A double-pane window has a vertical height of 0.9-m and a width of 1.4-m that consists of two layers of gla...

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A double-pane window has a vertical height of 0.9-m and a width of 1.4-m that consists of two layers of glass separated by a 10-cm air gap at atmospheric pressure. The room temperature is 26°C while the inner glass temperature is 18°C. Radiation heat transfer is neglected. Steady operating conditions exist.

**Properties** For natural convection between the inner surface of the window and the room air, the properties of air at 1 atm and the film temperature of $(T_x + T_{∞})/2 = (18 + 26)/2 = 22°C$ are: $Pr = 0.7304; k = 0.02529 \, W/m.K; 
u = 1.534 	imes 10^{-5} \, 	ext{kg/m}^3$

**Properties** For natural convection between the two glass sheets separated by an air gap, we can set an initial guess of $T_2 = 0°C$. The properties of air at 1 atm and the anticipated average temperature of $(T_1 + T_2)/2 = (18 + 0)/2 = 9°C$ are: $Pr = 0.7339; k = 0.02431 \, W/m.K; 
u = 1.417 	imes 10^{-5} \, 	ext{kg/m}^3$

(a) [20 marks] Calculate: (a) the temperature ($T_2$) of the outer glass layer; and (b) rate of heat loss ($Q$) through the window by natural convection. (Show all calculations)

CramX · Accepted Answer

Step 1: I will solve this problem step by step, following the formatting guidelines you provided.. **Problem:** A double-pane window has a vertical height of 0.9 m and a width of 1.4 m. There are two layers of glass separated by a 10-cm air gap at atmospheric pressure. The room temperature is 26°C, and the inner glass temperature is 18°C. **Given Data:** * Thermal conductivity, $k = 0.02529 \, W/m. K$ * Thermal conductivity, $k = 0.02431 \, W/m. K$ **Solution:** Where, Calculate the Grashof number: Calculate the Rayleigh number: Calculate the Nusselt number: Calculate the heat transfer coefficient: K}{0.9 \, m}$ K$ Calculate the temperature difference: K 	imes (18°C - T_2)$ Where, Calculate the heat flow rate: K 	imes (0.9 \, m 	imes 1.4 \, m) 	imes (18°C - T_2)}{0.1 \, m}$ K 	imes (0.9 \, m 	imes 1.4 \, m) 	imes (18°C - T_2)}{0.1 \, m}$ The heat flow rate is given by: Calculate the heat flow rate: K 	imes (18°C - 5.7°C) 	imes (0.9 \, m 	imes 1.4 \, m)$ ** Final Answer: (a) The temperature of the outer glass layer is approximately 5.7°C. (b) The rate of heat loss through the window is approximately 41.6 W.

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