# Essay 5 Tutorial for a Three-Dimensional Heat Conduction Problem Using ANSYS Workbench

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1 Essay 5 Tutorial for a Three-Dimensional Heat Conduction Problem Using ANSYS Workbench 5.1 Introduction The problem selected to illustrate the use of ANSYS software for a three-dimensional steadystate heat conduction problem is exhibited in Fig Fig Geometry of the selected three-dimensional solid for the heat conduction analysis The front face of the figure, shown in gray tones, is heated uniformly by a paste-on heating element. The heat flux is uniform over that face. All of the other five faces of the solid exchange heat by convection with the surrounding air environment. The temperature of the air is. The convective heat transfer coefficients on the two vertical sides are equal and have values of. On the vertical face at the far end of the solid, the heat transfer coefficient is. The top and bottom faces of the solid have a heat transfer coefficient of. The fact that the top and bottom faces have the same heat transfer coefficient means that the temperature of the solid is symmetric about a horizontal plane that bisects the height of the solid. That plane is indicated by the red lines in the figure. Similarly, the fact that the two sides have identical heat transfer coefficients creates a symmetry plane identified by the yellow lines. These planes subdivide the solid into four quadrants such that the temperature solution in each quadrant is identical. Therefore, it is only necessary to solve the heat conduction problem in one of the quadrants. The upper-right-hand quadrant will be selected for this purpose and is displayed in Fig

2 Fig Upper-right-hand quadrant of the solid of Fig. 5.1 For this newly defined geometry, it is appropriate to restate the boundary conditions. Of particular note are the bottom and left-hand faces of this new geometry. Both of these faces are symmetry planes. Since the temperatures above and below a symmetry plane are equal, there can be no heat transfer across the bottom face of the solid of Fig A similar conclusion follows for the left-hand face. As was stated in Essay 4, a no-heat-transfer surface of a solid is the default boundary condition for the numerical solution. The boundary conditions for the front face,, remains as before. On the right-hand face,, and on the end face,. Also, as before, the value of on the top face is. The desired results to be extracted from the ANSYS solution are: (a) A color-contour diagram showing the temperature distributions on the top, right-hand side, and far-end faces (b) The temperature distribution along the length of the solid at the symmetry point which is created by the intersection of the two symmetry planes 5.2 ANSYS Workbench Specifying problem physics: Select Steady-State Thermal from the toolbox to the left and drag it to the project schematic window (inside the green dashed box that has appeared) Renaming the project: Double-click on the project name, shown at the very bottom of the project schematic, and type tutorial

3 5.3 Engineering Data Editing engineering data: Double-click on engineering Data or right-click on it, and select Edit. Specifying material properties: Double click on Click here to add a new material and type the new materials name. From the Toolbox to the left, select Isotropic Thermal Conductivity and drag it to the properties list at the bottom of the window. Enter the conductivity value. Click on Return to Project from the toolbar. 5.4 ANSYS DesignModeler Entering DesignModeler: Edit the Geometry in project schematic by either doubleclicking on it, or right-clicking and selecting Edit. Creating the two-dimensional sketch: Select XY Plane from the tree outline to the left, and click on the New Sketch icon in the toolbar. Select the Sketching tab. Draw a rectangle using the Rectangle tool. Select the Dimensions tab, and use Horizontal and Vertical tools to assign the correct dimensions to the rectangle. 5.3

4 Creating the three-dimensional block: From the Tree Outline in the modeling tab, select the sketch, and click on Extrude to add an extrusion to the geometry. In the appeared Details View enter the Depth value. Click on Generate icon from the toolbar. Close the DesignModeler window. 5.5 ANSYS Mechanical Entering the ANSYS Mechanical: From the project schematic, double-click on Model. Selecting the material: From the Outline tree view, select the created solid, and select the desired material from Details of Solid window. Specifying element size: Select Mesh from the Outline tree view. Enter the desired element size in the Details of Mesh window. Generating the mesh: From the toolbar select Generate Mesh. Applying boundary conditions: Select the analysis from the Outline tree view, and the toolbar will change to display all the available boundary conditions. On the symmetry surfaces, there is no need to apply boundary conditions because, by default, the no-heat transfer condition is automatically applied. Applying heat flux BC: Select Heat then Heat Flux from the toolbar. 5.4

5 Select the front face > click on Apply > enter the heat flux value. Applying convection BCs: From the toolbar, select Convection. Select the right-hand face and then click on Apply. Enter the heat transfer coefficient as Film Coefficient. On the top and far-end faces, repeat the steps that were outlined for the right-hand face. 5.6 ANSYS Solver Select Solve from the toolbar. (This starts the solution) 5.4 ANSYS Post-Processor Displaying color-contour diagrams of temperature Select the solution. From the toolbar, select Thermal > Select Temperature. Right-click on the newly-created Temperature item in the outline view, and select Evaluate All Results. Rotate the geometry using the graphic tools on the right-hand side panel to reveal the appropriate faces. (top, far-end, and right-hand side respectively, one at a time) 5.5

6 In order to save the resulting picture as an image file, select the image icon, and then Image to File, then type in the file name, and select the file type. (The colors that appear on a color-contour diagram are keyed to a color stripe displayed at the left-hand side of the diagram. The temperature range exhibited are the lowest and highest temperatures obtained by the solution. Usually, there are nine color blocks in the stripe.) Displaying the temperature distribution along the symmetry axis of the solid In order to plot the temperature variation along the symmetry axis of the solid, we will create a path on the axis, and then map temperature values onto the path, and then plot the resulting map. Defining the path Select the Model. Select Construction Geometry from the toolbar. Select Path from the now-changed toolbar. Change the path type from Two points to Edge. Select the symmetry axis, and click on apply. Mapping the temperature distribution on the path Select the solution then, very similar to contour plot, select Thermal and then Temperature. Change the scoping method from Geometry Selection to Path. 5.6

7 Select the created path as Path. Displaying the graph Right-click on the newly-created object under the solution, and select Evaluate All Results. 5.7

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