The study focuses on the behavior of an electrically conducting non-Newtonian fluid with couple stress properties, using water-based bionanofluid. The fluid is analyzed as it flows across a porous stretching/shrinking sheet within its own plane. This Study also explores the Bejan Number and Entropy Generation. To facilitate this investigation, the governing nonlinear partial differential equations undergo a transformation, wherein they are converted into nonlinear ordinary differential equations through a suitable similarity transformation. An ideal strategy has been employed to achieve the desired results from the modeled challenge. The Homotopy Analysis Method is applied to determine the solution of the system of differential equations. The convergence of the applied method and their comparison with the numerical method are described through graphs and tables. The main features of the different profiles are briefly described. Graphs are used to analyze the impact of the Bejan number, concentration, temperature, velocity profile, and entropy production rate. Tables present the characteristics of skin friction, Nusselt, and Sherwood numbers for various limitations. The stretching and ambient fluid velocities should fluctuate linearly as the distance from the stagnation point increases. A rise in the magnetic and porosity parameters is accompanied by an increase in the velocity profile. While the velocity profile falls off as a Couple of fluid parameters are increased. The phenomenon of temperature boost is observed to be positively correlated with the increase in Brownian motion parameter while exhibiting no significant dependence on other parameters such as Brinkman number, Prandtl number Lewis number and Thermophoresis parameter. Entropy generation increases with the Brinkman number while decreasing with the radiation parameter and diffusion parameter as is plainly demonstrated.
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