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Wall heat transfer boundary condition

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Old   October 15, 2015, 06:29
Default Wall heat transfer boundary condition
Francesco Capuano
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I would like to model a radiative and convective heat transfer through a wall.
In practice, I would need an equilibrium boundary condition of the type

\dot{q_w} = -\lambda \left(\dfrac{\partial T}{\partial n}\right)_w = \sigma\epsilon \left(T_w^4-T_e^4\right) + h\left(T_w-T_e \right),

where T_w is the wall temperature and T_e is the environment temperature outside the domain. The wall temperature would then be calculated from (a discretized version of) the above equation to yield the heat flux exchanged at the wall.

Is there any available boundary condition to model such problem?
Or, did anyone encounter the same issue (and maybe developed a customized b.c.)?

Many thanks in advance.
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Old   October 18, 2015, 11:52
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A mixed boundary condition (i.e. groovyBC) should do the trick. I'm sure you can find a copy&paste solution here on the forum.
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Old   October 19, 2015, 06:11
Default GroovyBC
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We successfully modeled it with this implementation in file 'T' in directory '0'

type groovyBC;
refValue uniform 288;
refGradient uniform 0;
valueFraction uniform 1;
value uniform 288;
valueExpression "0";
gradientExpression "h*(T-Tinf)+(sigma)*E*(T*T*T*T-Tinf*Tinf*Tinf*Tinf)";
fractionExpression "0";
evaluateDuringConstruction 0;

After, we was forced to change the string thermoType>energy from 'sensibleEnthalpy' to 'sensibleInternalEnergy' in file 'thermophysicalProperties' in directory 'constant' for other reasons and we obtained a floating point exception error.
What is the problem? Is there an alternative method to implement heat transfer written above?
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heat transfer, radiation, wall boundary condition

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