The t = 4 -mm-thick glass windows of an automobile have a surface area of A = 2.6 m 2 . The outside temperature is T ∞ , o = 32 ° C while the passenger compartment is maintained at T ∞ , i = 22 ° C . The convection heat transfer coefficient on the exterior window surface is h o = 90 W/m 2 ⋅ K . Determine the heat gain through the windows when the interior convection heat transfer coefficient is h i = 15 W/m 2 ⋅ K . By controlling the air-flow in the passenger compartment the interior heat transfer coefficient can be reduced to h i = 5 W/m 2 ⋅ K without sacrificing passenger comfort. Determine the heat gain through the window for the reduced inside heat transfer coefficient.
The t = 4 -mm-thick glass windows of an automobile have a surface area of A = 2.6 m 2 . The outside temperature is T ∞ , o = 32 ° C while the passenger compartment is maintained at T ∞ , i = 22 ° C . The convection heat transfer coefficient on the exterior window surface is h o = 90 W/m 2 ⋅ K . Determine the heat gain through the windows when the interior convection heat transfer coefficient is h i = 15 W/m 2 ⋅ K . By controlling the air-flow in the passenger compartment the interior heat transfer coefficient can be reduced to h i = 5 W/m 2 ⋅ K without sacrificing passenger comfort. Determine the heat gain through the window for the reduced inside heat transfer coefficient.
Solution Summary: The author calculates the heat gain through a window at different interior heat transfer coefficients. The temperature inside the compartment is T_infty,i=22°
The
t
=
4
-mm-thick
glass windows of an automobile have a surface area of
A
=
2.6
m
2
.
The outside temperature is
T
∞
,
o
=
32
°
C
while the passenger compartment is maintained at
T
∞
,
i
=
22
°
C
.
The convection heat transfer coefficient on the exterior window surface is
h
o
=
90
W/m
2
⋅
K
.
Determine the heat gain through the windows when the interior convection heat transfer coefficient is
h
i
=
15
W/m
2
⋅
K
.
By controlling the air-flow in the passenger compartment the interior heat transfer coefficient can be reduced to
h
i
=
5
W/m
2
⋅
K
without sacrificing passenger comfort. Determine the heat gain through the window for the reduced inside heat transfer coefficient.
A cylindrical electrical heating element is used to heat up a baking oven. The heating element bears a voltage of 120 V/m, and has an electrical resistance of 1000 Ω/m. A ceramic pipe of inside radius rin = 2 mm, and outside radius rout = 5 mm encases the heating element. Thermal conductivity of the ceramic is k = 0.2 W/m-K. Given that the oven air temperature is T∞ = 180oC and convection coefficient h = 10 W/m2-K, find the temperature on the inside of the ceramic pipe.
Q1: Consider a large plane wall of thickness L = 0.4 m, thermal conductivity k=2.3 W/m °C,
and surface area A= 20 m2. The left side of the wall at x= 0 is subjected of T1 = 80°C. while
the right side losses heated by convection to the surrounding air at T-15 °C with a heat
transfer coefficient of h=24 W/m2 C. Assuming constant thermal conductivity and no heat
generation in the wall, (a) express the differential equation and the boundary conditions for
steady one-dimensional heat conduction through the wall, (b) obtain a relation for the
variation of temperature in the wall by solving the differential equation, and (c) evaluate the
rate of heat transfer through the wall
Ans : (c) 6030 W
Q1
The inner and outer surfaces a spherical shell with radii of 1
cm and 2 cm are 300°C and 100°C, respectively. If the
thermal conductivity of the shell is 2 W/m-K, determine the
heat transfer through the shell.
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