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Given the system below, how would the temperature profile in the wall change if the heat transfer in Fluid II was very fast?

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If the heat transfer in Fluid II is very fast, then the T-profile for $\ce{T_{2∞}}$ would experience less resistance and hence have a more linear slope. However, I don't understand how this would affect the T-profile inside the wall? Wouldn't Fluid II have the same temperature and interact with the interface at the same point, meaning nothing changes within the wall?

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  • $\begingroup$ Do you mean ‘wall is good thermal conductor’? $\endgroup$
    – xrfxlp
    Commented Jun 2, 2019 at 13:57

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If the heat transfer in fluid 2 is fast, the thickness of the boundary layer wall - fluid 2 is very small (the 'not so linear' part of the temperature profile on that side)

One can then approximate that the temperature of fluid 2 directly at the wall is equivalent to the bulk temperature.

So the temperature profile through the wall would be steeper, indicating a larger overall heatflux - see it as a self fullfilling prophecy: fast heat transfer will allow you to transfer heat faster

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