problem4-48 - PROBLEM 4.48 KNOWN Steady-state...

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PROBLEM 4.48 KNOWN: Steady-state temperatures ( ° C) associated with selected nodal points in a two-dimensional ystem. s FIND: (a) Temperatures at nodes 1, 2 and 3, (b) Heat transfer rate per unit thickness from the system urface to the fluid. s SCHEMATIC: A SSUMPTIONS: (1) Steady-state, two-dimensional conduction, (2) Constant properties. ANALYSIS: (a) Using the finite-difference equations for Nodes 1, 2 and 3: Node 1, Interior node, Eq. 4.29: 1 neighbors 1 T T 4 = ( ) 1 1 T 172.9 137.0 132.8 200.0 C 160.7 C 4 = + + + = D D < Node 2, Insulated boundary, Eq. 4.46 with h = 0, T m,n = T 2 ( ) 2 m-1,n m+1,n m,n-1 1 T T T 2T 4 = + + ( ) 2 1 T 129.4 45.8 2 103.5 C 95.6 C 4 = + + × = D D < Node 3, Plane surface with convection, Eq. 4.42, T m,n = T 3 ( ) 3 m-1,n m,n+1 m,n-1 h x 2h x 2 2 T 2T T T k k T Δ Δ + = + + + 2 h x/k 50W/m K 0.1m/1.5W/m K
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