## One Dimensional Steady Heat Transfer with Radiation

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.

**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:

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 as 926.97 K, which is the exact benchmark value to four significant digits.

**Source:** **1.** A.D. Cameron, J.A. Casey, and G.B. Simpson, NAFEMS Benchmark Tests for Thermal Analysis (Summary), NAFEMS, Glasgow, 1986. / **2.** COMSOL Multiphysics