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Steady-State 1D Heat Transfer with Radiation
Introduction
This example shows a 1D steady-state thermal analysis including radiation to a prescribed ambient temperature. The example is taken from a NAFEMS benchmark collection (Ref. 1).
Model Definition
This 1D model has a domain of length 0.1 m. The left end is kept at 1000 K, and at the right end there is radiation to 300 K. The model uses the following material properties:
•
For the radiation, the emissivity, ε, is 0.98.
•
The thermal conductivity is 55.563 W/(m·K).
Results
The following plot shows the temperature as a function of position:
Figure 1: Temperature as a function of position.
The benchmark result for the right end is a temperature of 927.0 K. The COMSOL Multiphysics model, using a default mesh with 15 elements, gives a temperature at the end of 926.97 K, which is the exact benchmark value to four significant digits.
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_radiation_1d
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  1D.
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
Interval 1 (i1)
1
In the Model Builder window, under Component 1 (comp1) right-click Geometry 1 and choose Interval.
2
In the Settings window for Interval, locate the Interval section.
3
In the table, enter the following settings:
Coordinates (m)
0
0.1
4
Click  Build All Objects.
Heat Transfer in Solids (ht)
Temperature 1
1
In the Physics toolbar, click  Boundaries and choose Temperature.
2
Select Boundary 1 only.
3
In the Settings window for Temperature, locate the Temperature section.
4
In the T0 text field, type 1000.
Surface-to-Ambient Radiation 1
1
In the Physics toolbar, click  Boundaries and choose Surface-to-Ambient Radiation.
2
Select Boundary 2 only.
3
In the Settings window for Surface-to-Ambient Radiation, locate the Surface-to-Ambient Radiation section.
4
From the ε list, choose User defined. In the associated text field, type 0.98.
5
In the Tamb text field, type 300.
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 55.563.
Initial Values 1
1
In the Model Builder window, click Initial Values 1.
2
In the Settings window for Initial Values, locate the Initial Values section.
3
In the T text field, type 1000.
Mesh 1
In the Model Builder window, under Component 1 (comp1) right-click Mesh 1 and choose Build All.
Study 1
In the Study toolbar, click  Compute.
Results
The benchmark value for the temperature at the right end is 927.0 K. To compare the value from the simulation, evaluate the temperature at this position.
Point Evaluation 1
1
In the Results toolbar, click  Point Evaluation.
2
Select Boundary 2 only.
3
In the Settings window for Point Evaluation, click  Evaluate.