3.3
KNOWN: PROBLEM Desired inner surface temperature of rear window with prescribed inside and outside air conditions. FIND: (a) Heater power per unit area required to maintain the desired temperature, and (b) Compute and plot the electrical power requirement as a function of T,o for the range -30 T,o 0C with ho of 2, 20, 65 and 100 W/m2K. Comment on heater operation needs for low ho. If h ~ Vn, where V is the vehicle speed and n is a positive exponent, how does the vehicle speed affect the need for heater operation? SCHEMATIC:
ASSUMPTIONS: (1) Steady-state conditions, (2) One-dimensional heat transfer, (3) Uniform heater flux, q , (4) Constant properties, (5) Negligible radiation effects, (6) Negligible film resistance. h PROPERTIES: Table A-3, Glass (300 K): k = 1.4 W/mK. ANALYSIS: (a) From an energy balance at the inner surface and the thermal circuit, it follows that for a unit surface area,
T ,i Ts,i 1 hi
q = h
Ts,i T ,o + q = h L k + 1 ho
T,i Ts,i 1 hi
2
o
Ts,i T ,o L k + 1 ho
15 C 10 C = 0.004 m 1.4 W m K
2
(
o
)
2
+
1 65 W m K
25 C 15 C 1 10 W m K
2
o
o
q = (1370 100 ) W m = 1270 W m h
<
(b) The heater electrical requirement power as a function of the exterior air temperature for different exterior convection coefficients is shown in the plot. When ho = 2 W/m2K, the heater is unecessary, since the glass is maintained at 15C by the interior air. If h ~ Vn, we conclude that, with higher vehicle speeds, the exterior convection will increase, requiring increased heat power to maintain the 15C condition.
3500 3000 Heater power (W/m^2) 2500 2000 1500 1000 500 0 -30 -20 -10 0
Exterior air temperature, Tinfo (C) h = 20 W/m^2.K h = 65 W/m^2.K h = 100 W/m^2.K
COMMENTS: With q = 0, the inner surface temperature with T,o = -10C would be given by h
T,i Ts,i T,i T ,o = 1 hi 0.10 = = 0.846, 1 h i + L k + 1 h o 0.118
or
Ts,i = 25 C 0.846 35 C = 4.6 C .
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o
o
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