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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.

Heat Transfer Illustration

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?

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  • $\begingroup$ You say $T_{amb}$ is controlled. Does that mean held constant? If so how could there be impact on $T_{amb}$ ? $\endgroup$
    – Keith McClary
    Commented Sep 3, 2019 at 1:45
  • $\begingroup$ Yes, it is held constant with the aid of a temperature chamber. Yes, you are right. I will reformulate the question. Thanks @KeithMcClary $\endgroup$
    – vtolentino
    Commented Sep 3, 2019 at 16:49
  • $\begingroup$ If it was regions of uniform temperature (eg., well stirred) separated by insulating barriers of known conductance, it is just the series resistance formulas. $\endgroup$
    – Keith McClary
    Commented Sep 3, 2019 at 20:39
  • $\begingroup$ @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. $\endgroup$
    – vtolentino
    Commented Sep 4, 2019 at 9:07
  • $\begingroup$ 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.) $\endgroup$
    – Keith McClary
    Commented Sep 4, 2019 at 13:22

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