problem4-52 - PROBLEM 4.52 KNOWN Long bar of square cross...

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PROBLEM 4.52 KNOWN: Long bar of square cross section, three sides of which are maintained at a constant temperature while the fourth side is subjected to a convection process. FIND: (a) The mid-point temperature and heat transfer rate between the bar and fluid; a numerical technique with grid spacing of 0.2 m is suggested, and (b) Reducing the grid spacing by a factor of 2, find the midpoint temperature and the heat transfer rate. Also, plot temperature distribution across the surface xposed to the fluid. e SCHEMATIC: ASSUMPTIONS: (1) Steady-state, two-dimensional conduction, (2) Constant properties. ANALYSIS: (a) Considering symmetry, the nodal network is shown above. The matrix inversion method of solution will be employed. The finite-difference equations are: Nodes 1, 3, 5 - Interior nodes, Eq. 4.29; written by inspection. Nodes 2, 4, 6 - Also can be treated as interior points, considering symmetry. Nodes 7, 8 - On a plane with convection, Eq. 4.42; noting that h Δ x/k = 10 W/m 2 K × 0.2 m/2W/m K = 1, find Node 7: (2T 5 + 300 + T 8 ) + 2 × 1
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