Mixed Thermal Boundary Condition

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All,

I'm trying to model three thermal boundary conditions at a non-gray wall - external convection, external heat flux (irradiation), radiative cooling. When the absorptivity and emissivity are equal, I can simply use the mixed BC and determine an equivalent radiation sink temeprature to handle both the irradiation and radiative cooling terms. However, in this case the absorptivity and emissivity are not equal. Any suggestions on how to model this BC?

thanks DAVID