heat_3_88 - PROBLEM 3.88 KNOWN: Radii and thermal...

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PROBLEM 3.88 KNOWN: Radii and thermal conductivities of reactor fuel element and cladding. Fuel heat generation rate. Temperature and convection coefficient of coolant. FIND: (a) Expressions for temperature distributions in fuel and cladding, (b) Maximum fuel element temperature for prescribed conditions, (c) Effect of h on temperature distribution. SCHEMATIC: ASSUMPTIONS: (1) Steady-state conditions, (2) One-dimensional conduction, (3) Negligible contact resistance, (4) Constant properties. ANALYSIS: (a) From Eqs. 3.49 and 3.23, the heat equations for the fuel (f) and cladding (c) are () c f 11 2 dT 1 d dT q 1 d 0rr r 0 r rr r dr dr r dr dr f k = ≤ ≤ = ΛΞ ΜΟ ΝΠ Hence, integrating both equations twice, 2 f1 1 f2 ff dT qr C qr C Tl n r C dr 2k k r 4k k = + = + + (1,2) c3 3 c4 cc dT C C n r C dr k r k == + (3,4) The corresponding boundary conditions are: )( ) ( ) 1 c 1 r0 dT dr 0 T r T r = (5,6) [] 2 fc c c 2 rr dT dT dT f kk k h T r T dr dr dr = = = ΞΞ Ξ Ο ΟΟ Π ΠΠ (7,8) Note that Eqs. (7) and (8) are obtained from surface energy balances at r 1 and r
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This note was uploaded on 01/24/2012 for the course MECHE 343 taught by Professor Professor during the Spring '11 term at Carnegie Mellon.

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heat_3_88 - PROBLEM 3.88 KNOWN: Radii and thermal...

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