You can try to create an interior surface at the bottom of the heat absorber, to allow heat and mass flow through it. This can be done by appending the mesh in the existing domain. Run the simulations for some iterations and use Fluxes in Results > Fluxes. There you can see the option for Radiation heat transfer rate and select the interior surface.
Now for natural convection heat loss, choose Total heat tansfer rate. Subtract Radiation heat from the Total heat, assuming there is no forced convection in the heat absorber. Total heat transfer = Natural convection + Radiation heat through the interior surface. Of course, the viscous dissipation loss will be included, but can be neglected here.
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