Perform the first computation in Sec. 28.1, but for the casewhere
To calculate: The solution for c if thedifferential equation for mass balance of single reactor is
Answer to Problem 1P
Solution:
The solution for c by the Heun method where
Heun withoutiteration | |
t | c |
0 | 10 |
10 | 25 |
20 | 34.375 |
30 | 40.23438 |
40 | 43.89648 |
50 | 46.1853 |
The solution for c by fourth-order RK method where
4th order RK | |
t | c |
0 | 10 |
10 | 25.72917 |
20 | 35.27317 |
30 | 41.06419 |
40 | 44.57801 |
50 | 46.71009 |
Explanation of Solution
Given Information:
The differential equation for mass balance of single reactor is,
The values,
The analytical equation for mass balance of single reactor is,
Formula used:
The iteration formula for Heun’s method is,
The fourth-order RK method for
Where,
Calculation:
Consider the analytical equation for mass balance of single reactor is,
Substitute the values
Now, use VB code to determine c at different value of t using Heun’s method and RK4 method as below,
The following output gets displayed in the excel after the execution of the above code:
To draw the graph, use excel as below,
Step 1: Select cells from B5 to B10 and C5 to C10, then go to Insert tab and select the Line option from Charts subgroup.
Step 2: Select cells from B17 to B22 and C17 to C22, then go to Insert tab and select the Line option from Charts subgroup
Step 3: Merge the graphs.
The graph obtained is,
Hence, both the method gives the same results.
Want to see more full solutions like this?
Chapter 28 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
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