Numerical Investigation of Forced Convection Nonequilibrium Effects on Heat and Mass Transfer in Porous Media

Abstract

A numerical investigation is performed to analyze the coupled heat and mass transfer in porous media with a strong exothermic reaction. Similar problems have received great attention due to their relevance in a wide variety of engineering applications, such as heat pipes, drying technologies, nuclear reactors, catalytic reactors, environmentally clean utilization of energy, and many others. The momentum transfer in the porous substrate is modeled with the Darcy–Brinkman–Forchheimer law, while the temperature and concentration fields are obtained subsequently from the energy and diffusion equations. The considered configuration consists of a cylindrical duct where a first-order reaction is supposed to occur. The governing equations are solved by using the finite-volume method. The SIMPLER algorithm is applied to solve the momentum and continuity equations. The power-law scheme is used to model the interaction between convection and diffusion terms. The effect of the main governing parameters, such as permeability, aspect ratio, solid-to-fluid conductivity ratio, Reynolds number, Biot number, and the modified Frank-Kamenetskii number, are studied. The comparison with previously published work shows excellent agreement.

Nomenclature

A	=	preexponential factor of Arrhenius, s−1
asf	=	specific surface area, m−1
Bint	=	interstitial Biot number;
Bi	=	Biot number;
C	=	concentration, mol.m−3
Cm	=	dimensionless bulk concentration, mol m−3;
Cp	=	specific heat, kJ/kg-K
Cw	=	wall concentration, mol m−3.
Cz	=	parameter
D	=	channel diameter, m
Deff	=	effective diameter, m
Di	=	molecular diffusion, m2 s−1
Da	=	Darcy number;
D2	=	dimensionless number defined in Eq. (15)(15)
D3	=	dimensionless number defined in Eq. (16)(16)
dp	=	pore diameter, m
E	=	activation energy, J mol−1
F	=	Forchheimer parameter
FKm	=	Frank–Kamenetskii number modified defined in Eq. (17)(17)
FK	=	Frank–Kamenetskii number.
H	=	channel length, m
h	=	heat transfer coefficient, W m−2 K−1
hsf	=	fluid-to-solid heat transfer coefficient,W m−2 K−1
K	=	permeability, m2
k	=	thermal conductivity, W m−1 K−1
Le	=	Lewis number;
M	=	molar mass, kg mol−1
Nuf	=	fluid Nusselt number
	=	average Nusselt number
P	=	pressure, N m−2
Pr	=	Prandtl number;
r	=	radial coordinate, m
R	=	cylinder radius, m
Rc	=	conductivity ratio; ,
RF	=	aspect ratio;
Rg	=	universal gas constant, J mol−1 K−1
Rv	=	viscosity ratio;
Ra	=	Rayleigh number
Re	=	Reynolds number; ,
Rep	=	particle Reynolds number; ,
Sco	=	source terms defined in Eq. (8)(8)
St	=	source terms defined in Eq. (7)(7)
Sc	=	Schmidt number;
	=	average Sherwood number
Shf	=	fluid Sherwood number
t	=	time, s
T	=	temperature, K
u	=	axial velocity, m s−1
u0	=	inlet velocity, m s−1
v	=	radial velocity, m s−1
V	=	dimensionless velocity
z	=	axial coordinate, m

Greek symbols

βm	=	mass coefficient of transfer, m s−1
ΔH	=	heat of reaction, J mol−1
∇	=	differential operator
ϵ	=	porosity
μ	=	dynamic viscosity, kg m−1 S−1
ν	=	kinematic viscosity, m2 s−1
ρ	=	density, kg m−3
σ	=	specific heat capacity ratio; σ =(ρ Cp)s/(ρ Cp)f
θ	=	dimensionless temperature
θm	=	dimensionless bulk temperature;
θw	=	dimensionless wall temperature
τ	=	tortuosity
φ	=	variable (T, C, U, V …)

Subscripts

0	=	inlet
eff	=	effective
f	=	fluid
m	=	mean
Mp	=	porous medium
s	=	solid
w	=	wall

Superscripts

*	=	dimensionless variable
→	=	vector

Additional information

Notes on contributors

Ali Bousri

Ali Bousri is a teacher at the University of Houari Boumediene, Algiers, Algeria. He teaches courses in thermodynamics, analytical mechanics, and combustion. He received in 2012 his Ph.D. degree from USTHB. His current research interests are transport phenomena, reactive reaction, heat and mass transfer, and porous media.

Rachid Nebbali

Rachid Nebbali obtained an engineer diploma in mechanical engineering in 1991 and a master's degree in mechanical engineering in 1995 at USTHB, Algiers, and at present he is preparing his Ph.D. thesis. He was employed as a head assistant in the years 1998–2001 and later as a date lecturer in the year 2001 at FGMGP, USTHB, Algiers.

Rachid Bennacer

Rachid Bennacer obtained his engineer diploma in mechanical engineering (1989), and received his Ph.D. degree at Pierre et Marie Curie University (Paris 6) in 1993. He worked as lecturer at the University Paris XI (1993/1994), became an associate professor at Cergy Pontoise University (1994), and obtained the title of Professor A. in 1998 and Professor in 2008. He moved as a senior professor to the prestigious school Ecole Normale superieure Cachan in 2010. In addition, he assumed positions as the director of the LEEVAM research (2003-2007) and the Transfer and Environmental Research Unit (within LMT-Lab/CNRS) teams and the head of License degrees (200–2010) and master research degrees (2011–2013) teams, and he has been the head of the Civil/Environmental Department since October 2012. His research fields cover several domains, including material science, energy system, pollution, and renewable energy, with an expertise in convection–diffusion problems in porous media.

Khedidja Bouhadef

Khedidja Bouhadef completed her License degree in fluid mechanics in 1975 and master in mechanical engineering in 1980 at USTHB, Algiers. In 1988 she obtained her Ph.D. in thermal sciences at Poitiers University, France. She was employed as a head assistant from 1975 to 1980, as a lecturer from 1980 to 1984 in FGMGP, USTHB, as a researcher from 1984 to 1988 in LESTE, Poitiers, France, and as a head lecturer (1988–1994) and later as a Date Professor (1994) in FGMGP, USTHB.

Hassen Beji

Hassen Beji is a professor of mechanics at the University Jules Verne, IUT Amiens, France. His received his Ph.D. degree from Paris VI University in 1989. His current research interests are transport phenomena within heterogeneous materials, thermoconvective instabilities, and multiphysics simulation. He is the L.T.I. laboratory chairman.