Enhanced cooling dynamics in slip-induced MHD Williamson nanofluid flow under thermal stratification

Abstract

The present investigation explores thermal transport characteristics in MHD Williamson nanofluid flowing over a permeable stretching surface subjected to velocity and thermal slip boundary conditions. Thermal stratification, Ohmic dissipation, and internal heat source/sink effects are embedded into the governing mathematical framework to reflect practical engineering scenarios. An aqueous suspension of silver nanoparticles (Ag–H₂O) serves as the working nanofluid throughout this analysis. Appropriate similarity variables are applied to reduce the nonlinear governing PDEs into a coupled ODE system, which is subsequently integrated numerically via the fourth-order Runge–Kutta shooting algorithm implemented in MATLAB. The numerical outcomes reveal that intensifying the applied magnetic field decelerates the fluid motion while simultaneously elevating temperatures across the thermal boundary layer. An increase in thermal stratification diminishes the wall temperature gradient, consequently leading to a reduction in the convective heat transfer rate at the surface. Incorporating silver nanoparticles into the base fluid markedly augments both the effective thermal conductivity and the momentum profiles, yielding a substantial improvement in overall heat transfer efficiency. The findings underscore the practical relevance of Williamson nanofluids in electromagnetic flow regulation and precision cooling systems, spanning aerospace thermal management, high-performance electronics, biomedical instrumentation, and industrial manufacturing operations.