problem4-35 - PROBLEM 4.35 KNOWN Boundary conditions that...

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PROBLEM 4.35 KNOWN: Boundary conditions that change from specified heat flux to convection. F IND: The finite difference equation for the node at the point where the boundary condition changes. SCHEMATIC: m,n m +1,n m -1,n y q 1 q 2 q 4 q 5 q 3 h, T x y/2 x m, n-1 s q ′′ ASSUMPTIONS: (1) Two dimensional, steady-state conduction with no generation, (2) Constant properties. ANALYSIS: Performing an energy balance on the control volume x • y/2, in out E- E = 0 ±± q 1 + q 2 + q 3 + q 4 + q 5 = 0 Expressing q 1 in terms of the specified heat flux, q 2 in terms of the known heat transfer coefficient and environment temperature, and the remaining heat rates using the conduction rate equation,
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