 Problem Statement

There is given a rectangular bar which is composed of two different materials, X and Y. Crosssection is 1mm width, 1mm of thickness and 3mm length for material X and 4.4mm length for material Y. Assume that all the sides are thermally insulated except left side of the bar where material X has temperature of 308.13K and ambient T=283.13K and right surface of the bar where Y material experiences diffusion and convection . X and Y materials have thermal conductivities of 0.3 W/mK and 0.014W/mK, respectively. Surface emissivity (ε=0.9) and convection ht coefficient h=2W/m^2K. We need to find contact surface temperature.
Ht radiation coefficient is given as h_r = 6W/m^2K.
 Relevant Equations

q=εσ(T_h^4T_c^4)
q_total=q_conv+q_cond+q_radiation
q_rad=h_radA(T_surT_amb)
There are similar problems with heat conduction only where for example, right side of the bar also has a certain temperature or incontact 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 use radiation heat transfer.
I did simulation of this problem and T_{contact} was around 304K. Now I need to compare simulation with theoretical value. However, I still could not get the answer
q_cond=kA/L(T_{x}T_{contact})
I did simulation of this problem and T_{contact} was around 304K. Now I need to compare simulation with theoretical value. However, I still could not get the answer
q_cond=kA/L(T_{x}T_{contact})
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