Problem4-53 - PROBLEM 4.53 KNOWN Volumetric heat generation in a rectangular rod of uniform surface temperature FIND(a Temperature distribution in

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PROBLEM 4.53 K NOWN: Volumetric heat generation in a rectangular rod of uniform surface temperature. FIND: (a) Temperature distribution in the rod, and (b) With boundary conditions unchanged, heat eneration rate causing the midpoint temperature to reach 600 K. g SCHEMATIC: ASSUMPTIONS: (1) Steady-state, two-dimensional conduction, (2) Constant properties, (3) Uniform volumetric heat generation. ANALYSIS: (a) From symmetry it follows that six unknown temperatures must be determined. Since all nodes are interior ones, the finite-difference equations may be obtained from Eq. 4.35 written in the form ( ) () i neighbors T1 4 T 1 4 qx yk =+ Δ ± Δ . With () qx y4 k ΔΔ ± = 62.5 K, the system of finite-difference equations is (1) () 1s 2 4 s T 0.25 T T T T 15.625 =+ + + + (2) () 2s 3 5 1 T 0.25 T T T T 15.625 =+ + + + (3) () 3s 2 6 2 T 0.25 T T T T 15.625 =+ + + + (4) () 41 5 1 s T 0.25 T T T T 15.625 =+ + + + (5) () 5
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This note was uploaded on 12/07/2010 for the course MAE Heat Trans taught by Professor Lee,j.s. during the Spring '10 term at Seoul National.

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