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Recently during a discussion with a colleague we got into an argument. The discussion involved imagining a heated solid body at some temperature $T$ which is immersed in a large fluid medium maintained at a temperature $t$. After a long enough time has passed the solid will ultimately come in thermal equilibrium with the surrounding fluid medium and attain the fluid temperature $t$.

My colleague argues that after the time when thermal equilibrium is reached the boundary of the solid body can be treated as insulated/adiabatic as there will be no heat transfer between the solid and the fluid.

Is his conclusion correct ?

Answers with mathematical explanation supporting or refuting the claim are a bonus.

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There won't be any heat transfer because the solid and the liquid are at the same temperature, so there would be no driving force for heat flow. This does not mean that the surface is insulated. The slightest difference in temperature between the two will cause heat to flow again.

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  • $\begingroup$ Thanks for the response. Seeing your bio, makes me want to further enquire about another doubt I have. Here it goes: If I want to model a cross-flow heat exchanger and I start with the separating plate between the two fluids, where I consider the plate as cuboidal (dimensions: $L,l,w$) in nature. In this configuration, I assume the two fluids are located at $z=0$ and $z=w$ plane flowing orthogonal to each other where I model them using third kind of b.c.(s). I am then left with four faces of the separating wall and these are at $x=0,L$ and $y=0,l$. $\endgroup$
    – Avrana
    Jul 25, 2020 at 12:12
  • $\begingroup$ What should be the boundary condition on these four lateral faces ? Would it be best to consider them insulated ? I hope you won't mind me digressing from the original question. $\endgroup$
    – Avrana
    Jul 25, 2020 at 12:13
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    $\begingroup$ I would treat the lateral faces as insulated. What is the nature of the flow, laminar or turbulent? And I would treat the very upper and very lower plates as insulated too. $\endgroup$ Jul 25, 2020 at 14:40
  • $\begingroup$ Its a miniaturuzed cross flow heat exchanger, so the flow regime will be laminar. Yes I meant even the top and lower plates. Can you elaborate the reasoning behind the recommendation for insulated faces ? $\endgroup$
    – Avrana
    Jul 25, 2020 at 14:58
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    $\begingroup$ I assume the large areas of heat transfer are the ones between the two fluids, and the other areas are negligible. $\endgroup$ Jul 25, 2020 at 15:23

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