Bi  Biot number, hL / k

Bo  Bond number,

Br  Brinkman number,

c_{p}  specific heat at constant pressure, J/kgK

c_{v}  specific heat at constant volume, J/kgK

C  heat capacity, J/K

C_{D}  drag coefficient

C_{f}  friction coefficient

D/Dt  substantial derivative

f  degree of freedom; weight function; friction coefficient; solid fraction; wave frequency, 1/s , molecular velocity distribution function

Fo  Fourier number, αt / L^{2}

Fr  Froude number, or U^{2} / (gL)

g  gravitational acceleration, m/s^{2}; specific Gibbs free energy, J/kg

G  Gibbs free energy, J; electronlattice coupling factor, W/m^{3}K; irradiance, W/m^{2}

Gr  Grashof number, gβΔTL^{3} / ν^{2}

h  heat transfer coefficient, W/(m^{2}K); specific enthalpy, J/kg

 latent heat of vaporization, J/kg

 latent heat of fusion, J/kg

h_{sv}  latent heat of sublimation, J/kg

H  enthalpy, J; height, m; magnetic field

H  magnetic field vector

I  intensity, W/m^{2}sr; electrical current, A

I_{0}  zeroth order modified Bessel function of the first kind

I_{1}  first order modified Bessel function of the first kind

I  unit tensor

j  volume flux, m/s; superficial velocity, m/s

J  total (diffusion + convection) flux; radiosity, W/m^{2}

J_{0}  zeroth order Bessel function of the first kind

J_{1}  first order Bessel function of the first kind

Ja  Jakob number,

k  thermal conductivity, W/(mK)

k  thermal conductivity tensor, W /(mK)

K_{0}  zeroth order modified Bessel function of the second kind

K_{1}  first order modified Bessel function of the second kind

k_{b}  Boltzmann constant, J/K

K  interface curvature, 1/m; Permeability, m^{2}; dielectric constant

K_{jk}  momentum exchange coefficient between phases j and k, kg/(m^{3}s)

Ka  Kapitza number,

Kn  Knudsen number, λ / L

L  (characteristic) length, m

Le  Lewis number, α / D

m  mass, kg

M  molecular mass, kg/kmol

Ma  Mach number,U / c; Marangoni number,

n  unit normal vector

N_{A}  Avogadro’s number (1/mol)

Nu  Nusselt number, hL / k

Nu_{x}  local Nusselt number, h_{x}x / k

p  pressure, Pa

Pe  Peclet number, UL / α

Pr  Prandtl number, ν / α

q  heat rate, W
q'  heat rate per unit length, W/m

q"  heat flux, W/m^{2}

q"  heat flux vector, W/m^{2}

q"_{max}  maximum (critical) heat flux in boiling, W/m^{2}

q"_{min}  minimum heat flux in boiling, W/m^{2}

q"_{solar}  solar constant, 1368 W/m^{2}

q"'  internal heat generation per unit volume, W/m^{3}

Q  total heat transfer, J

r  radial coordinate, m

r  position vector m

R  radius, m

R_{g}  gas constant, kJ/kgK

Ra  Rayleigh number, gβΔTL^{3} / (να)

Re  Reynolds number, UL / ν

s  specific entropy, J/(kgK)

S  entropy, J/K

Sc  Schmidt number, ν / D; subcooling parameter,

Sh  Sherwood number, h_{m}L / D_{12}

St  Stanton number, h / (ρc_{p}U)

Ste  Stefan number,

Sr  Strouhal number, Lf / U

t  time, s

T  temperature, K

T_{m}  melting point, K

T_{sat}  saturation temperature, K

u  velocity in the x direction, m/s

U  velocity, m/s;

v  specific volume, m^{3}/kg; velocity in the ydirection, m/s

V  volume, m^{3}

V  velocity vector, m/s

w  velocity in the zdirection or axial velocity, m/s, specific work, J/kg

W  work, J; width, m

We  Weber number, ρU^{2}L / σ

Wr  Womersley number,

x  Cartesian coordinate, m; vapor quality

X  material coordinate, m; dimensionless coordinate

y  Cartesian coordinate, m

Y  material coordinate, m

Y_{0}  zeroth order Bessel function of the second kind

Y_{1}  first order Bessel function of the second kind

z  Cartesian coordinate, axial coordinate, m

Z  material coordinate, m; compressibility factor, pv/RT
