Nomenclature

$A$	Area (m $^2$, ft $^2$)
${\vec a}$	Acceleration (m/s $^2$, ft/s $^2$)
$a$	Local speed of sound (m/s, ft/s)
$c$	Concentration (mass/volume, moles/volume)
$C_D$	Drag coefficient, defined different ways (dimensionless)
$c_p$, $c_{\rm v}$	Heat capacity at constant pressure, volume (J/kg-K, Btu/lb $_m$- $^\circ$F)
$d$	Diameter; $d_p, D_p$, particle diameter (m, ft)
$D_H$	Hydraulic diameter (m, ft)
${\cal D}_{ij}, D$	Mass diffusion coefficient (m $^2$/s, ft $^2$/s)
$E$	Total energy, activation energy (J, kJ, cal, Btu)
$f$	Mixture fraction (dimensionless)
${\vec F}$	Force vector (N, lb $_f$)
$F_D$	Drag force (N, lb $_f$)
${\vec g}$	Gravitational acceleration (m/s $^2$, ft/s $^2$); standard values = 9.80665 m/s $^2$, 32.1740 ft/s $^2$
Gr	Grashof number $\equiv$ ratio of buoyancy forces to viscous forces (dimensionless)
$H$	Total enthalpy (energy/mass, energy/mole)
$h$	Heat transfer coefficient (W/m $^2$-K, Btu/ft $^2$-h- $^\circ$F)
$h$	Species enthalpy; $h^0$, 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/m $^2$-s, lb $_m$/ft $^2$-s)
$K$	Equilibrium constant = forward rate constant/backward rate constant (units vary)
$k$	Kinetic energy per unit mass (J/kg, Btu/lb $_m$)
$k$	Reaction rate constant, e.g., $k_1$, $k_{-1}$, $k_{f,r}$, $k_{b,r}$ (units vary)
$k$	Thermal conductivity (W/m-K, Btu/ft-h- $^\circ$F)
$k_B$	Boltzmann constant ( $1.38 \times 10^{-23}$ J/molecule-K)
$k$, $k_c$	Mass transfer coefficient (units vary); also $K$, $K_c$
$\ell, l, L$	Length scale (m, cm, ft, in)
Le	Lewis number $\equiv$ ratio of thermal diffusivity to mass diffusivity (dimensionless)
$m$	Mass (g, kg, lb $_m$)
${\dot m}$	Mass flow rate (kg/s, lb $_m$/s)
$M_w$	Molecular weight (kg/kgmol, lb $_m$/lb $_m$mol)
M	Mach number $\equiv$ ratio of fluid velocity magnitude to local speed of sound (dimensionless)
Nu	Nusselt number $\equiv$ dimensionless heat transfer or mass transfer coefficient (dimensionless); usually a function of other dimensionless groups
$p$	Pressure (Pa, atm, mm Hg, lb $_f$/ft $^2$)
Pe	Peclet number $\equiv {\rm Re} \times {\rm Pr}$ for heat transfer, and $\equiv {\rm Re} \times {\rm Sc}$ for mass transfer (dimensionless)
Pr	Prandtl number $\equiv$ ratio of momentum diffusivity to thermal diffusivity (dimensionless)
$Q$	Flow rate of enthalpy (W, Btu/h)
$q$	Heat flux (W/m $^2$, Btu/ft $^2$-h)
$R$	Gas-law constant (8.31447 $\times \; 10^3$ J/kgmol-K, 1.98588 Btu/lb $_m$mol- $^\circ$F)
$r$	Radius (m, ft)
${\cal R}$	Reaction rate (units vary)
Ra	Rayleigh number $\equiv {\rm Gr} \times {\rm Pr}$; measure of the strength of buoyancy-induced flow in natural (free) convection (dimensionless)
Re	Reynolds number $\equiv$ ratio of inertial forces to viscous forces (dimensionless)
$S$	Total entropy (J/K, J/kgmol-K, Btu/lb $_m$mol- $^\circ$F)
$s$	Species entropy; $s^0$, standard state entropy (J/kgmol-K, Btu/lb $_m$mol- $^\circ$F)
Sc	Schmidt number $\equiv$ ratio of momentum diffusivity to mass diffusivity (dimensionless)
$S_{ij}$	Mean rate-of-strain tensor (s $^{-1}$)
$T$	Temperature (K, $^\circ$C, $^\circ$R, $^\circ$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., $v_x$, $v_y$, $v_z$, $v_r$)
$V$	Volume (m $^3$, ft $^3$)
${\vec v}$	Overall velocity vector (m/s, ft/s)
We	Weber number $\equiv$ ratio of aerodynamic forces to surface tension forces (dimensionless)
$X$	Mole fraction (dimensionless)
$Y$	Mass fraction (dimensionless)
$\alpha$	Permeability, or flux per unit pressure difference (L/m $^2$-h-atm, ft $^3$/ft $^2$-h-(lb $_f$/ft $^2$))
$\alpha$	Thermal diffusivity (m $^2$/s, ft $^2$/s)
$\alpha$	Volume fraction (dimensionless)
$\beta$	Coefficient of thermal expansion (K $^{-1}$)
$\gamma$	Porosity (dimensionless)
$\gamma$	Ratio of specific heats, c $_p$/c $_{\rm v}$ (dimensionless)
$\Delta$	Change in variable, final $-$ initial (e.g., $\Delta p$, $\Delta t$, $\Delta H$, $\Delta S$, $\Delta T$)
$\delta$	Delta function (units vary)
$\epsilon$	Emissivity (dimensionless)
$\epsilon$	Lennard-Jones energy parameter (J/molecule)
$\epsilon$	Turbulent dissipation rate (m $^2$/s $^3$, ft $^2$/s $^3$)
$\epsilon$	Void fraction (dimensionless)
$\eta$	Effectiveness factor (dimensionless)
$\eta'$, $\eta''$	Rate exponents for reactants, products (dimensionless)
$\theta_r$	Radiation temperature (K)
$\lambda$	Molecular mean free path (m, nm, ft)
$\lambda$	Wavelength (m, nm, Å, ft)
$\mu$	Dynamic viscosity (cP, Pa-s, lb $_m$/ft-s)
$\nu$	Kinematic viscosity (m $^2$/s, ft $^2$/s)
$\nu'$, $\nu''$	Stoichiometric coefficients for reactants, products (dimensionless)
$\rho$	Density (kg/m $^3$, lb $_m$/ft $^3$)
$\sigma$	Stefan-Boltzmann constant (5.67 $\times 10^8$ W/m $^2$-K $^4$)
$\sigma$	Surface tension (kg/m, dyn/cm, lb $_f$/ft)
$\sigma_s$	Scattering coefficient (m $^{-1}$)
$\overline{\overline{\tau}}$	Stress tensor (Pa, lb $_f$/ft $^2$)
$\tau$	Shear stress (Pa, lb $_f$/ft $^2$)
$\tau$	Time scale, e.g., $\tau_c$, $\tau_p$, $\tau_c$ (s)
$\tau$	Tortuosity, characteristic of pore structure (dimensionless)
$\phi$	Equivalence ratio (dimensionless)
$\phi$	Thiele modulus (dimensionless)
$\Omega$	Angular velocity; $\Omega_{ij}$, Mean rate of rotation tensor (s $^{-1}$)
$\omega$	Specific dissipation rate (s $^{-1}$)
$\Omega, \Omega'$	Solid angle (degrees, radians, gradians)
$\Omega_D$	Diffusion collision integral (dimensionless)