Concept explainers
Repeat Example 30.1, but use the midpoint method to generate your solution.
To calculate: The solution of the one-dimensional heat conduction equation using midpoint method for a thing rod of length
Answer to Problem 1P
Solution: The desired result is as shown below.
Explanation of Solution
Given Information:
The expression of the temperature distribution of long, thin rod is,
Calculation:
Calculate
and
The expression of temperature,
Rewrite the above equation,
Rewrite the above equation,
Substitute the value at t = 0.1 s for the node at x = 2 cm,
The results at the other interior points are,
Therefore,
Next,
And,
The value at t = 0.2 s; the interior points are four are,
Therefore,
Next,
And,
The Midpoint method in this subpart is,
And,
Use
predictor is calculating as follow:
Slop-midpoint,
Calculate corrector,
Use Excel to create the table as follow,
Use excel to solve this problem.
Step 1 Open the excel-spreadsheet and then press Alt+F11.
Step 2 Then there is a window opened in which write the coding to find optimal solution is as below,
Step 3 Now press F5, a new popup window will appear as shown below.
Step 4 Press run after selecting the program name, the desired result will be,
The flotation of the table is,
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Chapter 30 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
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