problem4-71 - PROBLEM 4.71 KNOWN Pin fin of 10 mm diameter...

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PROBLEM 4.71 KNOWN: Pin fin of 10 mm diameter and length 250 mm with base temperature of 100 ° C experiencing adiation exchange with the surroundings and free convection with ambient air. r FIND: Temperature distribution using finite-difference method with five nodes. Fin heat rate and elative contributions by convection and radiation. r SCHEMATIC: ASSUMPTIONS: (1) Steady-state conditions, (2) One-dimensional conduction in fin, (3) Constant properties, (4) Fin approximates small object in large enclosure, (5) Fin tip experiences convection and adiation, (6) h r fc = 2.89[0.6 + 0.624(T - T ) 1/6 ] 2 . ANALYSIS: To apply the finite-difference method, define the 5-node system shown above where Δ x = L/5. Perform energy balances on the nodes to obtain the finite-difference equations for the nodal temperatures. Interior node, n = 1, 2, 3 or 4 in out E E = ± ± 0 0 (1) a b c d q q q q + + + = ( ) ( ) n 1 n n 1 n r,n sur n c fc,n n c T T T T h P x T T kA h P x T T kA 0 x x + Δ + + Δ + = Δ Δ (2) where the free convection coefficient is (3) ( ) 2 1/6 fc,n n h 2.89 0.6
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