A 0.8m high and 1.5m wide double pane window consisting of two 3mm thick layers of glass(k=0.78W/mK) is separated by a 10mm wide stagnant air space(k=0.026 W/mK). The convection heat transfer coefficients on the inner and outer surfaces of the window are 10W/m^2K and 35W/m^2K respectively. For a day when the room is maintained at 25oC while the temperature outdoors is 10oC, determine:
i) the steady rate of heat transfer through this double pane window, and
ii) the temperature of its inner surface.
Why is the area not included in the upper part of the solution?
But does the total thermal resistance involves Area then?
And for U-value, it's equal to 1/(Total thermal resistance*Area)?
- 天同Lv 76 年前最愛解答
Thermal resistance of glass = 0.003 x 2/0.78 m^2.K/W = 0.007692
Thermal resistance of stagnant air = 0.01/0.026 m^2.K/W = 0.3846 m^2.K/W
Hence, total resistance = (0.007692 + 0.3846) m^2.K/W = 0.3923 m^2.K/W
U-value = 1/0.3923 W/m^2.K = 2.549 W/m^2.K
Let Q be the rate of flow of heat per unit area through the window.
Hence, Q = 10.(25 - Ti) = 2.549.(Ti - To) = 35.(To - 10)
where Ti and To are the temperature at the inner and outside surfaces of the window respectively.
Solve the equations for Ti gives Ti = 22.1 C
The rate of heat transfer through the window
= 10 x (25 - 22.1) x (0.8 x 1.5) W
= 34.8 W
2015-04-30 23:11:01 補充：
Q: Why is the area not included in the upper part of the solution?
A: Yes, you could include it in. But the area appears in all the three heat flow expressions, it will be cancelled away. Hence, working with heat flow per unit area is equally well.
2015-05-04 16:08:25 補充：
Q:But does the total thermal resistance involves Area then?And for U-value, it's equal to 1/(Total thermal resistance*Area)?
A: Both thermal resistance and U-vaule are defined using unit area.
2015-05-04 16:08:49 補充：
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