Nobody measures a film coefficient in the field. They correlate it — and every correlation is written in dimensionless groups, because a group that carries no units carries across scales, fluids and unit systems without being re-fitted. Five run this chapter, and the exam skill is telling them apart by what they COMPARE.

Reynolds, $\mathrm{Re} = \dfrac{\rho v D}{\mu}$ — density $\rho$ (say rho) in $\mathrm{kg/m^3}$, speed $v$ in m/s, a characteristic length $D$ in metres, viscosity $\mu$ (mu) in $\mathrm{Pa \cdot s}$. It weighs a fluid's inertia against its stickiness and decides laminar or turbulent. It knows nothing about heat.

Prandtl, $\mathrm{Pr} = \dfrac{\mu c_p}{k}$ — viscosity, specific heat $c_p$ in $\mathrm{J/(kg \cdot K)}$, and the FLUID's conductivity $k$ in $\mathrm{W/(m \cdot K)}$. Nothing about speed, size or temperature difference appears: Pr is a property of the fluid alone, and it says whether momentum or heat spreads faster. Air ≈ 0.7, water ≈ 7, oil in the hundreds.

Nusselt, $\mathrm{Nu} = \dfrac{hL}{k}$ — the answer, not a question. It is the film coefficient made dimensionless, measured against what the same fluid would conduct sitting perfectly still, so $\mathrm{Nu} = 1$ is the honest floor.

Grashof, $\mathrm{Gr} = \dfrac{g \beta \, \Delta T \, L^{3}}{\nu^{2}}$ — gravity $g$, the expansion coefficient $\beta$ (beta) in $1/\mathrm{K}$, the surface-to-fluid $\Delta T$, the length $L$, and the kinematic viscosity $\nu$ (nu) in $\mathrm{m^2/s}$. It is the still-air twin of Reynolds: buoyancy over viscosity, for fluid nothing is pumping. And Rayleigh, $\mathrm{Ra} = \mathrm{Gr} \cdot \mathrm{Pr}$, is the product natural convection actually depends on — a finding about the physics, not merely a definition.