For the first and second problems, it is not specified that it’s a steady-state conduction, as it would be more logical that the metals change temperature as there is a heat exchange between them. This was probably assumed, but it would be nice to have it explicitly said (the resolution was confusing without knowing that fact).
Thank you for the video and I have a question. Isn't the thermal resistance in this particular aluminium rod represented by the length divided by the thermal conductivity times the area(L/(k*A))? It does seem logical when the area gets bigger, the resistance becomes smaller. I learned that in school and wanted to check if it is right.
Can someone tell me at 14:53 why and is it viable to consider the heat current equal for the both sides. I mean the length and temperatures are different but still can we consider them equal?