To calculate: The thermocline depth and the flux across the interface by the use of a cubic spline fit where
Depth, m | 0 | 0.5 | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 |
Temperature, Celsius | 70 | 68 | 55 | 22 | 13 | 11 | 10 |
The provided graph shows the relationship between depth and temperature as,
Answer to Problem 6P
Solution:
The value of thermocline depth and the flux across the interface is
Explanation of Solution
Given Information:
The table is given as,
Depth, m | 0 | 0.5 | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 |
Temperature, Celsius | 70 | 68 | 55 | 22 | 13 | 11 | 10 |
The provided graph shows the relationship between depth and temperature as,
Calculation:
Consider the Fourier’s law,
The value of
From the graph, this can be interpreted that curve has zero slope at
Since, the cubic spline fit is required, so this problem can be solved by the Excel VBA(Visual Basic for applications). The steps are,
Step 1. Insert the data in excel as shown below,
Step 2. Press ALT+F11 and write the code as shown below,
Step 3. Press RUN then this dialog box appears.
Step 4. Enter the value of z.
Step 5. This output will appear.
Thus, the value of
Hence, the value of thermocline depth and the flux across the interface is
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Chapter 20 Solutions
Numerical Methods for Engineers
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