Important Dimensionless Number in chemical engineering

1. Sherwood Number (Sh) =k_cL/D_AB equivalent to Nussett Number (Nu) in Heat transfer
Nu= hd/k = conductive resistance of fluid / convective resistance
In Unsteady heat transfer Biot number is used.
Bi= hd/k = conductive resistance of solid / convective resistance

2. Schmidt Number (Sc) = μ/ρD_AB = ratio of momentum diffusivity and mass diffusivity
Similarly in H.T.
Pr = C_P µ/k = ratio of momentum diffusivity and thermal diffusivity

3. Peclet Number = Re.Pr in heat transfer
= Re.Sc in mass transfer
It is related to degree of mixing and is inversely proportional to dispersion number

4. Lewis Number = Sc/Pr
It is important where both heat and mass transfer take place together like humidification

5. In natural convection
Grashoff number= gβθL³ ρ ² / μ ²
Raleigh number Ra = Gr.Pr

6. Stanton number
St (M.T.) = Sh/(Sc.Re)
St (H.T.) = Nu/(Pr.Re)

7. Unsteady state heat transfer
Fourier number = αt/L²
Bi=hd/k

8. Graetz Number = Re.Pr.(d/L)

9. In agitation there are
Power number = P/ρN³D⁵
Froude number = N²D/g
Re=ρND²/μ

10. In centrifugal pumps
Power constant
Capacity constant
Head constant