Problem4-59 - PROBLEM 4.59 KNOWN Upper surface and grooves of a plate are maintained at a uniform temperature T1 while the lower surface is

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PROBLEM 4.59 KNOWN: Upper surface and grooves of a plate are maintained at a uniform temperature T 1 , while the ower surface is maintained at T l 2 or is exposed to a fluid at T . FIND: (a) Heat rate per width of groove spacing (w) for isothermal top and bottom surfaces using a inite-difference method with Δ x = 40 mm, (b) Effect of grid spacing and convection at bottom surface. f SCHEMATIC: (b) ASSUMPTIONS: (1) Steady-state, two-dimensional conduction, (2) Constant properties. ANALYSIS: (a) Using a space increment of Δ x = 40 mm, the symmetrical section shown in schematic (b) corresponds to one-half the groove spacing. There exist only two interior nodes for which finite- difference equations must be written. Node a: () a1 b 2 1 4T T T T T 0 −+ + += or ab 4T 200 T 20 200 0 + 4T T 420 = (1) Node b: b1 a 2 a 4T T T T T 0 + + = or ( ba 4T 200 2T 20 0 + = ) 2T 4T 220 (2) Multiply Eq. (2) by 2 and add to Eq. (1) to obtain 7T b = 860 or T b = 122.9 ° C From Eq. (1), 4T a - 122.9 = 420 or T a = (420 + 122.9)/4 = 135.7 ° C.
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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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Problem4-59 - PROBLEM 4.59 KNOWN Upper surface and grooves of a plate are maintained at a uniform temperature T1 while the lower surface is

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