Buoyancy driven bioconvective Casson nanofluid flow over a vertical stretching cylinder in Darcy–Forchheimer permeable medium with Arrhenius activation energy and chemical reaction

A mathematical framework is conceived to analyze the flow of Darcy–Forchheimer Casson nanofluid around a vertically stretchable cylinder, taking into account the convective boundary conditions. The heat and mass transport phenomena are visualized in the existence of activation energy and gyrotactic microorganisms with buoyancy effects. Additionally, an external magnetic field is applied to the flow problem. This particular model finds applications in biomedical engineering, the oil and gas industry, heat exchangers and thermal systems, environmental engineering, and renewable energy. By employing suitable transformations to transform partial differential equations into ordinary ones, the MATLAB function bvp4c package is utilized to numerically solve the equations. The findings presented through graphs illustrate the influence of various parameters on velocity, heat and mass transfer, and the density of gyrotactic microorganisms. The analysis revealed that fluid momentum decreases with increasing porosity numbers, while higher activation energy values enhance concentration. Moreover, an increase in the Peclet number reduces the microorganism’s distribution. Tables compute the motile microorganism’s density, Nusselt number, and Sherwood number. A substantial rise in activation energy prominently increases concentration, accompanied by a decrease in the Sherwood number. The density of microorganisms rises with higher values of the curvature parameter, Prandtl number, and Brownian motion parameter, but decreases with an increasing Hartman number. Noteworthy concordance is noted when juxtaposing the findings of this investigation with those of earlier scholarly research.