# Conceptual question on heat transfer at steady state after a heated body is immersed in a fluid medium at low temperature

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.

• 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 $y=0,l$. Jul 25, 2020 at 12:12