The Onset of Convection in an Anisotropic Porous Layer Using a Thermal Non-Equilibrium Model
Tóm tắt
The stability of a horizontal fluid saturated anisotropic porous layer heated from below and cooled from above is examined analytically when the solid and fluid phases are not in local thermal equilibrium. Darcy model with anisotropic permeability is employed to describe the flow and a two-field model is used for energy equation each representing the solid and fluid phases separately. The linear stability theory is implemented to compute the critical Rayleigh number and the corresponding wavenumber for the onset of convective motion. The effect of thermal non-equilibrium and anisotropy in both mechanical and thermal properties of the porous medium on the onset of convection is discussed. Besides, asymptotic analysis for both very small and large values of the interphase heat transfer coefficient is also presented. An excellent agreement is found between the exact and asymptotic solutions. Some known results, which correspond to thermal equilibrium and isotropic porous medium, are recovered in limiting cases.
Tài liệu tham khảo
N. Banu D. A. S. Rees (2002) ArticleTitleOnset of Darcy-Benard convection using a thermal non-equilibrium model, Int J. Heat Mass Transfer 45 2221–2228
G. Castinel M. Combarnous (1974) ArticleTitleCritere d’ apparition de la convection naturelle dans une couche poreuse anisotrope horizontal C. R. Acad. Sci 278 701–704
J. F. Epherre (1975) ArticleTitleCritere d’ apparition de la convection naturelle dans une couche poreuse anisotrope, Revue Gen. Thermique 168 949–950
D. B. Ingham I. Pop (Eds) (1998) Transport Phenomena in Porous Media Pergamon Oxford
A. Khalili I. S. Shivakumara M. Huettel (2002) ArticleTitleEffects of throughflow and internal heat generation on convective instabilities in an anisotropic porous layer J. Porous Media 5 187–198
A. V. Kuznetsov (1998) Thermal non-equilibrium forced convection in porous Media Derek B. Ingham I. Pop (Eds) Transport Phenomena in Porous Media Pergamon Oxford 103–130
O. Kvernvold P. A. Tyvand (1979) ArticleTitleNonlinear thermal convection in anisotropic porous media J. Fluid Mech 90 609–624
Malashetty, M. S., Shivakumara, I. S. and Sridhar, K.: 2004, The onset of Lapwood–Brinkman convection using a thermal non-equilibrium model, Int. J. Heat Mass Transfer (to appear).
R. McKibbin (1986) ArticleTitleThermal convection in a porous layer: effects of anisotropy and surface boundary conditions Transport Porous Media 1 271–292
D. A. Nield A. Bejan (1999) Convection in Porous Media EditionNumber2 Springer-Verlag New York
T. Nilsen L. Storesletten (1990) ArticleTitleAn analytical study of natural convection in isotropic and anisotropic porous channels Trans. ASME J. Heat Transfer 112 396–401
Y. Qin P. N. Kaloni (1994) ArticleTitleConvective instabilities in anisotropic porous media Studies in Applied Mathematics 91 189–204
D. A. S. Rees I. Pop (1999) ArticleTitleFree convective stagnation point flow in a porous medium using thermal non-equilibrium model Int. Commn. Heat Mass Transfer 26 945–954
D. A. S. Rees I. Pop (2000) ArticleTitleVertical free convective boundary layer flow in a porous medium using a thermal non-equilibrium model J. Porous Media 3 31–44
D. A. S. Rees I. Pop (2002) ArticleTitleVertical free convective boundary layer flow in a porous medium using a thermal non-equilibrium model: elliptic effects J. Appl. Math. Phys 53 1–12
L. Storesletten (1998) Effects of anisotropy on convective flow through porous media Derek B. Ingham I. Pop (Eds) Transport Phenomena in Porous Media Pergamon Press Oxford 261–283
P. A. Tyvand L. Storesletten (1991) ArticleTitleOnset of convection in an anisotropic porous medium with oblique principal axes J. Fluid Mech 226 371–382
K. Vafai (Eds) (2000) Handbook of Porous Media Marcel Dekker New York