Analysis of Newtonian and Joule heating in a bioconvective Williamson nanofluid flow with gyrotactic microorganisms incorporating modified forms of Fourier’s and Fick’s laws

This paper investigates the heat and mass transfer features in a time-dependent bioconvective flow of a Williamson nanofluid containing gyrotactic microorganisms over a radially stretching sheet. Bioconvection arises from the collective motion of motile microorganisms, such as algae or bacteria, which generates a density gradient and induces fluid motion. These microorganisms enhance the mixing and stability of nanofluids, making them highly relevant for microscale thermal systems, biomedical devices, and environmental applications. The Buongiorno nanofluid model is employed to describe nanoparticle transport driven by Brownian motion and thermophoresis. The energy and concentration equations are further modified using refined forms of Fourier’s and Fick’s laws to incorporate nonlinear thermal radiation, Joule heating, Newtonian heating, and a first-order chemical reaction. The resulting system of nonlinear partial differential equations is transformed into a set of ordinary differential equations using similarity transformations and solved numerically via the shooting method. The numerical results are validated through a comparison table with previously published data and show excellent agreement. Graphical key findings indicate that microorganism concentration decreases with increasing bioconvective Schmidt number, microorganism difference parameter, and Peclet number. This study presents a novel integration of multiple transport mechanisms and contributes to the design and optimization of nanofluid-based thermal systems.