Figure below shows schematically the heat transfer mechanisms between a house and its surroundings. Solar energy is transferred to the exterior surfaces (roof, walls, door). A portion of the solar energy is absorbed by the exterior surfaces and the rest is reflected to the surrounding. Heat is also exchanged between the house and the air. The indoor temperature is maintained at 19 °C. Your task is to apply the methods of heat transfer discussed in the class to analyze the heat transfer process in the roof. A sketch of the roof with a thermal conductivity of 2.4 W/m.K is depicted below. The inner surface temperature is 25 °C. The heat exchange between the inner surface and the indoor air occurs due to convection with a convective heat transfer coefficient of 10 W/m2.K. The solar radiation is 315W/m. The absorptivity and emissivity of the roof are 0.59 and 0.90, respectively. Assume that radiation heat transfer occurs with a far surrounding that is at 0 °C. You may neglect radiation mechanism between the inner surface and its surroundings. Task 1: Determine the thickness of the roof. Task 2: What is the surface temperature T.? Task 3: What would be the inner surface temperature if the solar radiation decreased to 250 W/m??

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