Analyzing the exothermic reactions of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si12.svg"> <mml:mrow> <mml:mi mathvariant="italic">Cu</mml:mi> </mml:mrow> </mml:math> nanoparticles with the Dufour effect and the influence of th

• Here the copper–water nanofluid flow is considered. • The impacts of the chemical reactions, Dufour number, heat generation, and permeability factors are considered. • The flow characteristics are explained over a porous moving surface. • The Finite difference method was used to exhibit the numerical results. The heat and mass concept is analyzed through the properties of the Dufour number, chemical reactions, and the heat generation parameters on MHD incompressible nanofluids flow. The MATLAB software with the finite difference method (FDM) was employed to find and graphically present the system’s numerical solutions. This study finds an increased Dufour number enhancing the flow speed and hotness of the nanofluid. The chemical reactions released heat energy to the surrounding environment, escalating the nanofluid’s temperature and decreasing the concentration of the nanoparticles. The rate of permeability strengthens the flow velocity by improving the flow network. The increased heat generation parameter influenced the increase in nanofluids’ velocity and temperature. This study can be considered in some applications, such as designing heat exchangers, solar cells, climate changes, and separation process industries.