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Chapter 5
Numerical Methods in Heat Conduction
586
The passive solar heating of a house through a Trombe wall is studied. The temperature distribution in
the wall in 12 h intervals and the amount of heat transfer during the first and second days are to be
determined.
Assumptions
1
Heat transfer is onedimensional since the exposed surface of the wall large relative to its
thickness.
2
Thermal conductivity is constant.
3
The heat transfer coefficients are constant.
Properties
The wall properties are given to be
k
= 0.70 W/m
⋅
°C,
, and
/s
m
10
44
.
0
2
6
−
×
=
α
κ
=
0.76. The
hourly variation of monthly average ambient temperature and solar heat flux incident on a vertical surface
is given to be
Time of day
Ambient
Temperature,
°
C
Solar insolation
W/m
2
7am10am
10am1pm
1pm4pm
4pm7pm
7pm10pm
10pm1am
1am4am
4am7am
0
4
6
1
2
3
4
4
375
750
580
95
0
0
0
0
Trombe
wall
Glazing
Sun’s
rays
Heat
loss
Heat
gain
h
in
T
in
h
out
T
out
Δ
x
•
•
•
•
•
•
0
1
2
3
4
5
h
in
T
in
h
out
T
out
Analysis
The nodal spacing is given to be
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Mass, Heat

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