Flow patterns in a fluid-saturated porous cube heated from below

Abstract

Natural convection in a cube of fluid-saturated porous medium heated from below and cooled from the top is studied numerically using a non-Darcy flow model. All vertical sidewalls are considered to be impermeable and adiabatic. The evolution of the various flow patterns is investigated from onset up to a Rayleigh number of 1000 where irregularly fluctuating convection prevails. New flow patterns have been found to exist in addition to those mentioned in the previous studies. In the present study, a total of ten steady flow patterns have been identified, of which five show oscillatory behaviour in some Rayleigh-number range. The results are presented in terms of average Nusselt number curves consisting of the solution branches of the convective patterns. The convective patterns are classified in terms of their symmetry properties, and the symmetries broken or gained during bifurcations from one flow structure to the other are identified.

Selection of steady regimes of a one-parameter family in the problem of plane convective flow through a porous medium

“…where F i,j is the right hand side of system (14), and = 10 −6 . To analyze the results, we constructed an experimental probability distribution function of the selection of the regime p(s), where s is the parameter in the family.…”

“…Many studies 10 demonstrate the existence of multiple flow patterns and show that the stability of the flow strongly depends on the Rayleigh number and the aspect ratio of the cavity (see, e.g. [5,11,12,13,14,15]). There are also many numerical and analytical studies of the transition of convective patterns from the stationary state to steady flows and then to unsteady chaotic regimes (see, e.g.…”

“…To solve the Cauchy problem for system (14) we mainly used the RungeKutta method of fourth order with variable step-size and automatic error con-…”

Asymptotic Profiles for the Blasius and Sakiadis flows in a Darcy–Brinkman Isotropic Porous Medium Either with Uniform Suction or with Zero Transverse Velocity

“…In the recent works by Nield (2007), Sezai (2005) and Malashetty et al (2005), the complete equations are given for the flow in a porous medium. For steady, two-dimensional boundary layer flow, the equations given in the above works take the following form continuity equation:…”

Three-dimensional model of the deep geothermal resources in the Taupo–Reporoa Basin, New Zealand

“…In some cases 3D convection may occur or sometimes 2D rolls are preferred (e.g. Sezai, 2005). In either case the distance between the plumes is dependent on the Rayleigh number.…”