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Middle East Technical University Mechanical Engineering Department

ME 413 Introduction to Finite Element Analysis Spring 2015 (Dr. Sert)

COMSOL1 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 𝑇𝑖𝑛 = 300 ℃, and the average

convection heat transfer coefficient inside the chimney is ℎ𝑖𝑛 = 70 W/(m2℃). The chimney is losing

heat from its outer surface to the ambient air at 𝑇𝑜𝑢𝑡 = 20 ℃ by convection with a heat transfer

coefficient of ℎ𝑜𝑢𝑡 = 21 W/(m2℃) . 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, 2006.

1 1 COMSOL 4.3 is used to prepare this tutorial

ℎ𝑖𝑛, 𝑇𝑖𝑛 ℎ𝑜𝑢𝑡, 𝑇𝑜𝑢𝑡

30 cm x 30 cm

10 cm x 10 cm 𝑘

𝑥

𝑦

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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.

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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

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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.

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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.

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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/(m2K) and Text as 293.15 K (= 20 oC).

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7. Repeat the previous step to create the “Inside Convection” BC. Values for h and Text are 70 W/(m2K)

and 573.15 K (= 300 oC)., respectively. In the “Geometry” tab select the edges of the inside square.

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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.

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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.

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10. To see the temperatures in oC, 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.

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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.

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12. To view the temperature contours as lines as well as the path of heat, click “Isothermal Contours”

under “Results“ of MB tab.

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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.

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13b. Right click on “Results” of MB tab and select “1D Plot Group”. Set “Data set” to the newly

generated “Cut Line 2D 1”

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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.

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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.