problem4-34 - PROBLEM 4.34 KNOWN External corner of a...

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PROBLEM 4.34 KNOWN: External corner of a two-dimensional system whose boundaries are subjected to prescribed onditions. c FIND: Finite-difference equations for these situations: (a) Upper boundary is perfectly insulated and side boundary is subjected to a convection process, (b) Both boundaries are perfectly insulated; ompare result with Eq. 4.43. c SCHEMATIC: ASSUMPTIONS: (1) Steady-state conditions, (2) Two-dimensional conduction, (3) Constant roperties, (4) No internal generation. p ANALYSIS: Consider the nodal point configuration shown in the schematic and also as Case 4, Table 4.2. The control volume about the node – shaded area above of unit thickness normal to the page – has dimensions, ( Δ x/2)( Δ y/2) 1. The heat transfer processes at the surface of the CV are identified as q 1 , q 2 ⋅⋅⋅ . Perform an energy balance wherein the processes are expressed using the ppropriate rate equations. a (a) With the upper boundary insulated and the side boundary subjected to a convection process, the
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