No Men

Nomenclature A

Area (m2 , ft2 )

~a

Acceleration (m/s2 , ft/s2 )

a

Local speed of sound (m/s, ft/s)

c

Concentration (mass/volume, moles/volume)

CD

Drag coefficient, defined different ways (dimensionless)

cp , cv Heat capacity at constant pressure, volume (J/kg-K, Btu/lbm -◦ F) d

Diameter; dp , Dp , particle diameter (m, ft)

DH

Hydraulic diameter (m, ft)

Dij , D Mass diffusion coefficient (m2 /s, ft2 /s) E

Total energy, activation energy (J, kJ, cal, Btu)

f F~

Mixture fraction (dimensionless)

FD

Drag force (N, lbf )

~g

Gravitational acceleration (m/s2 , ft/s2 ); standard values = 9.80665 m/s2 , 32.1740 ft/s2

Gr

Grashof number ≡ ratio of buoyancy forces to viscous forces (dimensionless)

H

Total enthalpy (energy/mass, energy/mole)

h

Heat transfer coefficient (W/m2 -K, Btu/ft2 -h-◦ F)

h

Species enthalpy; h0 , standard state enthalpy of formation (energy/mass, energy/mole)

I

Radiation intensity (energy per area of emitting surface per unit solid angle)

J

Mass flux; diffusion flux (kg/m2 -s, lbm /ft2 -s)

K

Equilibrium constant = forward rate constant/backward rate constant (units vary)

k

Kinetic energy per unit mass (J/kg, Btu/lbm )

k

Reaction rate constant, e.g., k1 , k−1 ,kf,r , kb,r (units vary)

k

Thermal conductivity (W/m-K, Btu/ft-h-◦ F)

kB

Boltzmann constant (1.38 × 10−23 J/molecule-K)

k,kc

Mass transfer coefficient (units vary); also K, Kc

Force vector (N, lbf )

`, l, L Length scale (m, cm, ft, in)

c Fluent Inc. January 11, 2005

Nom-1

Nomenclature

Le

Lewis number ≡ ratio of thermal diffusivity to mass diffusivity (dimensionless)

m

Mass (g, kg, lbm )

m ˙

Mass flow rate (kg/s, lbm /s)

Mw

Molecular weight (kg/kgmol, lbm /lbm mol)

M

Mach number ≡ ratio of fluid velocity magnitude to local speed of sound (dimensionless)

Nu

Nusselt number ≡ dimensionless heat transfer or mass transfer coefficient (dimensionless); usually a function of other dimensionless groups

p

Pressure (Pa, atm, mm Hg, lbf /ft2 )

Pe

Peclet number ≡ Re × Pr for heat transfer, and ≡ Re × Sc for mass transfer (dimensionless)

Pr

Prandtl number ≡ ratio of momentum diffusivity to thermal diffusivity (dimensionless)

Q

Flow rate of enthalpy (W, Btu/h)

q

Heat flux (W/m2 , Btu/ft2 -h)

R

Gas-law constant (8.31447 × 103 J/kgmol-K, 1.98588 Btu/lbm mol-◦ F)

r

Radius (m, ft)

R

Reaction rate (units vary)

Ra

Rayleigh number ≡ Gr × Pr; measure of the strength of buoyancy-induced flow in natural (free) convection (dimensionless)

Re

Reynolds number ≡ ratio of inertial forces to viscous forces (dimensionless)

S

Total entropy (J/K, J/kgmol-K, Btu/lbm mol-◦ F)

s

Species entropy; s0 , standard state entropy (J/kgmol-K, Btu/lbm mol-◦ F)

Sc

Schmidt number ≡ ratio of momentum diffusivity to mass diffusivity (dimensionless)

Sij

Mean rate-of-strain tensor (s−1 )

T

Temperature (K, ◦ C, ◦ R, ◦ F)

t

Time (s)

U

Free-stream velocity (m/s, ft/s)

u, v, w Velocity magnitude (m/s, ft/s); also written with directional subscripts (e.g., vx , vy , vz , vr ) V

Volume (m3 , ft3 )

~v

Overall velocity vector (m/s, ft/s)

We

Weber number ≡ ratio of aerodynamic forces to surface tension forces (dimensionless)

Nom-2

c Fluent Inc. January 11, 2005

Nomenclature

X

Mole fraction (dimensionless)

Y

Mass fraction (dimensionless)

α

Permeability (m2 , ft2 )

α

Thermal diffusivity (m2 /s, ft2 /s)

α

Volume fraction (dimensionless)

β

Coefficient of thermal expansion (K−1 )

γ

Porosity (dimensionless)

γ

Ratio of specific heats, cp /cv (dimensionless)

∆

Change in variable, final − initial (e.g., ∆p, ∆t, ∆H, ∆S, ∆T )

δ

Delta function (units vary)



Emissivity (dimensionless)



Lennard-Jones energy parameter (J/molecule)



Turbulent dissipation rate (m2 /s3 , ft2 /s3 )



Void fraction (dimensionless)

η

Effectiveness factor (dimensionless)

η 0 , η 00 Rate exponents for reactants, products (dimensionless) θr

Radiation temperature (K)

λ λ

Molecular mean free path (m, nm, ft) ˚, ft) Wavelength (m, nm, A

µ

Dynamic viscosity (cP, Pa-s, lbm /ft-s)

ν

Kinematic viscosity (m2 /s, ft2 /s)

ν 0 , ν 00 Stoichiometric coefficients for reactants, products (dimensionless) ρ

Density (kg/m3 , lbm /ft3 )

σ

Stefan-Boltzmann constant (5.67 ×108 W/m2 -K4 )

σ

Surface tension (kg/m, dyn/cm, lbf /ft)

σs

Scattering coefficient (m−1 )

τ

Stress tensor (Pa, lbf /ft2 )

τ

Shear stress (Pa, lbf /ft2 )

τ

Time scale, e.g., τc , τp , τc (s)

τ

Tortuosity, characteristic of pore structure (dimensionless)

φ

Equivalence ratio (dimensionless)

φ

Thiele modulus (dimensionless)

Ω

Angular velocity; Ωij , Mean rate of rotation tensor (s−1 )

c Fluent Inc. January 11, 2005

Nom-3

Nomenclature

ω

Specific dissipation rate (s−1 )

Ω, Ω0 Solid angle (degrees, radians, gradians) ΩD

Nom-4

Diffusion collision integral (dimensionless)

c Fluent Inc. January 11, 2005