Multiple Slips and Variable Transport Property Effect on Magnetohydromagnetic Dissipative Thermosolutal Convection in a Porous Medium

A mathematical study is presented to investigate the influence of variable transport properties, momentum, thermal, and mass slip on magnetohydrodynamic (MHD) momentum, heat, and mass transfer in a Darcian porous medium. Slip effects are simulated via careful imposition of boundary conditions at the wall. Joule heating and viscous dissipation are also studied. The governing partial differential boundary layer equations are analyzed using Lie group theory and rendered with appropriate transformations into a system of nonlinear, coupled ordinary differential equations. The multiphysical boundary value problem is dictated by 12 thermophysical parameters: concentration diffusivity ($D_c$), Hartmann magnetic number ($M$), permeability ($\mathrm{\Omega }$), Eckert number (Ec), momentum slip ($a$), thermal slip ($b$), mass (species) slip ($d$), Prandtl number ($\mathsf{Pr}$), Schmidt number ($\mathsf{Sc}$), power law index ($m$) for nonisothermal and nonisosolutal effects, viscosity variation ($A$), and thermal conductivity variation ($S$). A numerical solution is obtained for the effects of selected parameters on transport characteristics using the robust Runge-Kutta-Fehlberg fourth-fifth order numerical method. Excellent correlation is achieved between the present computational results and for the constant transport properties ($A=S=Dc=0$), nonporous ($\mathrm{\Omega }=0$), nonthermal slip ($b=0$), nonsolutal slip ($d=0$), and nondissipative solutions without joule heating ($\mathrm{Ec}=0$). Increasing momentum slip enhances temperatures, whereas increasing thermal slip reduces them. An increase in thermal conductivity boosts temperatures, whereas greater viscosity reduces temperatures. Increasing the magnetic parameter suppresses velocity and increasing permeability parameter elevates temperatures. Species concentration is enhanced with increasing concentration diffusivity and permeability parameter but depressed with increasing viscosity. Furthermore, concentration is enhanced with momentum slip but reduced with mass slip parameter. Increasing magnetic field is observed to aid species diffusion in the regime. The present study finds applications in trickle bed reactor hydromagnetics, magnetic polymeric materials processing, and MHD energy generator slip flows.