Numerical study of double-diffusive dissipative reactive convective flow in an open vertical duct containing a non-Darcy porous medium with Robin boundary conditions

A mathematical model for thermosolutal convection flow in an open two-dimensional vertical channel containing a porous medium saturated with reactive Newtonian fluid is developed and studied. Robin boundary conditions are prescribed, and a first-order homogenous chemical reaction is considered. The Darcy–Forchheimer model is used to simulate both the first- and second-order porous mediums’ drag effects. For the general non-Darcy-case, a numerical solution is presented using the Runge–Kutta quadrature and a shooting method. The influences of thermal \(( {0 \le \lambda _1 \le 15} )\) and solute Grashof numbers \(( {0 \le \lambda _2 \le 20} )\), Biot numbers \(( {1 \le \textit{Bi}_1 \le 10, \textit{Bi}_2 =10 } )\), Brinkman number \(( {0 \le \textit{Br} \le 0.5} )\), first-order chemical reaction parameter \(( {2 \le \alpha \le 8} )\), porous medium parameter \(( {2 \le \sigma \le 8} )\) and Forchheimer (inertial drag) parameter \(( {0 \le I \le 12} )\) on the evolutions of velocity, temperature and concentration (species) distributions are visualized graphically. Nusselt number and skin friction at the walls are also computed for specific values of selected parameters. The study is relevant to the analysis of geothermal energy systems with chemical reaction.