An investigation on the convective heat transportation features of a magnetised Williamson nanofluid over a radiative permeable sheet is presented in this article. The interaction of an irregular heat source/sink along with thermal radiation brings a novel approach to the flow phenomena. The nanofluid, comprising of two-phase model based upon the impact of Brownian and thermophoresis boosts up the thermal combined with solutal profile significantly under the influence of an applied magnetised field. The standard modelled partial differential equations are renovated into a couple of nonlinear ordinary differential equations by implementing suitable similarity transformations. Further, a numerical solution employing the Runge-Kutta fourth-order with an integrating shooting technique is adopted to resolve the resulting system of equations. The influence of pertinent parameters, including the magnetic field strength, thermal radiation parameter, and irregular heat source/sink parameters, is systematically analysed. The enhancement of heat transfer in nanofluid-based systems, influenced by magnetic fields and non-uniform heat sources or sinks, plays a critical role in various industrial and biological applications. This is particularly significant in designing and optimising of heat exchangers, electronic cooling systems, and energy-efficient processes, as well as in drug delivery systems. In an outstanding outcome it is revealed that, the dominance of elastic forces over the viscous forces for the increasing Williamson parameter significantly retards the velocity as well as temperature distribution.
Mishra et al. (Fri,) studied this question.