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 crude base liquids. It demands study and flow problem with non-uniform physical properties. This was conceived to analyze magnetohydrodynamic Eyring–Powell nanofluid transformations due slender sheets varying thicknesses. Temperature-dependent conductivity viscosity prevail. Bioconvection motivated dynamic microorganisms for fluid is a novel aspect herein. The governing PDEs are transmuted into nonlinear differential structure coupled ODEs using series viable similarity transformations. An efficient code Runge–Kutta method developed MATLAB script attain numeric solutions. These findings also compared previous research ensure that current accurate. Computational activities were carried out variation pertinent parameters perceive insights on quantities interest. Representative outcomes velocity, temperature, nanoparticles concentration, bioconvection distributions as well local transport different inputs portrayed both graphical tabular forms. results show fluid’s velocity increases mixed convection growing buoyancy effects temperature increased higher Brownian motion Nb thermophoretic Nt. numerical might be used create exchangers increasingly challenging thermo-technical manufacturing, construction, transportation.