Thermodynamics HW Solutions 428

Thermodynamics HW Solutions 428 - Chapter 5 Numerical...

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Unformatted text preview: Chapter 5 Numerical Methods in Heat Conduction 5-38 Two cast iron steam pipes are connected to each other through two 1-cm thick flanges, and heat is lost from the flanges by convection and radiation. The finite difference formulation of the problem for all nodes is to be obtained, and the temperature of the tip of the flange as well as the rate of heat transfer from the exposed surfaces of the flange are to be determined. Assumptions 1 Heat transfer through the flange is stated to be steady and one-dimensional. 2 The thermal conductivity and emissivity are constants. 3 Convection heat transfer coefficient is constant and uniform. Properties The thermal conductivity and emissivity are given to be k = 52 W/m C and = 0.8. h i T i x 0 1 2 3 4 5 6 h o , T T surr Analysis ( a ) The distance between nodes 0 and 1 is the thickness of the pipe, x 1 =0.4 cm=0.004 m. The nodal spacing along the flange is given to be x 2 =1 cm = 0.01 m. Then the number of =1 cm = 0....
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