Dynamics of Eyring–Powell Nanofluids When Bioconvection and Lorentz Forces Are Significant: The Case of a Slender Elastic Sheet of Variable Thickness with Porous Medium

We examine thermal management in the heat exchange of compact density nanoentities in crude base liquids. It demands the study of the heat and flow problem with non-uniform physical properties. This study was conceived to analyze magnetohydrodynamic Eyring–Powell nanofluid transformations due to slender sheets with varying thicknesses. Temperature-dependent thermal conductivity and viscosity prevail. Bioconvection due to motivated and dynamic microorganisms for Eyring–Powell fluid flow is a novel aspect herein. The governing PDEs are transmuted into a nonlinear differential structure of coupled ODEs using a series of viable similarity transformations. An efficient code for the Runge–Kutta method is developed in MATLAB script to attain numeric solutions. These findings are also compared to previous research to ensure that current findings are accurate. Computational activities were carried out with a variation in pertinent parameters to perceive physical insights on the quantities of interest. Representative outcomes for velocity, temperature, nanoparticles concentration, and bioconvection distributions as well as the local thermal transport for different inputs of parameters are portrayed in both graphical and tabular forms. The results show that the fluid’s velocity increases with mixed convection parameters due to growing buoyancy effects and the fluid’s temperature also increased with higher Brownian motion N b and thermophoretic N t . The numerical findings might be used to create efficient heat exchangers for increasingly challenging thermo-technical activities in manufacturing, construction, and transportation.