ezrabridger49
22.04.2020 •
Engineering
The ice on the rear window of an automobile is defrosted by attaching a thin, transparent, film type heating element to its inner surface. By electrically heating this element, a uniform heat flux may be established at the inner surface. The inside air temperature and convection heat transfer coefficient are T,i = 25°C and hi = 25 W/(m2 -K), while the outside air temperature is T,o = -10°C. For 4-mm thick window glass, determine (a) the electric power required per unit window area to maintain an inner surface temperature of 15°C and (b) the thermal conductivity of the windshield.
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Ответ:
A)Q = 1208.33 W/m²
B)K = 0.138 W/m.K
Explanation:
We are given;
inside air temperature;T_∞,i =25 °C = 25 + 273 = 298K
outside air temperature;T_∞,o = -10°C = - 10 + 273 = 263K
Inner surface temperature;T_s,i = 15 °C = 15 + 273 = 288K
Thickness, L = 4mm = 0.004m
convection heat transfer coefficient ; hi = 25 W/(m².K)
A) From an energy balance at the inner surface and the thermal circuit, the electric power required per unit window area is given as;
Q = [(T_s,i - T_∞,o)/((L/k) + (1/hi))] - [(T_∞,o - T_s,i)/(1/hi)]
Plugging in the relevant values with k for glass as 1.4 W/m.k, we have;
Q = [(288 - 263)/((0.004/1.4) + (1/25))] - [(263 - 288)/(1/25)]
Q = 583.33 + 625
Q = 1208.33 W/m²
B) The formula for thermal conductivity is;
K = (QL)/(AΔT)
Where;
K is the thermal conductivity in W/m.K
Q is the amount of heat transferred through the material
L is the distance between the two isothermal planes
A is the area of the surface in square meters
ΔT is the difference in temperature in Kelvin
ΔT = 298K - 263K = 35K
Now, since we have value of heat per unit area to be Q = 1208.33 W/m², let's rearrange the equation to reflect that; Thus ;
k = (Q/A) x (L/ΔT)
K = 1208.33 x (0.004/35)
K = 0.138 W/m.K
Ответ:
window
Explanation: