Middle East Technical University Mechanical Engineering Department ME 413 Introduction to Finite Element Analysis Spring 2015 (Dr.

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1 Middle East Technical University Mechanical Engineering Department ME 413 Introduction to Finite Element Analysis Spring 2015 (Dr. Sert) COMSOL 1 Tutorial 2 Problem Definition Hot combustion gases of a furnace are flowing through a chimney made of concrete (k = 1.4 W/(m ). The flow section of the chimney is 10 cm 10 cm, and the thickness of its wall is 10 cm. The average temperature of the hot gases in the chimney is T in = 300, and the average convection heat transfer coefficient inside the chimney is h in = 70 W/(m 2 ). The chimney is losing heat from its outer surface to the ambient air at T out = 20 by convection with a heat transfer coefficient of h out = 21 W/(m 2 ). Taking advantage of the symmetry, determine the temperature distribution inside the chimney and the rate of heat passing through a 1 m long section of the chimney. Reference : Y. Cengel, Heat and Mass Transfer A Practical Approach, Mc Graw-Hill, y 30 cm x 30 cm h in, T in h out, T out 10 cm x 10 cm k x 1 1 COMSOL 4.3 is used to prepare this tutorial 1

1. Start COMSOL. Select 2D and click the Next arrow. Select Heat Transfer in Solids and click the Next arrow. Select Stationary and click the Finish button. 2. In the Model Builder (MB) tab right click Geometry 1 and select Square.

2 1. Start COMSOL. Select 2D and click the Next arrow. Select Heat Transfer in Solids and click the Next arrow. Select Stationary and click the Finish button. 2. In the Model Builder (MB) tab right click Geometry 1 and select Square. An item called Square 1 will be created in the MB. In the Square tab, set Type to Solid, Side length to 0.03 m and Base to Corner at (0,0). Click Build Selected in the Square tab. 2

3 3. Repeat Step 2 to create the inner square. Its Side length is 0.1 m and base corner is at (0.1, 0.1). Created squares will look like this 3

4 4. To create a hole inside the larger square select both squares using the Ctrl key and press the Difference button on the toolbar. If the Difference button is not visible click on Geometry 1 of the MB tab. Problem domain is now created as a square with a square hole in it. 4

5 5. In the MB tab right click Material and select Material. In the Material tab enter 1.4 W/(mK) for Thermal Conductivity. For this steady problem density or heat capacity are not necessary, so leave them empty. 5

6. By default all boundaries are assigned Thermal Insulation BC, which needs to be changed. To define new BCs, right click Heat Transfer in Solids in the MB tab and select Convective Cooling.

6 6. By default all boundaries are assigned Thermal Insulation BC, which needs to be changed. To define new BCs, right click Heat Transfer in Solids in the MB tab and select Convective Cooling. An item called Convective Cooling 1 will be created. Right click on it and rename it as Outside Convection. In the Graphics tab select four edges of the outer square using the Ctrl key and click the Add to Selection button of the Convective Cooling tab. Enter the h value as 21 W/(m 2 K) and T ext as K (= 20 o C). 6

7 7. Repeat the previous step to create the Inside Convection BC. Values for h and T ext are 70 W/(m 2 K) and K (= 300 o C)., respectively. In the Geometry tab select the edges of the inside square. 7

8 8. Click Mesh 1 in MB tab. In the Mesh tab do not change the default settings. Click Build All. A triangular mesh will be created. Number of elements can be seen in the Messages tab. 8

9 9. Click Study 1 in the MB tab. Click the Compute button in the Study tab. Solution will finish in a couple of seconds and the following temperature contour will be generated. 9

10 10. To see the temperatures in o C, expand Results in the MB tab. Expand Temperature and click on Surface 1. In the Surface tab change Unit from K to degc. Click the Plot button. 10

11 11. To see the temperature distribution as a 3D plot, right click on Surface 1 under Results -> Temperature of the MB tab and select Height Expression. 3D plot will be seen in the Graphics tab. 11

12 12. To view the temperature contours as lines as well as the path of heat, click Isothermal Contours under Results of MB tab. 12

13 13a. To visualize the varıation of temperature along the line between points (0.15,0) and (0.15,0.1), first right click Data Sets under Results of MB tab and select Cut Line 2D. Enter the end points coordinates of the line and press the Plot button. Cut line will be shown in the Graphics tab. 13

14 13b. Right click on Results of MB tab and select 1D Plot Group. Set Data set to the newly generated Cut Line 2D 1 14

15 13c. Right click to the newly generated 1D plot Group 3 in the MB tab and select Line Graph. Change Unit to degc and press the Plot button. The variation of temperature along the cut line will be shown in the Graphics window. 15

To set the value we want to integrate, press Replace Expression button and select Heat Transfer in Solids -> Total normal heat flux.

16 14. To calculate the amount of heat passing from the hot gases to the chimney, right click on Derived Values under Results of MB tab and select Line Integration. Select the 4 edges of the inner square using the Ctrl key and press the Add to Selection button. To set the value we want to integrate, press Replace Expression button and select Heat Transfer in Solids -> Total normal heat flux. Press the Evaluate button. The result will be shown in the Messages window. This is amount of heat per unit length of chimney, i.e. W/m. 16

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