Study of Bioconvection Phenomenon in Jefferey Model in a Darcy-Forchheimer Porous Medium

The current work analyzes the role of various thermophysical variables in examining the Jeffrey model bioconvection phenomena in a stretched Darcy-Forchheimer medium. The non-Newtonian Jeffrey fluid model is significant because of its enormous applicability in the production of industrial fields, such as paints, oils, gels, and adhesives. Continuing measurements of the non-Newtonian model's flow dynamics and heat transfer shows complex fluctuations in the mass and heat flux rates. These observations, made under various physical conditions, help to clarify what its actual behavior is. The governing equations are converted to nonlinear ordinary differential equations utilizing a similarity transform and then solving analytically using the BVPh2.0 tool designed for optimal homotopic procedure in Mathematica. The temperature, velocity, concentration, and bioconvection microorganism analytical findings are generated and visually shown. Our investigation found that fluid velocity increased in the case of Jeffrey's fluid increase. Collisions between fluid particles produce Brownian motion, which increases fluid kinetic energy and nanoparticle activity and raises temperature; an increased Nt increases thermophoretic force, which pushes tiny particles far from the heated surface and produces a counter flow. By increasing the values of beta and the velocity profile increases. The profile of velocity is greater for the boundary layer with thickness eta = 0 without dimensions and then sharply decreases along the stretching sheet to zero. In the absence of magnetic fields, the profile of velocity is maximum, and in the presence of magnetic fields, it drops. By using the Jefferey model to investigate bioconvection in Darcy-medium, this work has practical implications that go beyond theoretical domains. These include groundwater management in environmental engineering and bioreactor optimization in biotechnology. Heat exchangers, distillation towers, cancer therapy, magnetic field-assisted wound healing, MHD Jeffrey fluid with porous media, and hyperthermia are just some of this fluid's industrial and medicinal uses.