Chapter 5 Numerical Methods in Heat Conduction 5-58 The exposed surface of a long concrete damn of triangular cross-section is subjected to solar heat flux and convection and radiation heat transfer. The vertical section of the damn is subjected to convection with water. The temperatures at the top, middle, and bottom of the exposed surface of the damn are to be determined. Assumptions 1 Heat transfer through the damn is given to be steady and two-dimensional. 2 There is no heat generation within the damn. 3 Heat transfer through the base is negligible. 4 Thermal properties and heat transfer coefficients are constant. Properties The thermal conductivity and solar absorptivity are given to be k = 0.6 W/m ⋅ °C and α s = 0.7. Analysis The nodal spacing is given to be Δ x = Δ x = l =1 m, and all nodes are boundary nodes. Node 5 on the insulated boundary can be treated as an interior node for which 04 node bottom right top left = − + + + T T T T T .
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