# Heat transfer between two isolated rooms/housings

Coming from an Electronic Engineering background I am currently a bit lost with a problem involving heat transfer. Essentially, I would like to know whether it is possible to roughly predict the final temperature of a sealed housing containing a heat source, which exchanges temperature with its surroundings. Refer to the following illustration where $$T_1$$, $$T_2$$ and $$T_\mathrm{amb}$$ denote respectively the temperature of the heat source, housing, and ambient/room.

Note: The housing is completely sealed and $$T_\mathrm{amb}$$ is controlled.

Without the sealed housing, I was able to roughly calculate the temperature using the thermal impedance of the heat source. However, with the addition of the housing, I cannot foresee how $$T_2$$ is going to suffer with the rather limited convective cooling. Any ideas about how it can be solved?

• You say $T_{amb}$ is controlled. Does that mean held constant? If so how could there be impact on $T_{amb}$ ? Commented Sep 3, 2019 at 1:45
• Yes, it is held constant with the aid of a temperature chamber. Yes, you are right. I will reformulate the question. Thanks @KeithMcClary Commented Sep 3, 2019 at 16:49
• If it was regions of uniform temperature (eg., well stirred) separated by insulating barriers of known conductance, it is just the series resistance formulas. Commented Sep 3, 2019 at 20:39
• @KeithMcClary What about the lack of convection? $T_2$ is increased by $T_amb$ and $T_1$, which in turn increases the surrounding temperature of the heat source, pushing its electronics to operated in a different operating point (e.g. more heat due to derating). In the worst case I thought that it could lead to a thermal runaway. Commented Sep 4, 2019 at 9:07
• Your system seems to be different from "regions of uniform temperature (eg., well stirred) separated by insulating barriers of known conductance", but I don't understand what you are describing. (I'm going on a trip so may not be able to comment.) Commented Sep 4, 2019 at 13:22