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 EE 0 = ±± , . f1c o n v f 1c o n 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 10 fc 0 1 0 TT kD qk A h P x 2 T T T T 2 D h x T T x4 x π ∞∞ =− Δ Δ ΔΔ ) 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 25 100
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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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