Oberbeck convection through vertical porous stratum

Natural convection through a vertical porous stratum is investigated both analytically and numerically. Analytical solutions are obtained using a perturbation method valid for small values of buoyancy parameter N and the numerical solutions are obtained using Runge-Kutta-Gill method. It is shown that analytical solutions are valid for N < 1 and several features of the effect of large values of N are reported. The combined effects of increase in the values of temperature difference between the plates and the permeability parameter on velocity, temperature, mass flow rate and the rate of heat transfer are reported. It is shown that higher temperature difference is required to achieve the mass flow rate in a porous medium equivalent to that of viscous flow

Double diffusive convection in a viscoelastic fluid-saturated porous layer using a thermal non-equilibrium model

The stability of a binary viscoelastic fluid-saturated porous layer which is heated from below is studied, where the fluid and solid phases are not in local thermal equilibrium. The modified Darcy-Oldroyd model is employed as a momentum equation, with the fluid and solid phase temperature fields modeled separately. It is found that the inter-phase heat transfer coefficient has a significant effect on the stability of the system. Competition between the processes of viscous relaxation and thermal diffusion cause the convection to set in through oscillatory rather than stationary instability, with the viscoelastic parameters inhibiting the onset of convection. In the case of weakly non-linear theory, both steady and unsteady cases are considered. In the unsteady case the transient behaviour of the Nusselt and Sherwood numbers is investigated. The effect of thermal non-equilibrium on heat and mass transfer is also discussed. © 2012 Springer-Verlag

Convective instability of Oldroyd-B fluid saturated porous layer heated from below using a thermal non-equilibrium model

The linear stability of a viscoelastic fluid saturated densely packed horizontal porous layer heated from below and cooled from above is investigated by considering the Oldroyd-B type fluid. A generalized Darcy model, which takes into account the viscoelastic properties, is employed as momentum equation and a two-field model is used for energy equation each representing solid and fluid phases separately. Linear stability analysis suggests that, there is a competition between the processes of viscous relaxation and thermal diffusion that causes the first convective instability to be oscillatory rather than stationary. Analytical expression for the occurrence of oscillatory onset is obtained, and it is found that the necessary condition for the existence of the same is � < 1. Besides, the effect of viscoelastic parameters and the thermal non-equilibrium on the stability of the system is analyzed. © Springer 2006