Heat Generation Due to Electrical Current

Given: A stainless steel wire is passing a current of 200 A. The wire is 1 m long and 3 mm in diameter. The wire is submerged in a 110°C fluid. the convection coefficient between the fluid and the wire is 0.004 W/(mm 2 °C)

Material Properties:

Thermal conductivity: 0.019 W/(mm°C)

Resistivity: 0.0007 W mm

Find: The temperature at the center of the wire.

This example only covers setting up and performing the analysis. For instructions on building the model, see Creating the Heat Generation Due to Electrical Current Model. If you have not built the model, you can open the heatgen_input.ach file in the Models subfolder of the Autodesk Simulation installation directory.

Design Scenario 1 will be the electrostatic analysis to determine the current flow, and Design Scenario 2 will be the heat transfer analysis to determine the temperature distribution.

  1. Knowing the resistivity of the material and the length and cross-sectional area of the wire, we can calculate the resistance from the equation R=(ρL)/A. For our 10 mm long section, this value is 9.9 x 10 -4 ω. Using Ohm's Law, we can determine that there is a 0.198 V difference across the wire. We will add nodal applied voltages at the ends of the wire to create this voltage difference.
  2. Use Selection Shape Rectangle and Selection Select Vertices to select the nodes along the top edge of the model. Right-click and select Add Nodal Applied Voltages. Type 0.198 in the Magnitude field, type 1e8 in the Stiffness field and click OK of the model. Select the nodes along the bottom edge of the model. Right-click and select Add Nodal Applied Voltages. Type 0 in the Magnitude field, type 1e8 in the Stiffness field and click OK.
  3. In the tree view, right-click the Element Type heading for Part 1 and select the 2D command.
  4. In the tree view, right-click the Element Definition heading for Part 1 and select the Edit Element Definition command. Select the Axisymmetric option in the Geometry Type drop-down box and click OK.
  5. In the tree view, right-click the Material heading for Part 1 and select the Edit Material command. Press the Edit Properties button. The electrical conductivity is the inverse of the resistivity value. Type 1428.57 in the Electrical Conductivity field and press the OK button twice.
  6. Select Analysis Analysis Run Simulation to analyze the model and view the results in the Results environment.
  7. Use Results Contours Voltage and Current Voltage to verify that the voltages vary linearly from 0 to 0.198V. (If not, the stiffness of the applied voltages needs to be increased.)
  8. To verify that we are modeling the equivalent of 200 A running through this wire, we will view the current flow. Select Results Contours Voltage and Current Current Rate Through Face. Select Results Contours Settings Smooth Results to deactivate the smoothing. Use Selection Select Faces and Selection Shape Rectangle to select the bottom edge of the model. (Be sure to draw the rectangle selection smaller than half of the bottom element; otherwise, the outlet face of the bottom elements are selected with a net current of 0.) Select Results Inquire Inquire Current Results and select the Sum option in the Summary drop-down box. The results should be close to 200 A.
  9. Use Tools Environments FEA Editor to move back to the FEA Editor environment.
  10. Next, run the heat transfer analysis to see what affect the current has on the temperature results. Do it in a separate Design Scenario. A quick way to get a new design scenario and analysis type in one step is to change the analysis type for the current Design Scenario 1. So, right-click Analysis Type in the tree view and choose Set Current Analysis Type Thermal Steady-State Heat Transfer. You are prompted Would you first like to copy your design scenario into a new one. Press Yes. This will create Design Scenario 2, set to heat transfer analysis, with a copy of the complete mesh.
  11. In the tree view, right-click the Element Definition heading for Part 1 and select the Edit Element Definition command. Select the Axisymmetric option in the Geometry Type drop-down box.
  12. In the tree view, right-click the Material heading for Part 1 and select the Edit Material command. Press the Edit Properties button. Type 0.019 in the Thermal Conductivity field and click OK twice. (Mass density and specific heat are not required in a steady state heat transfer analysis unless the part is a fluid.)
  13. Right-click the heading for Part 1 and select Add Heat Generation. Type 1 in the Internal Heat Generation field. This will act as a flag to tell the processor to use the heat generation values calculated from the electrostatic analysis for this part. Click OK.
  14. Click the + next to the Surface heading and right-click the Surface 2 heading. Select Add Surface Convection Load.
  15. Type 0.004 in the Temperature Independent Convection Coefficient field, type 110 in the Temperature field and click OK.
  16. Specify the file to use for the Joule heating. Right-click the Analysis Type heading in the tree view and select the Edit Analysis Parameters command. On the Electrical tab, activate the Use electrostatic results to calculate Joule Effects flag check box and click Browse. Navigate to the .efo file from the electrostatic analysis, which is located in the model's ds_data\1 folder and is named ds.efo. Click the Open button. Click OK to complete the Analysis Parameters.
  17. Select Analysis Analysis Run Simulation to analyze the model and view the results in the Results environment.
  18. The theoretical solution is 231.6 degrees in the center compares favorably with the calculated results of 232.2 degrees.

An archive of the model heatgen.ach is located in the Models subdirectory of the Autodesk Simulation installation directory. To analyze the model, you must go into the Electrical tab of the Analysis Parameters dialog and navigate to the proper location of the .efo file.

Reference:

J. P. Holman, Heat Transfer 7th Edition. McGraw Hill. Example 2-4 p. 42.

Parent topic: Electrostatic Current and Voltage