Homotopic analysis for bioconvection of Casson nanofluid flow over an exponential stretching sheet with activation energy and motile microorganism

This article delves into the theoretical analysis of hydromagnetic bioconvection involving a radiating and reacting Casson nanofluid containing motile microorganisms, past an exponentially stretching permeable vertical surface within a porous medium, incorporating heat and mass transfer characteristics. The model problem's nonlinear differential equations are derived by applying relevant conservation laws and subsequently solved numerically using the homotopy analysis method (HAM). The graphical representation and quantitative discussion of the effects of emerging parameters on various aspects, including nanofluid velocity, temperature distribution, nanoparticles, gyrotactic microorganisms concentration, skin friction, Nusselt number, Sherwood number,and Motile density number are presented. The findings reveal significant influences on both heat and mass transference rates, as well as motile microorganism rates, in response to variations in bioconvection parameters. Additionally, the integration of gyrotactic microbes into nanoparticles is identified as a crucial factor for enhancing the thermal performance of devices, such as microbial fuel cells, bacteria-activated micromixers, microfluidic tools, enzyme biosensors, and chip-like bio microsystems. The bioengineering implications of these results are noteworthy, providing valuable insights for the design and optimization of relevant technologies.