Equation for Convective Heat Transfer

Question

In this Wikipedia link: https://en.wikipedia.org/wiki/Convection_(heat_transfer)#Convective_heat_transfer on convective heat transfer, the following equation for convection is provided: $$\dot{Q}=hA(T-T_f)^b$$ where it is claimed that $b$ is some "scaling exponent". However, based solely on dimensional grounds, wouldn't $b$ have to be equal to $1$ in order to the units on both sides to match?

Answer 1

I always met this equation with $b=1$ as a simple model for convection, and thus $[h] = \frac{W}{m^2 \, K}$. This simple equation comes as a semi-empirical equation, thus it's possible that other correlations provide better results.

If you're using a dimensional version of the equation with $b \ne 1$, I guess that you need to take it into account in the physical dimensions of $[h] = \frac{W}{m^2 \, K^b}$.

Anyway, even in the classical form of heat transfer by convection, non-linear dependency on $\Delta T$ could be obtained, with a definition of $h$ as a function of $\Delta T$, through some non-dimensional numbers characteristic of the problem, like Rayleigh or Grashof numbers.