Chapter 5 Numerical Methods in Heat Conduction 5-118E A plane wall in space is subjected to specified temperature on one side and radiation and heat flux on the other. The finite difference formulation of this problem is to be obtained, and the nodal temperatures under steady conditions are to be determined. Assumptions 1 Heat transfer through the wall is given to be steady and one-dimensional. 2 Thermal conductivity is constant. 3 There is no heat generation. 4 There is no convection in space. Properties The properties of the wall are given to be k =1.2 W/m ⋅ °C, ε = 0.80, and α s = 0.45. T0 Δ x Radiation 1 q s • • • •0 2 3 T surr Analysis The nodal spacing is given to be Δ x = 0.1 ft. Then the number of nodes becomes 1 / + Δ = x L M = 0.3/0.1+1 = 4. The left surface temperature is given to be T0 = 520 R = 60 ° F. This problem involves 3 unknown nodal temperatures, and thus we need to have 3 equations to determine them uniquely. Nodes 1 and 2 are interior nodes, and thus for them we can use the general finite difference
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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.