The impacts of variable thermal conductivity and entropy generation in the MHD flow of Williamson nanofluid between stretching axisymmetric discs, considering nonlinear thermal radiation and non-uniform heat generation parameters, have been numerically simulated in this article. The proposed model’s partial differential equations are converted into ordinary one through similarity transformations, facilitating their numerical solution. The finite differences are operated to discretize the transformed equations and then simulated via relaxation methodology. The entropy generation behavior, velocity distribution, temperature profile, and nanoparticle concentration are analyzed for various relevant parameters through graphs. It is perceived that an upsurge in the magnetic parameter leads to a decline in all three velocity components (axial, radial, and tangential), whereas an increase in the Weissenberg number results in an opposite trend. Moreover, temperature profiles exhibit a significant decrease with increasing Reynolds and Prandtl numbers, whereas an upward trend is observed with higher values of the temperature ratio and thermophoresis parameters. An increase in the Lewis number and Brownian motion parameter leads to a decline in concentration profiles. The entropy generation rate between the stretchable discs increases with higher thermal radiation, Weissenberg number, Brinkman number, and magnetic parameter respectively. The study of entropy generation in the MHD flow of Williamson nanofluid between stretchable discs has significant industrial applications, including thermal management in cooling systems, energy optimization in heat exchangers, enhancement of polymer processing, and improvement of nanofluid-based lubrication and coating technologies.
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