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$A$ 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)

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