Abstract
Abstract
This paper investigates the two-dimensional flow of a Bingham plastic over a straining surface subjected to an externally applied magnetic field and surface slips. The study aims to understand the behavior of such flows and their response to external factors, which has applications in various industrial processes involving complex fluid dynamics. Through Lie group analysis, a new set of similarity transformations are derived to reduce the number of variables in the governing partial differential equations, facilitating a more tractable analysis. These transformations enable the conversion of the partial differential equations into a self-similar system of ordinary differential equations. A high-order, three-stage Lobatto IIIa formula along with appropriate boundary conditions is applied to solve this system. The solutions obtained for various physical parameters lead to several key deductions. It is found that under constant physical parameter values, the velocity layer thickness of the plastic flow is lower compared to the thermal layer thickness, indicating the dominance of the plastic flow behavior. Additionally, an increase in the magnetic field results in a reduction in the thickness of the plastic boundary layer, highlighting the significant influence of magnetic fields on the flow characteristics. These findings provide valuable insights into the control and optimization of processes involving Bingham plastic flows, particularly in the presence of magnetic fields and surface slips.