Dimensionless Parameters

Parameters that have no unit of measurement, commonly used in dimensional analysis for analyzing fluid flow.

All dimensionless parameters are just ratios of one thing to another.

- Dr. Paul (paraphrased)

In heat transfer many dimensionless parameters use the star notation.

Table of Heat Transfer Dimensionless Parameters

Table 6.2 is a list of dimensionless parameters applicable to heat transfer.

Group	Definition	Interpretation
Biot Number (Bi)	$\frac{h L}{k_{s}}$	Ratio of the internal thermal resistance of a solid to the boundary layer thermal resistance
Mass transfer Biot number (Bi_m)	$\frac{h_{m} L}{D_{AB}}$	Ratio of the internal species transfer resistance to the boundary layer species transfer resistance
Bond number (Bo)	$\frac{g (ρ_{l} - ρ_{υ}) L^{2}}{σ}$	Ratio of gravitational and surface tension forces
Coefficient of friction (C_f)	$\frac{τ_{s}}{ρ V^{2} / 2}$	Dimensionless surface shear stress
Eckert number (Ec)	$\frac{V^{2}}{c_{p} (T_{s} - T_{\infty})}$	Kinetic energy of the flow relative to the boundary layer enthalpy difference
Fourier number (Fo)	$\frac{α t}{L^{2}}$	Ratio of the heat conduction rate to the rate of thermal energy storage in a solid. Dimensionless time
Mass transfer Fourier number (Fo_m)	$\frac{D_{{AB}^{t}}}{L^{2}}$	Ratio of the species diffusion rate to the rate of species storage. Dimensionless time
Friction factor (f)	$\frac{Δ p}{(L / D) (ρ u_{m}^{2} / 2)}$	Dimensionless pressure drop for internal flow
Grashof number (Gr_L)	$\frac{g β (T_{s} - T_{\infty}) L^{3}}{ν^{2}}$	Measure of the ratio of buoyancy forces to viscous forces
Colburn j factor (j_H)	St Pr^2/3	Dimensionless heat transfer coefficient
Colburn j factor (j_m)	St_m Sc^2/3	Dimensionless mass transfer coefficient
Jakob number (Ja)	$\frac{c_{p} (T_{s} - T_{sat})}{h_{f g}}$	Ratio of sensible to latent energy absorbed during liquid–vapor phase change
Lewis number (Le)	$\frac{α}{D_{AB}}$	Ratio of the thermal and mass diffusivities
Mach number (Ma)	$\frac{V}{a}$	Ratio of velocity to speed of sound
Nusselt number (Nu_L)	$\frac{h L}{k_{f}}$	Ratio of convection to pure conduction heat transfer
Peclet number (Pe_L)	$\frac{V L}{α} = {Re}_{L} \Pr$	Ratio of advection to conduction heat transfer rates
Prandtl number (Pr)	$\frac{c_{p} μ}{k} = \frac{ν}{α}$	Ratio of the momentum and thermal diffusivities
Reynolds number (Re_L)	$\frac{V L}{ν}$	Ratio of the inertia and viscous forces
Schmidt number (Sc)	$\frac{ν}{D_{AB}}$	Ratio of the momentum and mass diffusivities
Sherwood Number (Sh_L)	$\frac{h_{m} L}{D_{AB}}$	Ratio of convection to pure diffusion mass transfer
Stanton number (St)	$\frac{h}{ρ V c_{p}} = \frac{{Nu}_{L}}{{Re}_{L} \Pr}$	Modified Nusselt number
Mass Transfer Stanton number (St_m)	$\frac{h_{m}}{V} = \frac{{Sh}_{L}}{{Re}_{L} Sc}$	Modified Sherwood number
Weber number (We)	$\frac{ρ V^{2} L}{σ}$	Ratio of inertia to surface tension forces