Thermodynamics HW Solutions 56

Thermodynamics HW Solutions 56 - Chapter 1 Basics of Heat...

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Chapter 1 Basics of Heat Transfer 1-108 The roof of a house with a gas furnace consists of a 15-cm thick concrete that is losing heat to the outdoors by radiation and convection. The rate of heat transfer through the roof and the money lost through the roof that night during a 14 hour period are to be determined. Assumptions 1 Steady operating conditions exist. 2 The emissivity and thermal conductivity of the roof are constant. Properties The thermal conductivity of the concrete is given to be k = 2 W/m ⋅° C. The emissivity of the outer surface of the roof is given to be 0.9. Analysis In steady operation, heat transfer from the outer surface of the roof to the surroundings by convection and radiation must be equal to the heat transfer through the roof by conduction. That is, && & QQ Q == roof, cond roof to surroundings, conv+rad The inner surface temperature of the roof is given to be T s,in = 15 ° C. Letting
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