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,
Want to see more full solutions like this?
Chapter 30 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
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