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Unformatted text preview: ACM 95/100c April 9, 2004 Problem Set II 1.- (20 pts) The heat transfer in a one-dimensional homogeneous bar in 0 < x < L is described by the equation T t- 2 T x 2 = 0 , where is a constant. The temperatures of the ends of the bar are fixed (by attaching each end to a large reservoir) such that T (0 ,t ) = T , T ( L,t ) = T 1 where T and T 1 are constant temperatures. (a) Show that using the transformation T = w ( x,t ) + 1 L ( T 1- T ) x + T an equation for w ( x,t ) can be obtained with homogeneous end conditions. (b) Solve the equation for w by a series-solution method with initial temperature distribution given by T ( x, 0) = f ( x ) , < x < L. Note: This is an initial condition for T , not w . (c) What is the temperature distribution in the bar when t ? 2.- (40 pts) A rod with insulated sides occupies the portion 1 < x < 2 of the x-axis. The thermal conductivity of the rod material is not constant but depends on x in such a way that the rod temperature T...
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This note was uploaded on 01/08/2011 for the course ACM 95c taught by Professor Nilesa.pierce during the Spring '09 term at Caltech.
- Spring '09