Unsteady Inclined MHD Powell-Eyring Fluid with Microorganisms Over an Inclined Permeable Stretching Sheet with Zero Mass Flux and Slip Condition

An analytical framework is developed to investigate the unsteady magnetohydrodynamic Powell-Eyring fluid flow in the presence of nonlinear thermal radiation and chemical reactions over a sliply stretched surface. The novelty of this study is accentuated by incorporating the effects of heat generation/absorption and introducing a unique zero mass flux with a melting/permeable condition at the sheet. Additionally, for a Nanofluid containing gyrotactic microorganisms, the recently proposed Buongiorno’s model is employed, encompassing the impacts of thermophoresis and Brownian motion. Employing suitable self-similar transformations, the set of highly nonlinear partial differential equations is transformed into a dimensionless system of ordinary differential equations. These transformed equations are subsequently numerically solved using the MATLAB built-in function bvp4c. The study systematically explores the influence of pertinent parameters on heat, mass transfer, and gyrotactic microorganism profiles, providing insights into their characteristics. The findings indicate that the temperature distribution exhibits an increasing trend concerning heat generation and nonlinear radiation parameters. Additionally, As the magnetic number, permeable parameter and \(\alpha\) $\alpha$ rise, the velocity profile declines, whereas temperature, concentration, and microorganism profile show enhancement. By analyzing all the figures, so can conclude that the trends of melting surface are a little bit higher than the permeable surface. Higher values of the chemical reaction parameter correspond to a decrease in the nanoparticle concentration profile. To bolster the credibility of the presented results, a comparative analysis with previously published studies in limiting cases is included, contributing to the robustness of the findings.