I have solved it and confirmed with the simulation. The simulation values are T_cont=307.59K (recalculated) and Ty=290.72K which coincide with analytical solution. Note that the rate of Q_rad is determined by the heat radiation coefficient. (x and y are the same materials as A and B in the...
Sir, to be honest, not yet. I have just tried to do simulation (comsol multiphysics) again and it appeared to be T_contact=306K.
This is my attempt (since I am not that good in heat transfer, main equation might be wrong that is where I am stuck).
-Qrad-Qconv=k_x/L(308.13-T_contact) and after...
There are similar problems with heat conduction only where for example, right side of the bar also has a certain temperature or in-contact with a hot material. However, in this case diffusion and convection occurs on the right side of the bar, more precisely on the Y material. I guess we have to...