PROBLEM 4.48 KNOWN:Steady-state temperatures (°C) associated with selected nodal points in a two-dimensional ystem. sFIND:(a) Temperatures at nodes 1, 2 and 3, (b) Heat transfer rate per unit thickness from the system urface to the fluid. sSCHEMATIC:ASSUMPTIONS:(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: 1neighbors1TT4=⋅∑()11T172.9 137.0 132.8200.0C160.7 C4=+++=DD<Node 2,Insulated boundary, Eq. 4.46 with h = 0, Tm,n= T22m-1,nm+1,nm,n-11T2T4+21T129.445.82 103.5C95.6 C4+×=DD<Node 3,Plane surface with convection, Eq. 4.42, Tm,n= T33m-1,nm,n+1m,n-1hx222T2TkkT∞ΔΔ+=+++⎡⎤⎢⎥⎣⎦2h x/k
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