UNSTEADY TRIPLE-DIFFUSIVE CONVECTION EMBEDDED WITH DARCY-BRINKMAN THREE-TEMPERATURE MODEL

Abstract

The theory of binary nanofluid layer heated and soluted from below under the effect of local thermal non-equilibrium has been investigated by applying the technique of superposition of basic feasible modes with one-term Galerkin residual method. The so-called Darcy-Brinkman model for the top-heavy distribution of nanoparticles has been employed. A three-temperature local thermal non-equilibrium (LTNE) model, assuming one-temperature field for the solid matrix, one for the base fluid, and one for the suspended nanosized particles, is employed, incorporating the effects of Brownian and thermophoretic diffusions. Numerical computations are carried out with the software Mathematica (version 12.0). The novelty of the problem lies in the fact that destabilizing influence of nanoparticles and solute is countered with stabilization due to the presence of Darcy-Brinkman porous medium. Further, it has been observed that the two LTNE parameters namely, Nield parameter for particles and modified solute thermal capacity ratio, have destabilizing effects which are balanced by the other two parameters, viz. Nield parameter for solute and modified thermal capacity ratio for particles. The impact of nanofluid parameters is found to destabilize this top-heavy configuration of nanoparticles. Due to the consideration of Darcy-Brinkman model, Darcy number came into existence, which postpones the onset of instability. Similar is the effect of porosity and modified thermal diffusivity ratios for the particles as well as the solute.