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Steady-State 2D Heat Transfer with Conduction
Introduction
This example shows a 2D steady-state thermal analysis including convection to a prescribed external (ambient) temperature. The example is taken from a NAFEMS benchmark collection (see Ref. 1).
Model Definition
This example considers 0.6 m-by-1.0 m domain. For the boundary conditions:
•
The left boundary is insulated.
•
The lower boundary is kept at 100°C.
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The upper and right boundaries are convecting to 0°C with a heat transfer coefficient of 750 W/(m2·°C).
In the domain use the following material property:
•
The thermal conductivity is 52 W/(m·°C).
Results
The plot in Figure 1 shows the temperature field in the modeling domain.
Figure 1: Temperature distribution resulting from convection to a prescribed external temperature.
The benchmark result for the target location (x = 0.6 m and y = 0.2 m) is a temperature of 18.25°C. The COMSOL Multiphysics model, using a mapped mesh with 9 × 15 quadratic elements, gives a temperature of 18.265°C.
Reference
1. A.D. Cameron, J.A. Casey, and G.B. Simpson, NAFEMS Benchmark Tests for Thermal Analysis (Summary), NAFEMS, Glasgow, 1986.
Application Library path: COMSOL_Multiphysics/Heat_Transfer/heat_convection_2d
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.
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 0.6.
4
Click  Build All Objects.
Heat Transfer in Solids (ht)
Temperature 1
1
In the Model Builder window, under Component 1 (comp1) right-click Heat Transfer in Solids (ht) and choose Temperature.
2
Select Boundary 2 only.
3
In the Settings window for Temperature, locate the Temperature section.
4
In the T0 text field, type 100[degC].
Heat Flux 1
1
In the Physics toolbar, click  Boundaries and choose Heat Flux.
2
Select Boundaries 3 and 4 only.
3
In the Settings window for Heat Flux, locate the Heat Flux section.
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From the Flux type list, choose Convective heat flux.
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In the h text field, type 750.
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In the Text text field, type 0[degC].
Solid 1
1
In the Model Builder window, 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.
No other material properties enter into the domain equations for this stationary model.
Mesh 1
Mapped 1
1
In the Mesh toolbar, click  Mapped.
2
In the Settings window for Mapped, click  Build All.
Study 1
In the Home toolbar, click  Compute.
Results
Surface
1
In the Model Builder window, expand the Results>Temperature (ht) node, then click Surface.
2
In the Settings window for Surface, locate the Expression section.
3
From the Unit list, choose degC.
Temperature (ht)
1
Click the  Zoom Extents button in the Graphics toolbar.
The first default plot group shows the temperature field; compare with Figure 1.
The benchmark value for the temperature at x = 0.6 m and y = 0.2 m is 18.25°C. To compare this value with that from the simulation, evaluate the temperature in this position.
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 X text field, type 0.6.
4
In the Y text field, type 0.2.
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
Locate the Expressions section. In the table, enter the following settings:
Expression
Unit
Description
T
degC
Temperature
5
Click  Evaluate.
Table
1
Go to the Table window.
The result should be close to 18.265°C.