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.

中文翻译：

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含有非达西多孔介质的开放垂直管道中双扩散耗散反应对流流动的数值研究与罗宾边界条件

开发并研究了热溶质对流在开放二维垂直通道中的数学模型，该通道包含充满反应性牛顿流体的多孔介质。规定了罗宾边界条件，并考虑一阶均相化学反应。Darcy-Forchheimer 模型用于模拟一阶和二阶多孔介质的阻力效应。对于一般的非达西情况，使用 Runge-Kutta 求积法和射击方法给出了数值解。热力 $$( {0 \le \lambda _1 \le 15} )$$ 和溶质 Grashof 数 $$( {0 \le \lambda _2 \le 20} )$$, Biot 数 $$( {1 \le \textit{Bi}_1 \le 10, \textit{Bi}_2 =10 } )$$，布林克曼数 $$( {0 \le \textit{Br} \le 0.5} )$$，一阶化学反应参数 $$( {2 \le \alpha \le 8} )$$, 多孔介质参数 $$( {2 \le \sigma \le 8} )$$ 和 Forchheimer（惯性阻力）参数 $$( {0 \le I \le 12} )$$ 关于速度、温度和浓度的演变（物种）分布以图形方式显示。还针对选定参数的特定值计算壁上的 Nusselt 数和皮肤摩擦。该研究与具有化学反应的地热能系统的分析有关。