A numerical study of heat and mass transfer in a Darcy porous medium saturated with a couple stress fluid under rotational modulation

Abstract

A theoretical investigation of the influence of time-dependent rotational modulation on the stability, heat, and mass transfer in a Darcy porous medium with a couple stress fluid is presented. A perturbation technique dependent on the infinitesimal amplitude of the disturbance parameter is used to study the consolidated effects of modulating rotation, solute gradient, and permeability on the stability of a porous medium. The Ginzburg Landau equation is obtained and used to quantify heat and mass transport as the Nusselt and Sherwood numbers respectively. The coupled nonlinear Lorenz equations are solved using a newly developed multidomain spectral collocation method. Simulations of the phase plane trajectories are used to represent and analyze limited sets of solutions. We find among other results, that the effect of increasing the modulation amplitude is to accelerate the heat and mass transport. The results from the Ginzburg Landau approach are qualitatively similar to that of the Lorenz approach although the Lorenz approach was more efficient.