EBK NUMERICAL METHODS FOR ENGINEERS
EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 8220100254147
Author: Chapra
Publisher: MCG
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Chapter 32, Problem 16P

Solve the nondimensional transient heat conduction equation in two dimensions, which represents the transient temperature distribution in an insulated plate. The governing equation is

2 u x 2 + 2 u y 2 = u t

where u = temperature, x and y are spatial coordinates, and t = time. The boundary and initial conditions are

Boundary conditions u | x , 0 , t | = 0
u | 0 , y , t | = 0
u | x , 0 , t | = 1
u | 1 , y , t | = 1
Initial conditions u | x , y , 0 | = 0 0 x < 1 0 y < 1

Solve using the alternating direction-implicit technique. Write a computer program to implement the solution. Plot the results using a three-dimensional plotting routine where the horizontal plan contains the x and y axes and the z axis is the dependent variable u. Construct several plots at various times, including the following: (a) the initial conditions; (b ) one intermediate time, approximately halfway to steady state; and (c ) the steady-state condition.

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