# Steady state thermal-electric with radiation heat transfer (very hot) will not converge

The use of a thermal-electric system to model the performance of a glowing, thermoelectrically heated filament in a vacuum in which radiation heat transfer dominates can be problematic. At times the sequential solutions of the radiosity solver (used for radiation heat transfer heat transfer calculations) and those of the thermal conduction solids are reluctant to converge, even after extensive experimentation with a number of settings that affect the way the calculations are performed. The problem can become worse as surfaces reach temperatures seen in glowing filaments (~2500 C).

A legacy strategy for calculating radiation heat transfer, called the AUX12 radiation matrix method, is available in MAPDL. The technology however is not natively exposed in Mechanical - a command object is required. One documented limitation of the AUX12 method is that the surface emissivity may not be temperature dependent. However, when heating a filament to the point that it glows, temperature dependent emissivity can be expected.

The attached 2019R3 project archive uses a command object to overcome this limitation, allowing use of the sometimes more numerically stable AUX12 radiation matrix when the temperature dependency of emissivity cannot be neglected. After an initial calculation is made using the AUX12 radiation matrix with a constant emissivity, the facets of the external surface are grouped by calculated temperature. Each group is then reassigned an emissivity from a lookup table (emissivity versus temperature). A new radiation view factor matrix is then created with this new distribution of emissivity values. The heat transfer calculation is then repeated a second time. After a third iteration of this process, the temperature change between the second iteration and the third is very small, suggesting that another iteration is not necessary.

The process is depicted in the images below.

The first iteration is done with constant emissivity (illustrated by the single color of the surface facets):

This gives a temperature distribution:

These temperatures are then used to define different values of emissivity for different facets from a lookup table. Each color in the image below has a different value of emissivity:

After resolving, the calculated temperature changes somewhat:

After another iteration, the final temperature is not much different:

--Bill

## Comments

Thanks!