Thermal Conduction Through A Fin

Problem: Rectangular fins are used to remove heat from a heated surface. Using Patran/MSC Nastran, calculate the temperature distribution of a rectangular fin with the dimensions of 100mm x 5mm x 1mm. The fin is attached to a heated surface which has a temperature of 100°C, and ambient temperature around the fin is 20°C. The fin is made of copper, which has a conductivity, k, of 345 W(m·°C), and a heat transfer coefficient, ß, of 25 W(m2·°C).

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1) Click on New from the File menu or from the Defaults Toolbar as shown.

2) Type the name of the new database as thermal_plate and click OK.

3) In the Approximate Maximum Model Dimensions box, input 0.1 and change the Analysis Type to Thermal. Click OK.





1) Under the Geometry tab, click on Surface and select XYZ.

2)Input the vector of <0.1 .005 0> in the Vector Coordinates List and click Apply. There are no units in Patran, and therefore it is important to stay consistent in units.

1) Under the Properties tab, select Isotropic.

2) Input copper as the Material Name and then select Input Properties.

3) Input 345 as the Thermal Conductivity. Click OK and Apply.



1) Click on Shell under the 2D Properties section.

2) Input Fin as the Property Set Name and then click on Input Properties .

3) Click on Select Material and select copper. Enter 0.001 as the Thickness. Click OK.

4) Click on Select Application Region and then click on the Select Members box. Screen pick the surface. Click Add, OK then Apply.





1) Select the Load/BCs tab. Under the Element Uniform section, select Convection.

2) Input Top Conv as the New Set Name, set the Target Element Type to 2D, and then click on Input Data.

3) Set Surface Option to Top. Input 25 for Top Surf Convection Coef and 20 for Ambient Temperature. Click OK.

4)Click on Select Application Region and then click on the Select Geometry Entries box. In the selection toolbar, select Surface or Face. Screen select the surface. Click Add, OK then Apply.

5) Repeat steps 2-4 using Bottom Conv as the New Set Name, and select Bottom for the Surface Option in the 3rd step.

6)Repeat steps 2-4 using Edge Conv as the New Set Name, select Edge for the Surface Option in the 3rd step, and using Edge from the selection toolbar select the right edge for the Application Region.





1) Click on Temperature under the Nodal section.

2) Input Temp as the New Set Name and click on Input Data.

3) Input 100 as the Boundary Temperature. Click OK.

4) Click on Select Application Region and then screen select the left edge of the surface. Click Add, OK then Apply.





1) Under the Meshing tab, click on Uniform Mesh Seeds.

2)Set the Number of Elements to 4. Click on the Curve List box and screen select the bottom curve. Click on Apply.

3) Click on Surface Meshers. Click on the Select Surface List box. Screen click the surface and input 0.005 as the Global Edge Length. Click Apply.



1) Under the Analysis tab, select Entire Model. Ensure that the Job Name box is filled with a name and click Apply.

1) Click on XDB under the Access Results submenu. .

2) Ensure the appropriate Job Name is selected and click Apply.

3) CUnder the Results tab, select Fringe/Deformation.

4) Plot Temperature. Click Apply.





1) Using the governing equation below, we are able to create four elements on the surface.

2) Results: U1 = 100°C, U2 = 82.283°C, U3 = 70.732°C, U4 = 64.204°C, U5 = 62.053°C Nastran Results: U1 = 1.000000E+02°C, U2 = 8.448576E+01°C, U3 = 7.420589E+01°C, U4 = 6.832597E+01°C, U5 = 6.636874E+01°C (You can open the 'thermal_plate.f06' file with Notepad to view your results)

3) The small difference in these results is due to MD Nastrans non-linear analysis of the equation, making it more accurate.