Heat Transfer in a Ceramic Strip

Two dimensional heat transfer of a ceramic strip with both radiation and convection on the top boundary. The ceramic has a thermal conductivity of 3 W/mK and the sides are fixed at a temperature of 900 °C while the bottom boundary is insulated. The surrounding temperature is 50 °C. The top boundary is exposed to both natural convection (with a film coefficient h = 50 W/m²K) and radiation (with emissivity ε = 0.7 and the Stefan-Boltzmann constant 5.669·10^-8 W/m²K⁴). The solution is sought at three points along the vertical symmetry line.

Tutorial

This model is available as an automated tutorial by selecting Model Examples and Tutorials... > Heat Transfer > Heat Transfer in a Ceramic Strip from the File menu. Or alternatively, follow the step-by-step instructions below. Note that the CFDTool interface differ slightly from the FEATool Multiphysics instructions described in the following.

1. To start a new model click the New Model toolbar button, or select New Model... from the File menu.
2. Select the Heat Transfer physics mode from the Select Physics drop-down menu. (Note that for CFDTool the physics selection is done in the Equation settings dialog box.)
3. Press OK to finish the physics mode selection.
4. To create a rectangle, first click on the Create square/rectangle Toolbar button. Then left click in the main plot axes window, and hold down the mouse button. Move the mouse pointer to draw the shape outline, and release the button to finalize the shape.
5. Select R1 in the geometry object Selection list box.
6. To modify and edit the selected rectangle, click on the Inspect/edit selected geometry object Toolbar button to open the Edit Geometry Object dialog box.
7. Enter 0 into the x_min edit field.
8. Enter 0.02 into the x_max edit field.
9. Enter 0 into the y_min edit field.
10. Enter 0.01 into the y_max edit field.
11. Press OK to finish and close the dialog box.
12. Switch to Grid mode by clicking on the corresponding Mode Toolbar button.
13. Enter 0.001 into the Grid Size edit field.
14. Press the Generate button to call the grid generation algorithm.
15. Switch to Equation mode by clicking on the corresponding Mode Toolbar button.
16. Enter 3 into the Thermal conductivity edit field. (Note that the Equation Settings dialog box may look different for CFDTool.)
17. Press OK to finish the equation and subdomain settings specification.
18. Switch to Boundary mode by clicking on the corresponding Mode Toolbar button.
19. Select 1 in the Boundaries list box.
20. Select Thermal insulation/symmetry from the Heat Transfer drop-down menu.
21. Select 2 and 4 in the Boundaries list box.
22. Select Temperature from the Heat Transfer drop-down menu.
23. Enter 900+273 into the Temperature edit field.
24. Select 3 in the Boundaries list box.
25. Select Heat flux from the Heat Transfer drop-down menu.
26. Enter 50 into the Heat transfer coefficient edit field.
27. Enter 50+273 into the Bulk temperature edit field.
28. Enter 0.7*5.669e-8 into the Radiation constant edit field.
29. Enter 50+273 into the Ambient temperature edit field.
30. Press OK to finish the boundary condition specification.
31. Switch to Solve mode by clicking on the corresponding Mode Toolbar button.
32. Press the = Toolbar button to call the solver. After the problem has been solved FEATool will automatically switch to postprocessing mode and plot the computed solution.

Evaluate the temperature in the points (0.01, 0.01), (0.01, 0.005), and (0.01, 0) and compare with the reference values T_ref = 984, 1064, and 1088.

1. Select Point/Line Evaluation... from the Post menu.
2. Enter 0.01 into the Evaluation coordinates in x-direction edit field.
3. Enter 0.01 into the Evaluation coordinates in y-direction edit field.
4. Press the Apply button.
5. Enter 0.005 into the Evaluation coordinates in y-direction edit field.
6. Press the Apply button.
7. Enter 0 into the Evaluation coordinates in y-direction edit field.
8. Press the Apply button.
9. Press OK to finish and close the dialog box.

The heat transfer in a ceramic strip heat transfer model has now been completed and can be saved as a binary (.fea) model file, or exported as a programmable MATLAB m-script text file (available as the example ex_heattransfer1 script file), or GUI script (.fes) file.

Reference

[1] Holman JP. Heat Transfer. Fifth Edition, New York: McGraw-Hill, page 96, Example 3-8, 1981.