problem4-32 - PROBLEM 4.32 KNOWN Internal corner of a...

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PROBLEM 4.32 KNOWN: Internal corner of a two-dimensional system with prescribed convection boundary onditions. c FIND: Finite-difference equations for these situations: (a) Horizontal boundary is perfectly insulated and vertical boundary is subjected to a convection process (T , h), (b) Both boundaries are perfectly nsulated; compare result with Eq. 4.41. i SCHEMATIC: ASSUMPTIONS: (1) Steady-state conditions, (2) Two-dimensional conduction, (3) Constant roperties, (4) No internal generation. p ANALYSIS: Consider the nodal network shown above and also as Case 2, Table 4.2. Having defined the control volume – the shaded area of unit thickness normal to the page – next identify the heat transfer processes. Finally, perform an energy balance wherein the processes are expressed using ppropriate rate equations. a (a) With the horizontal boundary insulated and the vertical boundary subjected to a convection rocess, the energy balance results in the following finite-difference equation:
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