Repeat Example 30.3, but for
To calculate: The temperature distribution of a long, thin aluminum rod with the given properties (refer Example 30.3, in the text book) when the rod is initially at
Answer to Problem 5P
Solution: The temperature distribution is,
Explanation of Solution
Given Information:
Consider, time is represented by variable t.
Length of the rod is 10 cm.
Here,
At,
Constant
Formula used:
At boundary node
From Crank Nicolson method, the difference equation for the nodes (except first and the last node) is expressed as,
Here,
Calculation:
For the first step at
Difference equation at node
Substitute
Since,
Therefore, the difference equations for node
Further, the system of equations (2), (3),(4), (5), (6), (7), (8), and (9) can be written in matrix form as,
Thus,
Execute the following code in MATLAB to evaluate the results in the above matrix equation
The output values thus obtained are:
Therefore,
Furthermore, for the second step to get the values at
Thus, solve as,
Execute the following code in MATLAB to evaluate the results in the above matrix equation
The output values thus obtained are:
Therefore,
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Chapter 30 Solutions
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Fundamentals of Differential Equations (9th Edition)
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