assignment6 - ME372ComputerAidedMechanicalEngineering

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ME 372 Computer-Aided Mechanical Engineering Instructor: Dr. Emre Alpman Assignment #6 Due Date: May 13 rd , 2010  1 Problem Statement Unsteady heat conduction along a rod with convection from side walls can be modeled using the  following parabolic PDE; u t = 2 u x 2  u (1) where  u is temperature above the ambient temperature.   α   and   β are given as 2.5x10 -5   m 2 /s and  5.0x10 -3  1/s, respectively The length of the rod is 20 cm. 2 Lab Assignment In the lab you are asked to solve the above equation using  semidiscrete approach . For this purpose  discretize this equation for space by generating  a uniform mesh   in  x -direction  by dividing the length  of the rod into  N  equal segments.  In the lab take  N  = 40 . Then discretize the space derivative of  using  central differencing  and convert the PDE to a system of ODEs as follows:
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This note was uploaded on 04/05/2012 for the course MECHANICAL ME372 CAME taught by Professor Emraalpman during the Spring '10 term at Yeditepe Üniversitesi.

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assignment6 - ME372ComputerAidedMechanicalEngineering

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