I Heat transfer coefficient and convection

[fluidistic]

I would like to fully understand two parameters involved in convection heat transfer systems. I have read the document https://fenicsproject.org/pub/tutorial/sphinx1/._ftut1005.html, and I am interested in the parameters $r$ and $s$ in eq. 69.

As far as I understand, when one solves the heat equation in a solid and that there is convection occurring on some side(s) of the solid, then one can model this convection effect as a Robin boundary condition on the interfaces air/solid. They take the form $-\kappa \frac{dT}{dn}=r(T-s)$.
Where $s$ seems the be the temperature of the fluid touching the surface and $r$ is the heat transfer coefficient. Is this correct?
I do not quite understand how to estimate or compute $r$. I have seen tables on the Internet of values of heat transfer coefficient, for air and water for example, as if it has a fixed value. I would have thought that $r$ would represent something along the quantity of heat that air can remove/induce into that surface area element into which it is in contact (based on the units of $r$). If that's the case then $r$ should not depend on the geometry of the solid, but it could depend on the relative humidity of air, for instance. Is that so?

Then in a real case, when we are blowing over a hot surface in order to cool it down, does $r$ change? If so, why? $s$ would change to near room temperature instead of being above room temperature. What about $r$?

 

[Chestermiller]

I don't know why you feel that s changes, since this is. simply the fluid temperature in the bulk fluid outside the boundary layer. On the other hand, the heat transfer coefficient r varies increases with the intensity of the flow, since this thins the boundary layer. If you are dealing with laminar flow, then r can be determined as a function of position along the surface and flow intensity. For turbulent flow, it can be estimated using CFD with a turbulence model. But, in many cases, experiments need to be carried out to develop a dimensionless correlation for estimating the heat transfer coefficient. For more details, see Transport Phenomena by Bird, Stewart, and Lightfoot.

 

[fluidistic]

I don't know why you feel that s changes, since this is. simply the fluid temperature in the bulk fluid outside the boundary layer. On the other hand, the heat transfer coefficient r varies increases with the intensity of the flow, since this thins the boundary layer. If you are dealing with laminar flow, then r can be determined as a function of position along the surface and flow intensity. For turbulent flow, it can be estimated using CFD with a turbulence model. But, in many cases, experiments need to be carried out to develop a dimensionless correlation for estimating the heat transfer coefficient. For more details, see Transport Phenomena by Bird, Stewart, and Lightfoot.

I thought s would change because I thought it was equal to the temperature of the fluid touching the solid.

 

[fluidistic]

Thanks, I've seen the reference and it seems a nightmare to estimate $r$. At least I now know it doesn't just depend on the fluid's properties, but also on the geometry of the solid and whether or not there is forced convection, etc.
And you were right about $s$, it seems to be the "bulk" fluid temperature, not the temperature of the fluid that touches the solid (I had to check other references such as p. 68 of "Finite Element Analysis with Error Estimators: An Introduction to the FEM.. " by Akin to be 100% of this.)