Mathematical Analysis and Numerical Simulation of Magnetized Williamson Nanofluid Flow over a Rotating Stretching Surface with Joule Heating and Thermal Radiation

ABSTRACT:

This study investigates the flow behaviour of a magnetohydrodynamic (MHD) Williamson nanofluid over a rotating stretching surface, considering the combined effects of Joule heating and nonlinear thermal radiation. A mathematical model is developed to describe the transport phenomena by coupling the momentum, energy, and nanoparticle concentration equations under the influence of an applied magnetic field. The governing partial differential equations are rendered dimensionless and transformed into a system of nonlinear ordinary differential equations using appropriate similarity transformations. The resulting equations are solved numerically using the collocation method, and the computed results are validated through comparison with MATLAB bvp4c, demonstrating excellent agreement with percentage errors below 1%, which confirms the accuracy and reliability of the numerical approach. The effects of the magnetic parameter, Williamson parameter, Joule heating parameter, thermal radiation parameter, Brownian motion, thermophoresis, and rotational parameter on the velocity, temperature, and nanoparticle concentration profiles are presented graphically and discussed. The engineering quantities of practical interest, namely the skin-friction coefficient, Nusselt number, and Sherwood number, are also evaluated. The results reveal that the magnetic field suppresses fluid velocity due to the Lorentz force, whereas Joule heating and thermal radiation significantly enhance the temperature distribution within the boundary layer. Brownian motion and thermophoresis increase nanoparticle diffusion and modify the concentration field, while the rotational effect enhances fluid motion near the stretching surface. The findings of this study provide useful insights into the design and optimization of thermal systems involving electrically conducting non-Newtonian nanofluids in engineering and industrial applications.

Keywords: Magnetohydrodynamics, Williamson nanofluid, rotating stretching surface, Joule heating, thermal radiation, Brownian motion, thermophoresis, collocation method