Effect of inertia on double diffusive bidispersive convection

Abstract

Convection thresholds in a saturated bidisperse porous material are calculated in the presence of a non-zero coefficient of inertia, the acceleration coefficient, for the fluid velocity in the macro pores. We concentrate on the case where the layer is heated from below and simultaneously salted from below. The effect of increasing the size of the acceleration coefficient is generally to increase the critical Rayleigh number above which convective motion commences, although the precise values depend on the interaction coefficient between the micro and macro pores, the porosities, and the Lewis number.

Continuous dependence on boundary and Soret coefficients in double diffusive bidispersive convection

“…Equation () 5 is the balance of energy for a single temperature, cf. Falsaperla et al, 28 Gentile and Straughan, 19 and Equation () 6 is the equation governing the solute concentration in the presence of the Soret term, see Straughan, 23,25 although we point out that only Nield and Kuznetsov, 12 employ Brinkman terms, the other writers restricting attention to Darcy theory.…”

“…For many real life problems, we believe a single temperature may suffice, while retaining independent velocity and pressure fields in the macro and micro pores. This approach has been applied successfully to various problems using Darcy porous media theory by Falsaperla et al, 17 Franchi et al, 18 Gentile and Straughan, 19,20 and by Straughan 22‐26 . In this work, we adopt a single temperature, but we employ a Brinkman porous medium theory in both the macro and micro pores, in keeping with the original work of Nield and Kuznetsov 12 .…”

The Effect of the Vadasz Number on the Onset of Thermal Convection in Rotating Bidispersive Porous Media

“…Recently, in [10], the effect of Vadasz number on thermohaline convection in a horizontal bidispersive layer, has been investigated. In particular, the destabilizing effect of heating from below opposite to the stabilizing effect of the layer salted from below is studied.…”

“…In this paper we reconsider the problem analyzed in [27], and investigate the effect of inertia in a rotating bidispersive porous medium. We consider the inertia term in the macro-phase only (since inertia effect can be neglected in the micro-phase) and show that inertia allows oscillatory convection at the instability threshold, as done in [10]. The plan of the paper is as follows.…”

Effect of anisotropic permeability on double‐diffusive bidisperse porous medium

“…He performed the linear instability of thermosolutal convection with the Soret effect in a saturated bidisperse porous medium when the layer is heated from below and salted from below or above. Straughan 57 also considered the effect of inertia on double‐diffusive bidispersive convection. He showed that the inertia term led to a very strong effect on the thermosolutal convection.…”