Heat transfer in thermally developed Williamson hybrid Zn-SiO2 /H2O nanofluid: dynamics of Darcy-Forchheimer flow, activation energy and radiation

The present study investigates the flow and heat transfer dynamics of Williamson hybrid Zn-SiO2/H2O nanofluid over a porous surface under the influence of thermal radiation, activation energy, and motile microbes. Hybrid nanofluids have shown superior thermal conductivity compared to conventional fluids, making them ideal for energy-efficient cooling applications in industries such as solar thermal collectors, biomedical engineering, and electronics cooling. However, the complex non-Newtonian behavior and interplay between fluid properties and external forces remain challenging to model accurately. To address this, we employ a scaling methodology to transform the governing nonlinear coupled partial differential equations into ordinary differential equations. These equations are solved using the MATLAB solver bvp4c, which implements a three-stage Lobatto finite difference scheme to ensure computational accuracy. The model reliability is confirmed by validating the results against existing literature. Key results indicate that an increase in the magnetic field parameter leads to a decrease in velocity, while the rotational parameter enhances motile microbe concentration. Additionally, higher Lewis and Peclet numbers reduce the motile microbe profile, affecting bioconvection stability. The inclusion of hybrid nanoparticles (Zn-SiO2) significantly improves the thermal conductivity, making this nanofluid an excellent candidate for compact cooling applications. The novelty of this study lies in the integration of non-Newtonian Williamson fluid properties, hybrid nanoparticle effects, and microbial dynamics in a porous medium with electromagnetic interactions. Results indicate when the values of radiation parameter varies from 0.2 to 0.8, increment noted about 21% from mono to hybrid nanofluid. Unlike previous studies, which primarily focused on Newtonian or single-phase nanofluids, this research provides a more comprehensive approach to predicting fluid behavior under complex physical conditions. These findings contribute to optimizing advanced heat transfer systems and next-generation nanofluid applications.