Finite Differencing Using Excel Learning how to use Surface Charts T 1 T 4 T 2 T 3

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1 Finite Differencing Using Excel Learning how to use Surface Charts T 1 T 2 T 4 T 2 Assuming a flat plate of a uniform thickness has four constant temperatures applied to outer and inner edges, the temperature distribution across the plate can be computed using finite differencing techniques. The general concept is that a temperature value at a specific location can be computed as a function of temperatures surrounding that particular location in space. Temperature values of adjacent points can be computed in a similar manner. This process is repeated over and over until the temperatures stabilize; ie they stop changing (or change very little) upon the next iteration. This assignment requires us to: 1) Change how EXCEL updates cell locations so that we can manually control the updating of the spreadsheet. 2) Model the system such that temperature values on the edges can be easily and quickly updated. 3) Generate a color surface chart of the plate so we have a graphical representation of the process. 4) Run the simulation. Step 1. Changing the calculation process. T 3 Select File Excel Options and change the Formulas Calculation option to appear as shown. 1

2 Step 2. Create a simple model to test the process. Set up an input area (yellow cells) for control temperatures and generate cell formulas that update as shown below. Test to make sure that you have true control over the edges. Add cell formulas to the inner locations. The formula for the cell at D12 is simply the average of the four cells surrounding it. In other words, (D11+E12+D13+C12)/4. Copy this formula to other open cells on the plate. 2

3 Center the values in the cells and format the plate cells to 1 place, then press F9 until the numbers appear to stop changing. You have now reached convergence. The result should appear as shown. Print (Grid/Header macro) your spreadsheet to document your success at this point. Drive your plate back to ambient temperature by setting all input values to 72 degrees and hold down the F9 key. The result should appear as shown. Print (Grid/Header macro) your spreadsheet again. Play with input values and manually recalculate to watch the temperatures change. You now have the confidence to do this task on a larger scale. 3

4 Actual Model: 20 wide plate, 26 tall. 5 x5 hole located on in the plate as shown. Note: Due to cell sizes, this is not to scale (NTS). Blue cells are for dimensional (reference) purposes Green cells are constant temperature values Color and dimensional values (blue cells) are critical. Internal cell values are not critical at this stage. Formatting (centering, number of places) is critical for viewing purposes. See the following page for a result with the following input: 4

5 General Idea of converged data showing a surface chart which is to be added. See the notes below on how to do this effectively. Make a copy of your chart and move this to a new sheet before printing the chart with a header. Drop box your completed (see instructions below!) spreadsheet to the appropriate folder into the V:/MET_107/Homework_16_section_n subdirectory Make sure you set all your temperatures to ambient (72) and recalculate all cells back to essentially 72 before saving. There should be the original chart displayed on the same worksheet with your data set as shown to the right. Remember, you made a copy of the chart for printing purposes. Your instructor will test the electronic version of your spreadsheet. There will be a 2 point deduction if the input values and initial plate temperatures are not initially set to 72 degrees upon loading the file. Other deductions (check your work!) No colors on outer temperatures -.25 No colors on outer dimensions -.25 No print of graphs -.5 Incorrect chart orientation -.5 Incorrect cell formulas -1.0 Sloppy formatting of cells -.25 See next page for enlarged version of these hints 5

6 You will be turning in: Four graphs (Column, Pie, Line and XY Scatter) Print out of the simple finite difference model using the Grid/Header macro (final values) Print out of the simple finite difference model using the Grid/Header macro (initial values) Graph of the completed large finite difference model. Note that you are not printing the spreadsheet for the large model, only the graph. 6