Effect of Buoyancy Ratio on Non-Darcy Mixed Convection in a Vertical Channel: A Thermal Non-equilibrium Approach
This article presents a numerical study of the doublediffusive
mixed convection in a vertical channel filled with porous
medium by using non-equilibrium model. The flow is assumed
fully developed, uni-directional and steady state. The controlling
parameters are thermal Rayleigh number (RaT ), Darcy number (Da),
Forchheimer number (F), buoyancy ratio (N), inter phase heat transfer
coefficient (H), and porosity scaled thermal conductivity ratio
(γ). The Brinkman-extended non-Darcy model is considered. The
governing equations are solved by spectral collocation method. The
main emphasize is given on flow profiles as well as heat and solute
transfer rates, when two diffusive components in terms of buoyancy
ratio are in favor (against) of each other and solid matrix and fluid
are thermally non-equilibrium. The results show that, for aiding flow
(RaT = 1000), the heat transfer rate of fluid (Nuf ) increases upto a
certain value of H, beyond that decreases smoothly and converges
to a constant, whereas in case of opposing flow (RaT = -1000),
the result is same for N = 0 and 1. The variation of Nuf in (N,
Nuf )-plane shows sinusoidal pattern for RaT = -1000. For both cases
(aiding and opposing) the flow destabilize on increasing N by inviting
point of inflection or flow separation on the velocity profile. Overall,
the buoyancy force have significant impact on the non-Darcy mixed
convection under LTNE conditions.
 D.A. Nield and A. Bejan, Convection in Porous Media, Springer, New
 K. Vafai, Handbook of Porous Media, Marcel Dekker, New York, 2000.
 V.V. Calmidi and R.L. Mahajan, "Forced convection in high porosity
foams", Trans. ASME J. of Heat Transfer, vol. 122 pp. 557-565, 2000.
 M.K. Khandelwal and P. Bera, "A thermal non-equilibrium perspective
on mixed convection in a vertical channel", Int. J. Thermal Sciences vol.
56 pp. 23-34, 2012.
 P. Bera, J. Kumar and A. Khalili, "Hot springs mediate spatial exchange of
heat and mass in the enclosed sediment domain: A stability perspective",
Adv. Water Resources, vol. 34 pp. 817-828, 2011.
 Z. Alloui1 and P. Vasseur, "Fully developed mixed convection of a binary
fluid in a vertical porous channel", The canadian J. Chem. Engineering,
 P. Bera, S. Kapoor and M.K. Khandelwal, "Double-diffusive mixed convection
in a vertical pipe: a thermal non-equilibrium approach" accepted
for publication in Int. J. Heat and Mass Transfer (2012).
 A. Kumar and P. Bera J.Kumar "Non Darcy mixed convection in a vertical
pipe filled with porous medium", Int. J. of Thermal Sciences vol. 50 pp.
 Y.C. Chen, J.N. Chung, C.S. Wu and Y.F. Lue, "Non-Darcy flow stability
of mixed convection in a vertical channel filled with a porous medium"
Int. J. Heat Mass Transfer vol. 43 pp. 2421-2429, 2000.
 P.G. Drazin and W.H. Reid, Hydrodynamic Stability Cambridge: Cambridge
University Press; 2004.
 Y.C. Su and J.N. Chung, "Linear stability analysis of mixed-convection
flow in a vertical pipe", J. Fluid Mechanics vol. 422 pp. 141-166, 2000.