FEATool Multiphysics
v1.10 Finite Element Analysis Toolbox |

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/m ^{2}K*) and radiation (with emissivity ε = 0.7 and the Stefan-Boltzmann constant

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.

- To start a new model click the
**New Model**toolbar button, or select*New Model...*from the*File*menu. - Select the
**Heat Transfer**physics mode from the*Select Physics*drop-down menu. - Press
**OK**to finish the physics mode selection. - 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. - Select
**R1**in the geometry object*Selection*list box. - 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. - Enter
`0`

into the*x*edit field._{min} - Enter
`0.02`

into the*x*edit field._{max} - Enter
`0`

into the*y*edit field._{min} - Enter
`0.01`

into the*y*edit field._{max} - Press
**OK**to finish and close the dialog box. - Switch to
**Grid**mode by clicking on the corresponding*Mode Toolbar*button. - Enter
`0.001`

into the*Grid Size*edit field. - Press the
**Generate**button to call the grid generation algorithm. - Switch to
**Equation**mode by clicking on the corresponding*Mode Toolbar*button. - Enter
`3`

into the*Thermal conductivity*edit field. - Press
**OK**to finish the equation and subdomain settings specification. - Switch to
**Boundary**mode by clicking on the corresponding*Mode Toolbar*button. - Select
**1**in the*Boundaries*list box. - Select
**Thermal insulation/symmetry**from the*Heat Transfer*drop-down menu. - Select
**2**and**4**in the*Boundaries*list box. - Select
**Temperature**from the*Heat Transfer*drop-down menu. - Enter
`900+273`

into the*Temperature*edit field. - Select
**3**in the*Boundaries*list box. - Select
**Heat flux**from the*Heat Transfer*drop-down menu. - Enter
`50`

into the*Heat transfer coefficient*edit field. - Enter
`50+273`

into the*Bulk temperature*edit field. - Enter
`0.7*5.669e-8`

into the*Radiation constant*edit field. - Enter
`50+273`

into the*Ambient temperature*edit field. - Press
**OK**to finish the boundary condition specification. - Switch to
**Solve**mode by clicking on the corresponding*Mode Toolbar*button. - 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*,

- Select
**Point/Line Evaluation...**from the*Post*menu. - Enter
`0.01`

into the*Evaluation coordinates in x-direction*edit field. - Enter
`0.01`

into the*Evaluation coordinates in y-direction*edit field. - Press the
**Apply**button. - Enter
`0.005`

into the*Evaluation coordinates in y-direction*edit field. - Press the
**Apply**button. - Enter
`0`

into the*Evaluation coordinates in y-direction*edit field. - Press the
**Apply**button. - 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, or GUI script (.fes) file.

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