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The object of this study is to investigate the question of convective movement of a reacting solute in a viscous incompressible occupying a plane layer in a saturated bidisperse porous material. Among the characteristics of a bidisperse porous medium are pores, called macropores, but porosity in the solid skeleton, known as microporosity, arises where there are cracks or fissures in that skeleton. In this paper, a comparison is made between the thresholds for linear instability and those obtained from a global nonlinear energy stability analysis.

In this paper, we study the problem of thermosolutal convection in a Navier-Stokes-Voigt fluid when the layer is heated from below and simultaneously salted from above or below. This problem is studied under the effects of Soret and slip boundary conditions. Both linear and nonlinear stability analyses are employed. When the layer is heated from below and salted from above, the boundaries exhibit great concordance, resulting in a very narrow region of probable subcritical instabilities. This proves that linear analysis is reliable enough to forecast the beginning of convective motion. Chebyshev collocation technique and QZ algorithm have been used to solve systems of linear and nonlinear theories. For thermal convection in a dissolved salt field with a complex viscoelastic fluid of the Navier-Stokes-Voigt type, instability boundaries are computed. When the convection is of the oscillatory type, the Kelvin-Voigt parameter is observed to play a crucial role in functioning as a stabilizing agent. This effect's quantitative size is shown.

Analysis of fluid flow in a bidispersive medium with reactions is explored. The Darcy model is used in the momentum equation with the density being a linear function in temperature and salt concentration. Two cases are regarded which are heated below and salted above system and heated and salted below system. It is presumed that the equilibrium solute concentration follows a linear relationship to temperature. A linear instability and nonlinear stability theories are conducted, and from the outputs of the analysis, the Chebyshev collocation approach is used to solve the resulting eigenvalue systems. The effects of the chemical reaction and other parameters on temperature Rayleigh number are described graphically.

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