problem4-49 - PROBLEM 4.49 KNOWN Nodal temperatures from a...

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PROBLEM 4.49 KNOWN: Nodal temperatures from a steady-state finite-difference analysis for a cylindrical fin of prescribed diameter, thermal conductivity and convection conditions ( T , h). F IND: (a) The fin heat rate, q f , and (b) Temperature at node 3, T 3 . SCHEMATIC: T 0 = 100.0 ° C T 1 = 93.4 ° C T 2 = 89.5 ° C ASSUMPTIONS: (a) The fin heat rate, q f , is that of conduction at the base plane, x = 0, and can be found from an energy balance on the control volume about node 0, in out E E 0 = ± ± , . f 1 conv f 1 con q q q 0 or q q q + + = = − v Writing the appropriate rate equation for q 1 and q conv , with A c = π D 2 /4 and P = π D, ( )( ) ( ) ( ) ( 2 1 0 f c 0 1 0 T T kD q kA hP x 2 T T T T 2 Dh x T T x 4 x π π = − Δ = − Δ Δ Δ ) 0 Substituting numerical values, with Δ x = 0.010 m, find ( ) ( ) ( ) 2 f 2 15W m K 0.012m q 93.4 100 C 4 0.010m 0.012m 25W m K 0.010m 25
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