1.
A furnace of cubical shape with external dimensions of 0.35 m is constructed from a
refractory brick having thermal conductivity k=1.15 W/m•K.
If the wall thickness is
50 mm, the inner surface temperature is 600°C, and the outer surface temperature is
75°C, calculate the heat loss from the furnace.
0.35 m
0.05 m
L
Plane wall
25
.
1
05
.
0
)
25
.
0
)(
25
.
0
(
L
A
S
W
=
=
=
m
Edge
135
.
0
)
25
.
0
)(
54
.
0
(
L
54
.
0
S
E
=
=
=
m
Corner
0075
.
0
)
05
.
0
)(
15
.
0
(
t
15
.
0
S
C
=
=
=
m
)
T
T
)(
S
8
S
12
S
6
(
k
)
T
T
(
kS
q
2
1
C
E
W
2
1

+
+
=

=
=
)
75
600
)(
0075
.
0
8
135
.
0
12
)
25
.
1
6
)(
15
.
1
(

×
+
×
+
×
=5.5 kW
2.
A solid having volume V, surface area A
s
, and thermal conductivity k is exposed to a
fluid with convective heat transfer coefficient h and ambient temperature T
∞
.
For
Biot number Bi<<1,
(a) The solid’s spatial temperature distribution is uniform (isothermal) at each
instant in time.
Why???
(b) For an initial solid temperature T
i
, derive the temperature in the solid as a
function of time and the total heat transfer rate.
(a) The temperature gradient in the solid is small compared to the fluid. Relative to
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 Fall '08
 Kuznetsov
 Heat, Heat Transfer, convective heat transfer, geometric center temperature

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