Exploring the impact of Joule heating and Brownian motion on assisting and opposing flows in Eyring-Prandtl fluid

The basic aim of this investigation is to explore the energy transfer impact on Eyring-Prandtl fluid, a topic that has not been previously examined, thereby paving the way for future researchers. The present literature is crucial for advancing thermal management in engineering applications. This study aims to numerically investigate the thermophoretic effects and Brownian motion of non-Newtonian nanofluid relying on Eyring-Prandtl fluid model across the stretching sheet. The sheet is along the vertical direction under applied magnetic field. Energy and mass transfer rate is explored by considering Joule heating, thermal radiations and chemical reaction effects.

The increasing potential of Eyring-Prandtl fluid lies in its applications in heat and mass transfer. The current analysis holds significant promise, particularly in scenarios where non-Newtonian working fluids are utilized. This research aids in optimizing industrial processes, designing of efficient cooling systems in electronic devices, and in polymer and food processing.

The similarity transformations are utilized to turn a set of partial differential equations (PDEs) into a system of ordinary differential equation (ODE). The resulting system is modified and effectively solved by mean of numerical method known as the Runge Kutta method with bvp4c in MATLAB.

Graphical results show the behavior of several physical parameters across boundary layers of buoyancy assisting and buoyancy opposing region. The magnetic field enhances the thermal conductance of the fluid flow that give rise to flow rate at the surface as well as within the boundary layers. The existing outcomes in the study are attained as a special case of current study. Eyring-Prandtl fluids, with their unique rheological properties can improve the design and efficiency of microfluidic systems used in various applications such as chemical synthesis, drug delivery, and biomedical diagnostics.