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Assignment_2 - MAE4030 Fall 2011 Assignment 2 umerical...

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MAE4030 Fall 2011 Assignment 2: glyph1197umerical Methods for Heat Transfer Due Wednesday, glyph817ovember 16, 2011 1. Given a cylindrical rod of Length L = 1 Thermal diffusivity α = 1 Initial temperature distribution T 0 (x) = u 0 (x) (using Tutorial 6’s notation) Insulated boundaries And no heat generation The following 1D transient heat conduction problem (with no heat generation) can be formulated. 2 2 T T x t = Using Tutorial 6’s notation the equation above can be rewritten as, ( , ) ( , ) 0 1 and 0 xx t u x t u x t x t = > Subjected to initial and boundary conditions, 0 0 1/ 2 ( ,0) ( ) 1 1/ 2 1 x x u x u x x x = = (0, ) 0 (1, ) 0 0 x x u t and u t for t = = > With the help of the syntax introduced and Example 1 in Tutorial 6, a. Solve the above problem using Matlab pdepe function. Describe your approach (the definitions of the various input parameters of the function) and include your Matlab codes in the Appendix for review.

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