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Steady-State 2D Axisymmetric Heat Transfer with Conduction
Introduction
The following example illustrates how to build and solve a conductive heat transfer problem using the Heat Transfer interface. The model, taken from a NAFEMS benchmark collection, shows an axisymmetric steady-state thermal analysis. As opposed to the NAFEMS benchmark model, the COMSOL Multiphysics simulation uses the kelvin temperature unit instead of degrees Celsius.
Model Definition
The modeling domain describes the cross section of a 3D solid as shown in Figure 1.
Figure 1: Model geometry and boundary conditions.
You set three types of boundary conditions:·
•
Prescribed heat flux
•
Insulation/Symmetry
•
Prescribed temperature
The governing equation for this problem is the steady-state heat equation for conduction with the volumetric heat source set to zero:
The thermal conductivity k is 52 W/(m·K).
Results
The plot in Figure 2 shows the temperature distribution.
Figure 2: Temperature distribution.
The benchmark result for the target location (r = 0.04 m and z = 0.04 m) is a temperature of 59.82 °C (332.97 K). The COMSOL Multiphysics model, using a default mesh with about 540 elements, gives a temperature of 332.96 K at the same location.
Reference
1. A.D. Cameron, J.A. Casey, and G.B. Simpson, NAFEMS Benchmark Tests for Thermal Analysis (Summary), NAFEMS, 1986.
Application Library path: Heat_Transfer_Module/Tutorials,_Conduction/cylinder_conduction
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  2D Axisymmetric.
2
In the Select Physics tree, select Heat Transfer>Heat Transfer in Solids (ht).
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select General Studies>Stationary.
6
Click  Done.
Geometry 1
Rectangle 1 (r1)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 0.08.
4
In the Height text field, type 0.14.
5
Locate the Position section. In the r text field, type 0.02.
Point 1 (pt1)
1
In the Geometry toolbar, click  Point.
2
In the Settings window for Point, locate the Point section.
3
In the r text field, type 0.02 0.02.
4
In the z text field, type 0.04 0.1.
5
In the Geometry toolbar, click  Build All.
Heat Transfer in Solids (ht)
Solid 1
1
In the Model Builder window, under Component 1 (comp1)>Heat Transfer in Solids (ht) click Solid 1.
2
In the Settings window for Solid, locate the Heat Conduction, Solid section.
3
From the k list, choose User defined. In the associated text field, type 52.
4
Locate the Thermodynamics, Solid section. From the Cp list, choose User defined. From the ρ list, choose User defined.
Temperature 1
1
In the Physics toolbar, click  Boundaries and choose Temperature.
2
In the Settings window for Temperature, locate the Temperature section.
3
In the T0 text field, type 273.15[K].
4
Select Boundaries 2, 5, and 6 only.
Heat Flux 1
1
In the Physics toolbar, click  Boundaries and choose Heat Flux.
2
In the Settings window for Heat Flux, locate the Heat Flux section.
3
In the q0 text field, type 5e5.
4
Select Boundary 3 only.
Mesh 1
In the Model Builder window, under Component 1 (comp1) right-click Mesh 1 and choose Build All.
Study 1
In the Home toolbar, click  Compute.
Results
Temperature (ht)
The default plot shows the temperature field on the 2D slice.
1
Click the  Zoom Extents button in the Graphics toolbar.
Add Predefined Plot
1
In the Home toolbar, click  Windows and choose Add Predefined Plot.
2
Go to the Add Predefined Plot window.
Add a predefined plot showing a 3D temperature distribution on a revolved surface; compare with Figure 2.
3
In the tree, select Study 1/Solution 1 (sol1)>Heat Transfer in Solids>Temperature (ht).
4
Click Add Plot in the window toolbar.
Results
Temperature 3D (ht)
1
In the Settings window for 3D Plot Group, type Temperature 3D (ht) in the Label text field.
2
Click the  Zoom Extents button in the Graphics toolbar.
Add another predefined plot showing isothermal contours in 2D section.
Add Predefined Plot
1
In the Home toolbar, click  Windows and choose Add Predefined Plot.
2
Go to the Add Predefined Plot window.
3
In the tree, select Study 1/Solution 1 (sol1)>Heat Transfer in Solids>Isothermal Contours (ht).
4
Click Add Plot in the window toolbar.
Results
Isothermal Contours (ht)
To obtain the temperature value at any point, just click at that point in the Graphics window; The result appears in the Table window at the bottom of the COMSOL Desktop.
Alternatively, you can create a Cut Point dataset and Point Evaluation feature as follows.
Cut Point 2D 1
1
In the Results toolbar, click  Cut Point 2D.
2
In the Settings window for Cut Point 2D, locate the Point Data section.
3
In the R text field, type 0.04.
4
In the Z text field, type 0.04.
Point Evaluation 1
1
In the Results toolbar, click  Point Evaluation.
2
In the Settings window for Point Evaluation, locate the Data section.
3
From the Dataset list, choose Cut Point 2D 1.
4
Click  Evaluate.
Table 1
1
Go to the Table 1 window.
The result is approximately 333 K.