Dimensionless Numbers & their Significance

Reynolds Number (Re) = Inertial Forces / Viscous Forces = (ρ.v.d)/μ

ρ = density of fluid , v = velocity of fluid , d = diameter of pipe , μ = dynamic viscosity of the fluid .

Analysis of different flow regimes like laminar, turbulent or transition state.

Viscous force dominates in laminar flow and Inertial force dominates in turbulent flow.

Prandtl Number (Pr) = Momentum Diffusivity /Heat Diffusivity = (Cp.μ /k)

Cp = specific heat capacity at constant pressure , μ = dynamic viscosity of the fluid , k = thermal conductivity .

Pr < 0.1   (Liquid metal) , 0.5<Pr<1  (Gases) , 1<Pr <20  (Water & light liquid)  , Pr >20  (Oil & viscous liquid) .

Ratio of velocity boundary layer to thermal boundary layer .

Pr (low) → rate of thermal diffusion (heat) is more than rate of momentum diffusion (velocity) .

Pr (low) → Thickness of thermal diffusion (heat) is more than thickness of momentum diffusion (velocity) .

Schmidt Number (Sc) = Momentum diffusivity /Mass diffusivity = μ /ρ.(Dab)

Dab = mass diffusivity , μ = dynamic viscosity of the fluid , ρ = density of fluid .

It is also ratio of fluid boundary layer to mass transfer boundary layer thickness.

Schmidt number is useful to find mass transfer coefficient using Sherwood number.

Lewis Number (Le) = Heat Diffusivity /Mass Diffusivity = k/ ρ.(Dab).Cp 

k = thermal conductivity , ρ = density of fluid , Dab = mass diffusivity , Cp= specific heat capacity at constant pressure .

Ratio of thermal diffusivity to mass diffusivity.

Ratio of Schmidt number to Prandtl number .

Fluid flow with simultaneous Heat & mass transfer by convection .

Peclret Number (Pe) = (Characteristic length × Characteristic velocity)/(Diffusivity) = (Lch ×Vch)/(k/ρ.Cp )

Heat transported by convection /Heat transported by conduction.

Product of Re & Pr for Pe(Heat Transfer) & product of Re & SC for Pe(Mass Transfer)

Stanton Number (St) = Heat transfer coefficient / Momentum transfer coefficient

St(Heat Transfer) = Nu/(Re.Pr) & St(Mass Transfer) = Sh/(Re.Sc)

Ratio of  heat transferred to the fluid to the heat transported by the fluid

Ratio of Nusselt number to Peclet number