Transport II Dimensionless Groups (copy)

Debye Decay Length Definition

Length over which potential decays away

(((epsilon)(epsilon0)(kb)(T))/(2(e^2)(z^2)(nb)))^(1/2)

Debye Decay Length

(alpha)/(Dab)

Lewis Number

Lewis Number Definition

Ratio of thermal diffusion rate to mass diffusion rate

Hatta Number Definition

Film depth/diffusion length

Second Damkohler Number Definition

ratio of reaction rate to diffusion rate (important for rate limited runs)

(k)(delta)/Dab

Second Damkohler Number

Theile Effectiveness Factor

((k1)a(R^2)/(Da))^(1/2)

Thiele Modulus

L/((Dab)/(k))^(1/2)

Hatta Number

Sherwood Number Definition

overall mass transfer/diffusive mass transfer

(Km)d/(Dab)

Sherwood Number

h(ext)L/k(int)

Biot Number

F(drag)/((1/2)(rho)(U^2)(A))

Drag Coefficient

(U^2)/(Lg)

Froude Number (Fr)

Definition of Biot Number

external heat transfer/internal heat transfer

Definition of Drag Coefficient

Drag/inertial forces

Froude Number Definition

inertial forces/gravitational forces

(g)(beta)(delta T)H/(nu^2)

Grashof Number (Gr)

Grashof Number Definition

buoyancy due to thermal expansion/viscous dissipation

hL/k

Nusselt Number (Nu)

Nusselt Number Definition

total heat transfer/conductive heat transfer

LU/(aplha)=(Re)(Pr)

Peclet Number (Pe)

Peclet Number Definition

convection/diffusion

(nu)/(alpha)

Prandtl Number (Pr)

Definition of Prandtl Number

momentum diffusivity/thermal diffusivity

g(beta)(deltaT)H^3/(alpha) = (Gr)(Pr)

Rayleigh Number (Ra)

Definition of Rayleigh Number

buoyancy due to thermal expansion/dissipation

UD/(nu)

Reynolds Number (Re)

Definition of Reynolds Number

inertial forces/viscous forces

((omega)(alpha^2)/(nu))^1/2 = (alpha)/((nu)/(omega))^1/2

Womersley Number (alpha)

Womersley number Definition

penetration depth/tube length

h/((rho)(Cp)(U))=Nu/(RePr)

Stanton Number

Stanton Number Definition

heat transfer/convective heat transfer

(Tauw)/((1/2)(rho)(U^2)

fanning friction factor

definition of fanning friction factor

wall shear stress/dynamic pressure

StPr^(2/3)= ff/2

Colburn Analogy

h=\~ p\*Uinf**Cp*(ff/2)*Pr^(-2/3)*

Colburn Analogy

(nu)/D

Schmidt Number (Sc)

Definition of Schmidt Number

momentum diffusivity/mass diffusion