Computational Analysis of Prandtl on the Fluid Relaxation Time Features for the Energy and Concentration Nanomaterial Flow of Motile Microorganisms Induced by a Deformable Sheet With Chemical Reactions

This study investigates the phenomenon of bioconvection in a Darcy–Forchheimer flow of a Prandtl fluid on a stretching sheet, considering dual diffusive processes and incorporating the Cattaneo–Christov heat conduction model. For the conversion of modeled equations to dimensionless, a suitable set of variables has been incorporated. The governing equations are solved numerically using the bvp4c technique, and the effects of key parameters, including the Forchheimer parameter, Prandtl number, and bioconvection Lewis number are comprehensively analyzed. The research reveals complex interactions between buoyancy‐driven bioconvection, porous media resistance, and non‐Fourier heat conduction, providing insights into their applications in fields such as microbial remediation and geothermal reservoir engineering. It has been revealed in this work that velocity of fluid is augmented with an escalation in fluid flow parameters and elastic factor while retarded with the upsurge in porosity and inertia factors. Thermal distribution is enlarged with progression in thermophoresis, Brownian factors, and thermal source parameter, while it is retarded with escalation in Prandtl number. Concentration distribution escalates with the upsurge in Schmidt number and thermophoresis factor while retards with the escalation in Brownian, elastic, and chemical reactivity factors. Microorganisms’ profiles retard gradually with an escalation in Peclet and bioconvective Lewis numbers. The Nusselt number is enhanced by 14.50% as thermal relaxation is augmented by 0.2–0.8. Moreover, as the mass relaxation is enhanced from 1.2 to 1.8, the Sherwood number is intensified by 22.56% showing boosted mass transport in the prince of non‐Fick theory. The agreement of the current result verified with earlier literature and found an outstanding achievement.