QQuestionPhysics
QuestionPhysics
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; \nu = 1.534 \times 10^{- 5} \, \text{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; \nu = 1.417 \times 10^{- 5} \, \text{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)
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Q \approx 41.6 \, W
**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 \times (18°C - T_2) Where, Calculate the heat flow rate: K \times (0.9 \, m \times 1.4 \, m) \times (18°C - T_2)}{0.1 \, m} K \times (0.9 \, m \times 1.4 \, m) \times (18°C - T_2)}{0.1 \, m} The heat flow rate is given by: Calculate the heat flow rate: K \times (18°C - 5.7°C) \times (0.9 \, m \times 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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