5-12 - 298 Finite Element Analysis and Design 12 Consider a...

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298 Finite Element Analysis and Design 12. Consider a wall built up of concrete and thermal insulation. The outdoor temperature is T o = 17 C and the temperature inside is T i = 20 C. The wall is subdivided into three elements. The thermal conductivity for concrete is k c = 1.7 W/m/ o C, and that of the insulator is k i = 0.04 W/m/ o C. Convection heat transfer occurs at both surfaces with convection coefficients of h 0 = 14 W/m 2 / o C and h i = 5.5 W/m 2 / o C. Calculate the temperature distribution in the wall. Also, calculate the amount of heat flow through the outdoor surface. Solution: Assuming that the wall is wide enough, we model the problem unit area of the wall, i.e., A= 1 m 2 . The element matrix equations become Element 1: (1) 11 2 2 24.286 24.286 24.286 24.286 Tq T q         Element 2: (2) 22 (2) 3 3 0.4 0.4 0.4 0.4 T q  

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5-12 - 298 Finite Element Analysis and Design 12 Consider a...

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