Nusselt number represents:

Convection to conduction in the fluid layer

Heat transferred to thermal capacity

Practice · 5 marks

Dimensionless numbers in convection

Short answer

Re = VL/ν (inertia/viscous), Pr = ν/α (momentum/thermal diffusivity), Nu = hL/k (convection/conduction), Gr = gβΔT L^3/ν^2 (buoyancy/viscous), St = h/(ρVc_p) (heat transferred/thermal capacity). Forced convection: Nu = f(Re,Pr); natural: Nu = f(Gr,Pr) with Ra = Gr Pr.

Define Reynolds, Prandtl, Nusselt, Grashof and Stanton numbers. State the physical significance of each and the relation between them in forced and natural convection.

Dimensionless numbers let results from one experiment be applied to similar situations of different size, fluid or velocity.

Number	Definition	Physical significance
Reynolds, $Re$	$\dfrac{\rho V L}{\mu} = \dfrac{VL}{\nu}$	Inertia force / viscous force. Decides laminar or turbulent flow
Prandtl, $Pr$	$\dfrac{\mu c_p}{k} = \dfrac{\nu}{\alpha}$	Momentum diffusivity / thermal diffusivity. Fluid property; compares thickness of velocity and thermal layers
Nusselt, $Nu$	$\dfrac{hL}{k}$	Convection / conduction in the fluid layer of thickness $L$ ; dimensionless heat transfer coefficient
Grashof, $Gr$	$\dfrac{g\beta\Delta T L^3}{\nu^2}$	Buoyancy force / viscous force in natural convection
Stanton, $St$	$\dfrac{h}{\rho V c_p} = \dfrac{Nu}{Re\,Pr}$	Heat transferred to the fluid / thermal capacity of the flowing fluid

Relations

Forced convection: $Nu = f(Re, Pr)$ , e.g. $Nu = 0.023\,Re^{0.8}Pr^{0.4}$ for turbulent flow in tubes.
Natural convection: $Nu = f(Gr, Pr)$ , usually written $Nu = C\,(Gr\,Pr)^m$ , where the product $Gr\,Pr$ is the Rayleigh number $Ra$ .
Mixed convection: $Gr/Re^2$ near 1 shows both effects are important.
$St\,Pr^{2/3} = f/2$ is the Colburn analogy linking heat transfer with skin friction.

✓ Answer checked by Claude Sonnet 5.5

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Dimensionless numbers in convection

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