problem4-30

# problem4-30 - PROBLEM 4.30 KNOWN Dimensions and thermal...

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PROBLEM 4.30 KNOWN: Dimensions and thermal conductivities of a heater and a finned sleeve. Convection onditions on the sleeve surface. c FIND: (a) Heat rate per unit length, (b) Generation rate and centerline temperature of heater, (c) ffect of fin parameters on heat rate. E SCHEMATIC: ASSUMPTIONS: (1) Steady state, (2) Constant properties, (3) Negligible contact resistance between heater and sleeve, (4) Uniform convection coefficient at outer surfaces of sleeve, (5) Uniform heat eneration, (6) Negligible radiation. g A NALYSIS: (a) From the thermal circuit, the desired heat rate is () ss t,o tot cond 2D TT q RR R ∞∞ −− == ′′ + T he two-dimensional conduction resistance, may be estimated from Eq. (4.21) and Case 6 of Table 4.2 ( ) 4 cond 2D ln 1.08w / D ln 2.16 1 R5 S k 2 k 2 240W / m K ππ = = × . 1 1 1 0 m K / W The thermal resistance of the fin array is given by Equation (3.103), where η o and A t are given by Equations. (3.102) and (3.99) and η f is given by Equation (3.89). With L c = L + t/2 = 0.022 m, m = 2h/k s t) 1/2 = 32.3 m -1 and mL c = 0.710, ( c f c tanh mL 0.61 0.86

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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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problem4-30 - PROBLEM 4.30 KNOWN Dimensions and thermal...

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