Nomenclature

From Thermal-FluidsPedia

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.

1 English Symbols
2 Greek Symbols
3 Subscripts
4 Superscripts

English Symbols

Bi	Biot number, $h L / k$
Bo	Bond number, $(\rho _\ell - \rho _v )gL^2 /\sigma$
Br	Brinkman number, $\mu u_m^2 /[k(T_s - T_c )]$
c_p	specific heat at constant pressure, J/kg-K
c_v	specific heat at constant volume, J/kg-K
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, $α t / L 2$
Fr	Froude number, $U/\sqrt {gL}$ or $U 2 / (g L)$
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, $g βΔ T L 3 / ν 2$
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
$h s v$	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
k_b	Boltzmann constant, J/K
K	interface curvature, 1/m; Permeability, m²; dielectric constant
K_jk	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
N_A	Avogadro’s number (1/mol)
Nu	Nusselt number, $h L / k$
Nu_x	local Nusselt number, $h x x / k$
p	pressure, Pa
Pe	Peclet number, $U L / α$
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
R_g	gas constant, kJ/kg-K
Ra	Rayleigh number, $g βΔ T L 3 / (να)$
Re	Reynolds number, $U L / ν$
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, $h m L / D 12$
St	Stanton number, $h / (ρ c p U)$
Ste	Stefan number, $c_p \left\| {T_w - T_m } \right\|/h_{s\ell }$
Sr	Strouhal number, $L f / U$
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, 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, $ρ U 2 L / σ$
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
β_m	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
δ_t	thermal boundary layer thickness, m
ε_M	momentum eddy diffusivity, m²/s
ε_H	thermal eddy diffusivity, m²/s
η	similarity variable, fin efficiency
θ	inclination angle, rad; contact or wetting angle, rad; dimensionless temperature
Θ_n	eigen function
λ	mean free path, m; wavelength, m
λ_n	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

Subscripts

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

Superscripts

n	normal component
t	tangential component, turbulent
´	fluctuation
*	dimensionless
+	dimensionless

Retrieved from "http://thermalfluidscentral.org/encyclopedia/index.php/Nomenclature"

Nomenclature

From Thermal-FluidsPedia

Contents

English Symbols

Greek Symbols

Subscripts

Superscripts

Views

Personal tools

Navigation

Search