Thermo-solutal convection with Soret effect

In the present study, the onset of thermal convection in a liquid layer overlying a porous layer where the whole system is being laterally heated is investigated. The non-linear two-dimensional Navier Stokes equations, the energy equation, the mass balance equation and the continuity equation are solved for the liquid layer. Instead of the Navier Stokes equations, the Brinkman model is used for the porous layer. The partial differential equations are solved numerically using the finite element technique. A two-dimensional geometrical model with lateral heating is considered. Two different cases are analyzed in this thesis. In the first case, the gravity driven buoyancy convection and the Marangoni convection are studied. For the Marangoni convection, the microgravity condition is considered and the surface tension is assumed to vary linearly with temperature. Different aspect ratios, as well as thickness ratios, are studies in detail for both the buoyancy and the Marangoni convection. Results revealed that for both the buoyancy and the Marangoni cases, flow penetrates into the porous layer, only when the thickness ratio is more than 0.90. In the case of thermo-solutal convection in the presence of Soret effect, it has been found that the isopropanol component goes either towards the hot or the cold walls depending on the fluid mixtures which has been used in the system.

Thermo-solutal convection with Soret effect

In the present study, the onset of thermal convection in a liquid layer overlying a porous layer where the whole system is being laterally heated is investigated. The non-linear two-dimensional Navier Stokes equations, the energy equation, the mass balance equation and the continuity equation are solved for the liquid layer. Instead of the Navier Stokes equations, the Brinkman model is used for the porous layer. The partial differential equations are solved numerically using the finite element technique. A two-dimensional geometrical model with lateral heating is considered. Two different cases are analyzed in this thesis. In the first case, the gravity driven buoyancy convection and the Marangoni convection are studied. For the Marangoni convection, the microgravity condition is considered and the surface tension is assumed to vary linearly with temperature. Different aspect ratios, as well as thickness ratios, are studies in detail for both the buoyancy and the Marangoni convection. Results revealed that for both the buoyancy and the Marangoni cases, flow penetrates into the porous layer, only when the thickness ratio is more than 0.90. In the case of thermo-solutal convection in the presence of Soret effect, it has been found that the isopropanol component goes either towards the hot or the cold walls depending on the fluid mixtures which has been used in the system.

Solutal Convection in Layered Sorbing Porous Media

<p>We study convective instability in the vertically layered porous media saturated with mixture. The mixture consists of a carrier fluid and solid nanoparticles. The nanoparticles are considered as solute within the continuous approach. The porous media are two horizontal sublayers with different permeabilities. The solute concentration is maximal near the upper boundary and is zero near the lower boundary of the superposed sublayers. Thus, one has suitable conditions for the onset of solutal convection in the gravitational field.</p><p>The porous sublayers are reactive media, which can absorb nanoparticles. The mixture transport here is accompanied by immobilization. It is described by the mobile/immobile media model. The mobile phase is carried by fluid flow, while the immobile phase is absorbed by porous matrix. The linear kinetic equation for the mixture redistribution between the phases is applied. The Boussinesq approximation is used in the equations for convection in each of the sublayers. Numerical simulation is performed by the shooting method.</p><p>We apply a linear stability theory to find the threshold Rayleigh-Darcy number for the onset of solutal convection. This similarity criterion is determined through the average permeability and porosity of uncontaminated porous sublayers. For the first time, we introduce a solutal pore shrinkage coefficient, which is analogous to the thermal expansion coefficient for thermal natural convection. This coefficient shows that porosity decreases as the concentration of immobile phase grows in the presence of sorption. Particles in this case join the surface of pores and shrink the void space.</p><p>Firstly, we find the permeability ratios for bimodal marginal stability curves in the uncontaminated sublayers. Here, the sublayer permeabilities differ by approximately 100 times. The bimodal curves demonstrate the competition between two convective instabilities. One of them is for the local convective rolls that generate within the more permeable layer and the other is for the large-scale rolls penetrating both layers. The rolls are similar to thermal natural convection in the multi-layered porous media studied by McKibbin and O'Sullivan (1980). For sorbing porous media, the type of convective rolls strongly depends on the solutal pore shrinkage coefficient. Even a small change in its value can produce a large variation of flow streamlines from the convective rolls localized within the upper highly permeable sublayer to the rolls covering both the upper and lower sublayers. The observed sorption effect on the transition from local to large-scale convection is due to the fact that the permeability ratio depends on the solutal pore shrinkage coefficient. It is also found that sorption effect delays the onset of solutal convection.</p><p>The work was supported by the Russian Science Foundation (Grant No. 20-11-20125).</p>

Thermosolutal convection of a nanofluid in ∧-shaped cavity saturated by a porous medium

Purpose The purpose of this study is to simulate the thermo-solutal convection resulting from a circular cylinder hanging in a rod inside a ∧-shaped cavity. Design/methodology/approach The two dimensional ∧-shaped cavity is filled by Al2O3-water nanofluid and saturated by three different levels of heterogeneous porous media. An incompressible smoothed particle hydrodynamics (ISPH) method is adopted to solve the governing equations of the present problem. The present simulations have been performed for the alteration of buoyancy ratio (−2≤N≤2), radius of a circular cylinder (0.05≤Rc≤0.3), a height of a rod (0.1≤Lh≤0.4), Darcy parameter (10−3≤Da≤10−5), Lewis number (1≤Le≤40), solid volume fraction (0≤ϕ≤0.06), porous levels (0≤η1=η2≤1.5)and various boundary-wall conditions. Findings The performed numerical simulations indicated the importance of embedded shapes on the distributions of temperature, concentration and velocity fields inside ∧-shaped cavity. Increasing buoyancy ratio parameter enhances thermo-solutal convection and nanofluid velocity. Adiabatic conditions of the vertical-walls of ∧-shaped cavity augment the distributions of the temperature and concentration. Regardless the Darcy parameter, a homogeneous porous medium gives the lowest values of a nanofluid velocity. Originality/value ISPH method is used to simulate thermo-solutal convection of a nanofluid inside a novel ∧-shaped cavity containing a novel embedded shape and heterogeneous porous media.