How would a temperature profile in wall change if the rate of heat transfer increases

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

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?

• Do you mean ‘wall is good thermal conductor’? Jun 2, 2019 at 13:57

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