Thermodynamics HW Solutions 152

Thermodynamics HW Solutions 152 - Chapter 2 Heat Conduction...

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Chapter 2 Heat Conduction Equation 2-131E The concrete slab roof of a house is subjected to specified temperature at the bottom surface and convection and radiation at the top surface. The temperature of the top surface of the roof and the rate of heat transfer are to be determined when steady operating conditions are reached. Assumptions 1 Steady operating conditions are reached. 2 Heat transfer is one-dimensional since the roof area is large relative to its thickness, and the thermal conditions on both sides of the roof are uniform. 3 Thermal properties are constant. 4 There is no heat generation in the wall. Properties The thermal conductivity and emissivity are given to be k = 1.1 Btu/h ft °F and ε = 0.9. Analysis In steady operation, heat conduction through the roof must be equal to net heat transfer from the outer surface. Therefore, taking the outer surface temperature of the roof to be T 2 (in ° F), ] ) 460 [( ) ( 4 sky 4 2 2 2 1 T T A T T hA L T T kA + + = σε x T h T o L T sky
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