Abstract
A local thermal non-equilibrium model for the temperature representing the solid and fluid phases separately is used to study the onset of free convection in a sparsely packed porous layer using the Brinkman-extended Darcy model. The lower boundary of the porous layer is considered to be rigid and isothermal, while the upper isothermal boundary is assumed to be either rigid or free. The Galerkin method is used to obtain the eigenvalue equation, which is then solved numerically. The effects of thermal non-equilibrium and other physical parameters on the onset of convection are analyzed and compared for two types velocity boundary conditions considered. Besides, some known results available in the literature are compared with those obtained from the present study and good agreement is found.
Similar content being viewed by others
References
Walker K, Homsy GM (1977) A note on convective instabilities in Boussinesq fluids and porous media. ASME J Heat Transf 45: 338–339
Rees DAS (2002) The onset of Darcy-Brinkman convection in a porous layer: an asymptotic analysis. Int J Heat Mass Transf 45: 2213–2220
Vafai, K (eds) (2000) Handbook of porous media. Marcel Dekker, New York
Vafai, K (eds) (2005) Handbook of porous media. Taylor and Francis/CRC, Boca Raton
Nield DA, Bejan A (2006) Convection in porous media, 3rd edn. Springer-Verlag, New York
Vafai K, Amiri A (1998) Non-Darcian effects in combined forced convective flows. In: Ingham DB, Pop I (eds) Transport phenomena in porous media. Oxford, Pergamon, pp 313–329
Kuznetsov AV (1998) Thermal non-equilibrium forced convection in porous media. In: Ingham DB, Pop I (eds) Transport phenomena in porous media. Oxford, Pergamon, pp 103–130
Rees DAS, Pop I (1999) Free convective stagnation-point flow in a porous medium using a thermal non-equilibrium model. Int Commun Heat Mass Transf 26: 945–954
Rees DAS, Pop I (2000) Vertical free convective boundary layer flow in a porous medium using a thermal non-equilibrium model. J Porous Media 3: 31–44
Rees DAS, Pop I (2002) Vertical free convective boundary-layer flow in a porous medium using a thermal non-equilibrium model: elliptic effects. J Appl Math Phys 53: 1–12
Banu N, Rees DAS (2002) Onset of Darcy–Benard convection using a thermal non-equilibrium model. Int J Heat Mass Transf 45: 2221–2228
Postelnicu A, Rees DAS (2003) The onset of Darcy-Brinkman convection in a porous medium using a thermal non-equilibrium model. Part 1: stress-free boundaries. Int J Energy Res 27: 961–973
Baytas AC, Pop I (2002) Free convection in a square porous cavity using a thermal non-equilibrium model. Int J Thermal Sci 41: 861–870
Baytas AC (2004) Thermal non-equilibrium free convection in a cavity filled with a non-Darcy porous medium. In: Ingham DB, Bejan A, Mamut E, PopI (eds) Emerging technologies and techniques in porous media. Kluwer Academic, Dordrecht, pp 247–258
Saeid NH (2004) Analysis of mixed convection in a vertical porous layer using non-equilibrium model. Int J Heat Mass Transf 47: 5619–5627
Rees DAS, Pop I (2005) Local thermal non-equilibrium in porous medium convection. In: Ingham DB, Pop I (eds) Transport phenomena in porous media, vol III. Elsevier, Oxford, pp 147–173
Malashetty MS, Shivakumara IS, Kulkarni S (2005) The onset of Lapwood–Brinkman convection using a thermal non-equilibrium model. Int J Heat Mass Transf 48: 1155–1163
Malashetty MS, Shivakumara IS, Kulkarni S (2005) The onset of convection in an anisotropic porous layer using a thermal non-equilibrium model. Trans Porous Media 60: 199–215
Straughan B (2006) Global nonlinear stability in porous convection with a thermal non-equilibrium model. Proc R Soc Lond A 462: 409–418
Malashetty MS, Shivakumara IS, Kulkarni S, Swamy M (2006) Convective instability of Oldroyd-B fluid saturated porous layer heated from below using a thermal non-equilibrium model. Trans Porous Media 64: 123–139
Shivakumara IS, Malashetty MS, Chavaraddi KB (2006) Onset of convection in a viscoelastic fluid-saturated sparsely packed porous layer using a thermal non- equilibrium model. Can J Phys 84: 973–990
Nouri-Borujerdi A, Noghrehabadi AR, Rees DAS (2007) Onset of convection in a horizontal porous channel with uniform heat generation using a thermal non-equilibrium model. Trans Porous Media 69: 343–357
Nouri-Borujerdi A, Noghrehabadi AR, Rees DAS (2007) The effect of local thermal non-equilibrium on impulsive conduction in porous media. Int J Heat Mass Transf 50: 3244–3249
Postelnicu A (2008) The onset of a Darcy-Brinkman convection using a thermal nonequilibrium model. Part II. Int J Thermal Sci 47: 1587–1594
Guo J, Kaloni PN (1995) Double diffusive convection in a porous medium, nonlinear stability and the Brinkman effect. Stud Appl Math 94: 341–358
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Shivakumara, I.S., Mamatha, A.L. & Ravisha, M. Boundary and thermal non-equilibrium effects on the onset of Darcy–Brinkman convection in a porous layer. J Eng Math 67, 317–328 (2010). https://doi.org/10.1007/s10665-010-9362-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10665-010-9362-3