A	chemical affinity, J mol−1
CA	reagent concentration, mol m−3
cp	heat capacity, J kg−1 K−1
DA	diffusivity, m2 s−1
Dh	hydraulic diameter, = 4εSv−1, m
Fc	reactor cross-sectional area, m2
f	Fanning friction factor, = $\varrho$w02L(2ΔPDhε2)−1
JA	diffusional mass flux, mol s−1 m−2
Ji	stream (flux) of irreversible process, Equation (9)
kC	mass transfer coefficient, m s−1
kr	kinetic rate constant of the first-order reaction, referred to the catalyst surface area, m s−1
k∞	pre-exponential coefficient in Arrhenius equation, m s−1
kCr = kCkr/(kC+kr)	combined transfer-reaction coefficient, m s−1
L	bed length, m
ΔP	pressure drop, Pa/m
q	heat flux, W m−2
R	gas constant, J mol−1 K−1
rA	reaction rate, mol m−2 s−1
S	entropy production rate, J K−1mol−1
sef	film thickness, m
Sv	specific surface area, m2 m−3
T	temperature, K
W	pumping power, W
w0	superficial fluid velocity, m s−1
yi	mole fraction
ΔHR	reaction enthalpy, J mol−1
ΔGR	reaction Gibbs energy, J mol−1
Greek symbols
α	heat transfer coefficient, W m−2 K−1
ε	porosity
η	dynamic viscosity, Pa s
λ	thermal conductivity, W m−1 K−1
µ	chemical potential, J mol−1
ν	stoichiometric coefficient
Δπ	driving force of irreversible process
$\varrho$	density, kg m−3
σ	entropy production per m3 of reactor volume, W m−3 K−1
Dimensionless numbers
L+	dimensionless length for the hydrodynamic entrance region, = LDh−1Re−1
L*	dimensionless length for the thermal entrance region, = LDh−1Re−1Pr−1
L*M	dimensionless length for the mass transfer entrance region, = LDh−1Re−1Sc−1
Pr	Prandtl number, = ηcpλ−1
Re	Reynolds number, = w0Dh $\varrho$η−1ε−1
Sc	Schmidt number, = η $\varrho$−1DA−1
Sh	Sherwood number, = kCDhDA−1
Subscripts
A	key reactant
D	entropy production due to mass transfer
F	entropy production due to flow friction
H	entropy production due to heat transfer
P	total entropy production
R	entropy production due to chemical reaction
S	catalyst surface
x	reactor arbitrary axial coordinate
0, L	reactor inlet, outlet