problem4-38 - PROBLEM 4.38 KNOWN Heat generation and...

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PROBLEM 4.38 K NOWN: Heat generation and thermal boundary conditions of bus bar. Finite-difference grid. F IND: Finite-difference equations for selected nodes. SCHEMATIC: ASSUMPTIONS: (1) Steady-state conditions, (2) Two-dimensional conduction, (3) Constant roperties. p ANALYSIS: (a) Performing an energy balance on the control volume, ( Δ x/2)( Δ y/2) 1, find the FDE or node 1, f ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) o 1 u 1 t,c 6 1 t,c o u 2 6 k y/2 1 T T x h 1 T T T R / y/2 1 2 x k x/2 1 T T q x/2 y/2 1 0 y x/kR T h x/k T T T Δ Δ + + ′′ Δ Δ Δ + + Δ Δ = Δ ′′ Δ + Δ + + ± 2 1 T < ( ) ( ) ( ) 2 t,c u 1 q x / 2k x/kR h x/k 2 T 0. ′′ + Δ Δ + Δ + = ± ( b) Performing an energy balance on the control volume, (
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