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Transient Natural Convection in Differentially Heated Porous Enclosures

Volume 3, Issue 2, 2000, 14 pages
DOI: 10.1615/JPorMedia.v3.i2.60
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ABSTRACT

The problem of steady, laminar, hydromagnetic simultaneous heat and mass transfer by natural convection flow over a vertical cone and a wedge embedded in a uniform porous medium is investigated. Two cases of thermal boundary conditions, namely the uniform wall temperature (UWT) and the uniform wall heat flux (UHF), are considered. A nonsimilarity transformation for each case is employed to transform the governing differential equations to a form whereby they produce their own initial conditions. The transformed equations for each case are solved numerically by an efficient implicit, iterative, finite-difference scheme. The obtained results are checked against previously published work on special cases of the problem and are found to be in excellent agreement. A parametric study illustrating the influence of the magnetic field, porous medium inertia effects; heat generation or absorption; lateral wall mass flux; concentration to thermal buoyancy ratio; and the Lewis number on the fluid velocity, temperature, and concentration as well as the Nusselt and the Sherwood numbers is conducted. The results of this parametric study are shown graphically and the physical aspects of the problem are discussed. It is concluded that while the local Nusselt number decreases owing to the imposition of the magnetic field, it increases as a result of the fluid's absorption effects. Also, both the local Nusselt and Sherwood numbers increase as the buoyancy ratio increases. This is true for both uniform wall temperature and heat flux thermal conditions. Furthermore, including the porous medium inertia effect in the mathematical model is predicted to decrease the local Nusselt number for both the isothermal and isoflux wall cases.

CITED BY
  1. MERRIKH A.A., LAGE J.L., FROM CONTINUUM TO POROUS–CONTINUUM: THE VISUAL RESOLUTION IMPACT ON MODELING NATURAL CONVECTION IN HETEROGENEOUS MEDIA, in Transport Phenomena in Porous Media III, 2005. Crossref

  2. Goldstein R.J., Eckert E.R.G., Ibele W.E., Patankar S.V., Simon T.W., Kuehn T.H., Strykowski P.J., Tamma K.K., Bar-Cohen A., Heberlein J.V.R., Davidson J.H., Bischof J., Kulacki F.A., Kortshagen U., Garrick S., Heat transfer – a review of 2000 literature, International Journal of Heat and Mass Transfer, 45, 14, 2002. Crossref

  3. Hooman K., Gurgenci H., Effects of temperature-dependent viscosity on Bénard convection in a porous medium using a non-Darcy model, International Journal of Heat and Mass Transfer, 51, 5-6, 2008. Crossref

  4. Merrikh Ali Akbar, McNamara Andrew J., Parametric evaluation of foster RC-network for predicting transient evolution of natural convection and radiation around a flat plate, Fourteenth Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm), 2014. Crossref

  5. Imani Gholamreza, Hooman Kamel, Lattice Boltzmann Pore Scale Simulation of Natural Convection in a Differentially Heated Enclosure Filled with a Detached or Attached Bidisperse Porous Medium, Transport in Porous Media, 116, 1, 2017. Crossref

  6. Nield Donald A., Bejan Adrian, Internal Natural Convection: Heating from the Side, in Convection in Porous Media, 2017. Crossref

  7. Nield Donald A., Bejan Adrian, Internal Natural Convection: Heating from the Side, in Convection in Porous Media, 2013. Crossref

  8. Shi Yu-Shu, Liu Di, Wang Yu, Zhao Fu-Yun, Li Yu-Xing, Forced flow structure and mixed convection in a ventilated porous enclosure with a local contaminant source, International Journal of Heat and Mass Transfer, 131, 2019. Crossref

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