ai Activity of a species

A Area

Bj Sensitivity matrix

cD Constant of Prandtl model

cP Specific heat at constant pressure

Cs Smagorinsky constant

C Concentration, Chapman-Rubesin parameter

d, D Material derivative

Di Mass diffusivity, thermal diffusivity

dx Infinitesimal element in x-direction

dy Infinitesimal element in y-direction

dz Infinitesimal element in z-direction

dV Control volume

e Specific energy

e- Electron

eint Internal energy

E Energy, error

Ea Activation energy

Eh Electric potential

Eo(V ) Reduction potential

fi Surface force

f, F Functions

F Faraday’s constant

→ Vector force

→,gi Gravitational acceleration

G Gibbs free energy, flame front position

h Specific enthalpy, time-step

H Enthalpy

I Ionic strength, identity matrix

IAB Index of importance

ji Diffusive flux

˙i Mass flow

n Number of moles, number of species, exponent of temperature

→ Normal vector

N Number of nodes, number of time-steps

O() Order of ()

p Pressure

pe Electrochemical potential

pH Potential of hydrogen

P Product, probability

˙j Heat flow by conduction

˙v Volumetric source of heat (internal, chemical)

qr Heat transfer due to radiation

Q Heat of combustion

Qe Activity product

˙ Potential energy

r Radius

R Gas constant

→ Residuum vector

→ Surface vector

→i Source term

sL Laminar flame velocity

sT Turbulent flame velocity

S Entropy, area, stiffness measure

t Time

T Temperature, period of time

Uc Axial velocity

j,v→ Velocity vector

(vx , vy , vz ) Velocity vector

V Volume

xj , (x, y, z) Cartesian coordinate system

Xi Molar fraction of a species

y0 Distance from the wall

Yi Mass fraction

w Vorticity, velocity component in z-direction

˙ Reaction rate

→ Vector of flow variables

˙ Rate of work crossing the boundaries

Wi Molecular weight

zi Ionic charge of a species

Z Mixture fraction

Special Symbols

a Thermal diffusivity, angle, coefficient

β Coefficient of thermal expansion, coefficient

δi,j Kronecker delta

∆ Variation, Laplacian, filter size

∈ Viscous dissipation, error

η Kolmogorov length, similarity variable, generalized coordinate

γ Parameter

γi Activity coefficient

Γi Gamma function

k Thermal conductivity, von Kárman constant

λ Eigenvalue

Λ Matrix of eigenvalues

μ Chemical potential, dynamic viscosity, mean

v', vi Stoichiometric coefficient

vT Turbulent viscosity

ξ Radio by length relation, generalized coordinate

ρ Density

σ Standard deviation

σi,j Stress tensor

τ Time, tortuosity

τi,j Viscous stress tensor

τw Wall shear stress

ϕ, Φ Variable

Φ Viscous dissipation

χ Scalar dissipation rate

ψ Variable

Ω Element of volume

 Partial derivative

 Gradient operator

 Divergence operator

 Curl operator

Subscripts and superscripts

Subscripts

b Burned

c Chemical

cl Center line

d Droplet

D Diffusivity

f Fluid

F Fuel

i, j, k Species, coordinate directions

ig Ignition

int Internal

m Constant

n Normal, constant

N Numerical...