hw3 2011

hw3 2011 - C HEMICAL E NGINEERING 1 20B H omework 3 d ue M...

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CHEMICAL ENGINEERING 120B Homework 3 due Monday, January 31, 2010 1. An alloy metal fin (k = 64 Btu/h/ft:;OF) is used on a wall with heat transfer coefficient h 50Btu/h.ft 2 °F. The fin has a rectangular cross section, a base 0.05 inch thick, a length of 1 inch, and a width 4 inches. a. What is the thermal decay length>. in the fin? Is it short or long compared with the length of the fin? Based on this, do you expect the fin efficiency to be high or low? a. Find t he fin efficiency. c. What is the rate of heat loss from a single fin if the wall is at 200 F and the air is at 80F? 2. Derive a differential equation for the steady temperature distribution in a circumferential fin of constant base thickness 2b, inner radius RJ and outer radius R2 (length L = R2 - Rd, sticking out of a cylinder of radius R 1 . Just as in class, assume no heat transfer out the end, that convection follows Newton's law (heat transfer coefficient It), and conduction follows Fourier's law (thermal conductivity k). What are boundary conditions? Non-dimensionalize
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hw3 2011 - C HEMICAL E NGINEERING 1 20B H omework 3 d ue M...

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