In this paper, we analyse the numerical approximation of the heat transfer problem between two subdomains that we will consider filled with a fluid and separated by a thin solid wall. First of all, we state the problem in the whole domain with discontinuous physical properties. As an alternative and under certain assumptions on the separating walls, a classical Robin boundary condition between the fluid domains is obtained, thus eliminating the solid wall, and according to which the heat flux is proportional to the temperature difference between the two subdomains. Apart from discussing the relation between both approaches, we consider their numerical approximation, considering different alternatives for the first case, that is, the case in which temperatures are also computed in the solid wall.
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