Thermodynamics HW Solutions 491

Thermodynamics HW Solutions 491 - Chapter 5 Numerical...

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Chapter 5 Numerical Methods in Heat Conduction 5-93 The roof of a house initially at a uniform temperature is subjected to convection and radiation on both sides. The temperatures of the inner and outer surfaces of the roof at 6 am in the morning as well as the average rate of heat transfer through the roof during that night are to be determined. Assumptions 1 Heat transfer is one-dimensional. 2 Thermal properties, heat transfer coefficients, and the indoor and outdoor temperatures are constant. 3 Radiation heat transfer is significant. Properties The conductivity and diffusivity are given to be k = 1.4 W/m. ° C and . The emissivity of both surfaces of the concrete roof is 0.9. α 069 10 6 . m 2 / s Analysis The nodal spacing is given to be Δ x = 0.03 m. Then the number of nodes becomes 1 / + Δ = x L M = 0.15/0.03+1 = 6. This problem involves 6 unknown nodal temperatures, and thus we need to have 6 equations. Nodes 2, 3, 4, and 5 are interior nodes, and thus for them we can use the general
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This note was uploaded on 01/22/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.

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