Swimming of microbes in entropy optimized nano-bioconvective flow of Prandtl–Erying fluid

Microbes swimming in a fluid that contains nanoparticles is an intriguing characteristic having ramifications in biomedicine, petroleum science, biofuels, and biotechnology applications. This study gives a theoretical evaluation of the bioconvection phenomena with swimming microorganisms in a Prandtl–Erying nanofluid constructed by an exponential stretched surface, given the amazing applications of bioconvection and nanoparticles. Additionally, the problem is modeled by considering intriguing phenomena such as thermophoretic particle deposition, Darcy–Forchheimer medium, exothermic/endothermic process, and activation energy vitality. The leading problem comprises nonlinear, coupled, partial differential expressions. To run the appraisal process, the controlling problem is transfigured into dimensionless patterns through the usual transformations. A computational finite difference approach is used to quantify the numerical evaluation of fabricated flow problems. To obtain the parametric constraints, stability and convergency were also assessed. Improved visualizations (streamlines, isothermal line, iso-concentration, iso-microorganisms) of ongoing flow fields are also illustrated. It is unveiled that the augmentation in velocity ratio factor improves nanofluid velocity and its related boundary layer wideness. The concentration of microbes and nanoparticles is reduced against the bio-Lewis number and Lewis number precisely. The rate of change in heat transfer is the highest for the presence/absence of the thermophoresis factor. Moreover, Entropy production and Bejan number display the reverse impact for the Brinkman number. The change in entropy rate is 30.60% for the presence/absence of microbes' diffusion parameter. This evaluation could help reduce energy waste and improve the performance and efficiency of industrial and engineering appliances like nuclear power plants, and solar energy production.