Arabian Journal for Science and Engineering

, Volume 44, Issue 2, pp 1379–1392 | Cite as

Some Insights on Unsteady Double Diffusive Natural Convection of Porous Medium in Vertical Open-Ended Cylinder

  • N. HimraneEmail author
  • D. E. Ameziani
  • M. El Ganaoui
  • H. Ragueb
Research Article - Mechanical Engineering


The work presented in this paper deals with combined heat and mass transfer by natural convection in porous media. The aim is to investigate numerically the effect of control parameters on the flow behavior as well as the enhancement of heat transfer in vertical porous enclosure. The side wall temperature is periodic function of time which is the case in several physical problems. The Darcy’s flow model coupled with the energy and mass equations is considered. The numerical results show that the flow’s behavior is strongly dependent on the buoyancy ratio values. Three types of flows take place: chimney, reversal and top aspiration flow. Further, the effect of buoyancy ratio (N) at which the different flow types occur is significantly influenced by the values of control parameters. The relative heat transfer enhancement between constant and periodical wall temperature is profoundly affected by thermal Rayleigh number (Ra), buoyancy ratio and dimensionless amplitude (XA). In the case of opposing double diffusive flow, the relative difference becomes to the favor of the stationary case for high Ra and XA.


Double diffusive convection Porous medium Open-ended channel Darcy’s flow model 



Aspect ratio, \({A}={R}/{H}\)


Reaction rate, \(\hbox {s}^{-1}\)


Dimensionless lumped reaction rate


Biot number

\({ Bi}_{\mathrm{m}}\)

Mass transfer Biot number


Specific heat, J \(\hbox {kg}^{-1}~\hbox {K}^{-1}\)


Non-dimensional concentration


Solutal diffusivity, \(\hbox {m}^{2}~\hbox {s}^{-1}\)


Acceleration of the gravity, m \(\hbox {s}^{-2}\)


Convective heat transfer coefficient, \(\hbox {J}~\hbox {m}^{-2}~\hbox {K}~\hbox {s}^{-1}\)


Cylinder height, m


Thermal conductivity, J \(\hbox {m}^{-1}~\hbox {K}~\hbox {s}^{-1}\)


Permeability of porous media, \(\hbox {m}^{2}\)


Lewis number, \(Le=\alpha _\mathrm{f} /{D}_{\mathrm{eff}} \)


Local Nusselt number


Buoyancy ratio


Non-dimensional pressure


Recirculation flow


Non-dimensional radial coordinate


Cylinder radius, m


Thermal Rayleigh number


Conductivity ratio


Non-dimensional temperature


Non-dimensional time

U, V

Dimensionless velocity components


Non-dimensional axial coordinate


Non-dimensional amplitude

Greek symbols

\(\alpha \)

Thermal diffusivity, \(\hbox {m}^{2}~\hbox {s}^{-1}\)

\(\beta _\mathrm{T}\)

Thermal expansion coefficient, \(\hbox {kg}~\hbox {m}^{-3}\hbox { K}^{-1}\)

\(\beta _\mathrm{C}\)

Solutal expansion coefficient

\(\mu \)

Dynamic viscosity, kg \(\hbox {m}^{-1}\hbox { s}^{-1}\)

\(\rho \)

Fluid density, \(\hbox {kg}~\hbox {m}^{-3}\)

\(\sigma \)

Heat capacity ratio, \(\frac{( {\rho {C}_\mathrm{P} } )_{\mathrm{eff}} }{( {\rho {C}_\mathrm{P} } )_\mathrm{f} }\)

\(\varepsilon \)


\(\tau \)

Non-dimensionless period

















dimensional quantity


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Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  • N. Himrane
    • 1
    • 2
    Email author
  • D. E. Ameziani
    • 2
  • M. El Ganaoui
    • 3
  • H. Ragueb
    • 1
  1. 1.Laboratoire Energétique, Mécanique et Ingénierie (LEMI)Université M’Hamed Bougara Boumerdes (UMBB)BoumerdèsAlgeria
  2. 2.Laboratoire des Transports Polyphasiques et Milieu Poreux (LTPMP)Université des Sciences et de la Technologie Houari BoumedieneBab EzzouarAlgeria
  3. 3.Université de Lorraine, IUT Henri Poincaré de Longwy (LERMAB-Longwy)NancyFrance

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