Heat and Mass Transfers on the Chemically Reactive Thermosolutal Convective Flow of Rivlin-Ericksen Fluid over a Porous Medium with Viscous Dissipation Effect

Chemically reacting flows of non-Newtonian fluids through porous media have numerous medical and industrial applications, including targeted drug delivery, polymer processing, and extrusion operations. In these contexts, convective heat transfer is a critical mechanism that must be accurately predicted. This article analyzes the thermosolutal convection of a chemically reactive Rivlin-Ericksen fluid in a porous medium, accounting for viscous dissipation, using both linear and nonlinear stability approaches. The nonlinear analysis is performed using a truncated Fourier series method, while the linear stability is examined via the normal mode technique. It is found that oscillatory convection occurs only when the solutal Rayleigh-Darcy number is negative. The range of this number that allows oscillatory convection depends on several physical parameters. An increase in the Rivlin-Ericksen parameter, the modified heat capacity ratio, and the Péclet number reduces this range, whereas a higher Lewis number expands it. Moreover, the Lewis number, solutal Rayleigh-Darcy number, and Gebhart number accelerate the onset of convective waves, while the Rivlin-Ericksen parameter and the modified heat capacity ratio delay it. Additionally, both convective heat and mass transfer rates decrease with increasing Rivlin-Ericksen parameter and modified heat capacity ratio, but they increase with higher values of the thermal and solutal Rayleigh-Darcy numbers, the Lewis number, the chemical reaction parameter, the Péclet number, and the Gebhart number.