Double-diffusive fingering convection in a porous medium
Journal
International Journal of Heat and Mass Transfer
Journal Volume
36
Journal Issue
3
Pages
793-807
Date Issued
1993
Author(s)
Abstract
We consider nonlinear two-dimensional, horizontally periodic, double-diffusive fingering convection in a saturated porous medium. The Darcy equation, including Brinkman and Forchheimer terms to account for viscous and inertia effects, respectively, is used for the momentum equation. A mixed Galerkin-finite difference method (Galerkin in the horizontal direction, finite difference in the vertical direction) is developed to solve the initial boundary value problem. Different values of the stabilizing temperature gradient, characterized by a thermal Rayleigh number RT, ranging between 1 and 50 are considered. The stability boundaries which separate regions of different type of convective motion are identified in terms of RT and RS, the solute Rayleigh number. For RT = 1, for instance, the steady convective flow which bifurcates from the motionless conduction solution at RS1 = 4π2+1 persists in the face of small disturbances up to at least RS = 10RS1. At approximately RS2 = 440, a transition to time-periodic convection occurs. For a larger stabilizing temperature gradient (RT = 50), the steady-convective motion is stable with respect to small disturbances for RS1 = 4π1 + 50 < RS < 4RS1. At approximately RS2 = 405, a periodic convection occurs and persists up to RS3 = 440, at which a multipeaked periodic solution is found. © 1993 Pergamon Press Ltd.
Type
journal article