A numerical investigation of heat and mass transfer in the bioconvective Oldroyd B nanofluid flow through the porous stretching Riga surface with gyrotactic microorganism

Multidisciplinary insights are gained from the investigation of Oldroyd-B nanofluid flow with microorganisms across a porous Riga plate. Research can improve environmental processes, optimize heat and mass transport in industrial systems, and progress biomedical advances. Thus, the objective of this research is to examine the activation energy linked with the bioconvection nanoflow's propagation across the Riga plate through the Arrhenius effect. A time-varying Lorentz force induces vertical current flow in the fluid, an effect modeled using a Riga plate under an applied electromagnetic field. The model has significant applications in industrial cooling, biomedical devices, and microfluidic systems, where the control of thermal and solutal transport is critical. Oldroyd-B solutions and energy activation are both contained in the governing equations. The Riga plate's flexible layer can mimic microbial movement driven by bioconvection, making it a useful model for studying this phenomenon. The governing PDEs are derived from conservation laws and subsequently reduced to a system of ODEs. The differential transform method is used to evaluate the current analysis, and the results are displayed graphically. The findings indicate that the heat transport is enhanced by thermophoresis. The Nusselt number increases by approximately 15 % when the thermophoresis parameter is doubled. Similarly, the Sherwood number rises notably with increasing Schmidt number and activation energy, indicating improved mass transport. Also, the local density number is increased by bioconvection Lewis and Peclet numbers. Finally, the results could be used to increase performance in chemical reactors, power systems, and biomedical equipment, as well as to reduce drag, improve cooling, and prevent biofouling.