Computational insights into double diffusive magneto-radiative and chemically reactive Williamson nanofluid transport through porous media: Bio-heat transport for drug delivery

Abstract

The aim of this study is to analyze the effects of unsteady magneto-radiative flow in a Williamson nanofluid model through a porous medium with dual diffusion effects. The mathematical model includes the combined effects of Brownian motion; thermophoresis; Soret and Dufour phenomena; thermal radiation; internal heat generation; and a transverse magnetic field with a porous medium, where the Williamson non-Newtonian model characterizes the shear-thinning behavior of blood and Darcy's law represents the resistance offered by porous biological tissues. The governing equations of this model, partial differential equations, are converted into ordinary differential equations using lubrication approximation and solved analytically using perturbation techniques. The result demonstrates that significant changes in velocity increase the Hartmann number, whereas higher radiation and heat generation parameters significantly elevate temperature distribution. Furthermore, stronger Brownian motion and thermophoretic effects increase nanoparticle concentration that enhances mass transfer. The Hartmann number and thermal and rheological parameters play vital roles in regulating Williamson nanofluid transport in biomedical environments, as they influence the flow characteristics and heat transfer efficiency, which are critical for applications such as drug delivery and thermal therapies.