Exploring Insights on Magnetized Hybrid Nanofluid Flow Through Porous Configuration With Microbial Movement and Variable Thermophysical Properties

The existing investigation organized a novel analysis of the 3D flow features of ternary and penta‐hybrid nanofluids flow across porous space, along with the corresponding heat‐transfer mechanisms across an extended porous channel incorporating gyrotactic microbial movement and internal heat generation. This study marks a substantial advancement over past investigations on ternary and Penta (HNF) models by incorporating enhanced and unique thermal properties via the inclusion of five distinctive types of tiny material particles in the formulation of the model equations. The Buongiorno model of nanofluid is introduced to account for the effects of convective heating, Brownian movement, and thermophoretic diffusion on the nanoparticles. The resulting complex system of nonlinear governing PDEs is changed into ODEs by employing proper transformation functions and subsequently computed through the RKF45 discretization method, yielding closed‐form approximate solutions for various flow profiles within the MATLAB programing platform. A comprehensive parametric analysis reveals that increases in porous‐media permeability, magnetic factor, and ratio parameter enhance the velocity profiles in both directions. Notably, the Penta (HNF) demonstrates superior thermal and mass‐transport performance relative to the ternary (HNF). To validate the computed results accuracy obtained through the RKF45 technique, tabulated comparisons with two independent algorithms were performed, showing strong agreement between the methods. These computational insights into nanofluid flow and microbial dynamics offer valuable insights for optimizing heat transfer and control mechanism in advanced energy systems.