This article explores the influence of activation energy and microorganisms on the flow of Jeffrey nanofluid over an electrically conducting stretching surface, considering key factors such as Brownian motion, thermophoresis, Joule heating, and thermal radiation. The fluid dynamics entail a stretching surface subjected to prescribed surface temperature and constant wall surface temperature. Through similarity transformations, the governing equations are solved using MATLAB’s bvp4c function. Employing a numerical and perturbative approach, the study examines critical parameters’ effects on flow distribution, heat transfer, mass transport, and microorganism density. Graphical illustrations and tabulations are utilized to illustrate these effects, including the elucidation of Nusselt, Sherwood, friction coefficient, and motile microbe. The study’s findings hold promise for optimizing processes in environmental remediation, bioengineering, and nanotechnology. It is seen that thermophoresis reduced the coefficients of motile density number, Sherwood number, and Nusselt number. Peclet and bio-convective Schmidt numbers enhanced the spread of microorganisms. CWT profile exhibits greater dominance compared to PST profile.
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