problem4-78 - PROBLEM 4.78 KNOWN Longitudinal rib(k = 10...

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PROBLEM 4.78 KNOWN : Longitudinal rib (k = 10 W/m K) with rectangular cross-section with length L= 8 mm and width w = 4 mm. Base temperature T b and convection conditions, T and h, are prescribed. FIND : (a) Temperature distribution and fin base heat rate using a finite-difference method with Δ x = Δ y = 2 mm for a total of 5 × 3 = 15 nodal points and regions; compare results with those obtained assuming one-dimensional heat transfer in rib; and (b) The effect of grid spacing by reducing nodal spacing to Δ x = Δ y = 1 mm for a total of 9 × 3 = 27 nodal points and regions considering symmetry of the centerline; and (c) A criterion for which the one-dimensional approximation is reasonable; compare the heat rate for the range 1.5 L/w 10, keeping L constant, as predicted by the two-dimensional, finite-difference method nd the one-dimensional fin analysis. a SCHEMATIC : ASSUMPTIONS : (1) Steady-state conditions, (2) Constant properties, and (3) Convection coefficient niform over rib surfaces, including tip. u ANALYSIS:
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