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In order to make the symbols in the Thermal-FluidsPedia consistent from all contributors, please adhere to the following common symbols. For the symbols that are not listed below, please define them after the equations in your articles.


English Symbols

Bi Biot number, hL / k
Bo Bond number, (\rho _\ell   - \rho _v )gL^2 /\sigma
Br Brinkman number, \mu u_m^2 /[k(T_s  - T_c )]
cp specific heat at constant pressure, J/kg-K
cv specific heat at constant volume, J/kg-K
C heat capacity, J/K
CD drag coefficient
Cf 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 / L2
Fr Froude number, U/\sqrt {gL} or U2 / (gL)
g gravitational acceleration, m/s2; specific Gibbs free energy, J/kg
G Gibbs free energy, J; electron-lattice coupling factor, W/m3-K; irradiance, W/m2
Gr Grashof number, gβΔTL3 / ν2
h heat transfer coefficient, W/(m2-K); specific enthalpy, J/kg
h_{\ell v} latent heat of vaporization, J/kg
h_{s\ell } latent heat of fusion, J/kg
hsv latent heat of sublimation, J/kg
H enthalpy, J; height, m; magnetic field
H magnetic field vector
I intensity, W/m2-sr; electrical current, A
I0 zeroth order modified Bessel function of the first kind
I1 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/m2
J0 zeroth order Bessel function of the first kind
J1 first order Bessel function of the first kind
Ja Jakob number, c_p \Delta T/h_{\ell v}
k thermal conductivity, W/(m-K)
k thermal conductivity tensor, W /(m-K)
K0 zeroth order modified Bessel function of the second kind
K1 first order modified Bessel function of the second kind
kb Boltzmann constant, J/K
K interface curvature, 1/m; Permeability, m2; dielectric constant
Kjk momentum exchange coefficient between phases j and k, kg/(m3-s)
Ka Kapitza number, \mu _\ell ^4 g/[\left( {\rho _\ell   - \rho _v } \right)\sigma ^3 ]
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, \left( {dT/dy} \right)\left( {d\sigma /dT} \right)\delta ^2 /\left( {\alpha _\ell  \mu _\ell  } \right)
n unit normal vector
NA Avogadro’s number (1/mol)
Nu Nusselt number, hL / k
Nux local Nusselt number, hxx / 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/m2
q" heat flux vector, W/m2
q"max maximum (critical) heat flux in boiling, W/m2
q"min minimum heat flux in boiling, W/m2
q"solar solar constant, 1368 W/m2
q"' internal heat generation per unit volume, W/m3
Q total heat transfer, J
r radial coordinate, m
r position vector m
R radius, m
Rg gas constant, kJ/kg-K
Ra Rayleigh number, gβΔTL3 / (να)
Re Reynolds number, UL / ν
s specific entropy, J/(kg-K)
S entropy, J/K
Sc Schmidt number, ν / D; subcooling parameter, c_{ps} (T_m  - T_i )/h_{s\ell }
Sh Sherwood number, hmL / D12
St Stanton number, h / (ρcpU)
Ste Stefan number, c_p \left| {T_w  - T_m } \right|/h_{s\ell }
Sr Strouhal number, Lf / U
t time, s
T temperature, K
Tm melting point, K
Tsat saturation temperature, K
u velocity in the x- direction, m/s
U velocity, m/s;
v specific volume, m3/kg; velocity in the y-direction, m/s
V volume, m3
V velocity vector, m/s
w velocity in the z-direction or axial velocity, m/s, specific work, J/kg
W work, J; width, m
We Weber number, ρU2L / σ
Wr Womersley number, \sqrt {\omega R^2 /\nu }
x Cartesian coordinate, m; vapor quality
X material coordinate, m; dimensionless coordinate
y Cartesian coordinate, m
Y material coordinate, m
Y0 zeroth order Bessel function of the second kind
Y1 first order Bessel function of the second kind
z Cartesian coordinate, axial coordinate, m
Z material coordinate, m; compressibility factor, pv/RT

Greek Symbols

α thermal diffusivity, m2/s; relaxation factor; accommodation coefficient; wave number, void fraction; absorptivity of a surface
β wedge angle, rad; coefficient of thermal expansion, 1/K; contact angle measured in degrees; volumetric flow fraction
βm composition coefficient of volume expansion
Γ general diffusion coefficient; liquid mass flow rate per unit width, kg/m-s
δ velocity boundary layer thickness, liquid or vapor film thickness, m; thermal penetration depth, m; laser irradiation penetration depth, m; thickness of the deposited film, m; thickness of surface element, m; Kronecker delta
δt thermal boundary layer thickness, m
εM momentum eddy diffusivity, m2/s
εH thermal eddy diffusivity, m2/s
η similarity variable, fin efficiency
θ inclination angle, rad; contact or wetting angle, rad; dimensionless temperature
Θn eigen function
λ mean free path, m; wavelength, m
λn eigenvalue
μ dynamic viscosity, kg/(m-s); chemical potential, J/mol; magnetic permeability
ν kinematic viscosity, m2/s; frequency (Hz)
ρ density, kg/m3; reflectivity of a surface
σ surface tension force, N/m; collision diameter, Å, Stefan-Boltzmann constant
τ shear stress, N/m2; thermal relaxation time, s; dimensionless time,; optical thickness, m
τ stress tensor, N/m2
φ Lennard-Jones potential, J; inclination angle; wave amplitude; pressure drop multiplier in two-phase flow
ψ stream function, m2/s


0 reference variables; initial condition
a adiabatic, acceleration
b control volume face at bottom; blood; blackbody
c critical point, condenser, cutoff value
cap capillary
CV control volume
E east neighbor point
e equilibrium; evaporator; control volume face at east
eff effective value
f final; fuel; thin film
g gas (vapor); gravity
\ell liquid
L left; characteristic length
m mean; melting point or mushy zone; metabolic
men meniscus
N north neighbor grid point
n normal to surface; control volume face at bottom
nb general neighbor grid points
P central grid point under consideration
p product; particle; pulse
rad radiation
ref reference frame
S south neighbor grid point
s shaft; solid; surface; control volume face at south
sat saturation
T top neighbor grid point; temperature
t turbulent; control volume face at top
v vapor phase
W west neighbor grid point
w wall; control volume face at west
ambient or bulk property


n normal component
t tangential component, turbulent
´ fluctuation