Element Analysis and Design
12. Consider a wall built up of concrete and thermal insulation.
The outdoor temperature
is
T
o
=
17
C and the temperature inside is
T
i
= 20
C.
The wall is subdivided into
three elements.
The thermal conductivity for concrete is
k
c
= 1.7 W/m/
o
C, and that of
the insulator is
k
i
= 0.04 W/m/
o
C.
Convection heat transfer occurs at both surfaces
with convection coefficients of
h
0
= 14 W/m
2
/
o
C and
h
i
= 5.5 W/m
2
/
o
C.
Calculate the
temperature distribution in the wall.
Also, calculate the amount of heat flow through
the outdoor surface.
Solution:
Assuming that the wall is wide enough, we model the problem unit area of the wall, i.e.,
A=
1 m
2
.
The element matrix equations become
Element 1:
(1)
11
2
2
24.286
24.286
24.286
24.286
Tq
T
q
Element 2:
(2)
22
(2)
3
3
0.4
0.4
0.4
0.4
T
q
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 Fall '08
 Staff
 Heat, Finite Element Analysis, Heat Transfer, Insulation, TI, convection heat transfer, element matrix equations

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