Study of Nonlinear EMHD Convective Duct Flow Under the Influence of Hall Current Effects

ABSTRACT The study of electromagnetohydrodynamic (EMHD) fluid flow through a rectangular duct is significant in heating, ventilation, and air conditioning (HVAC) systems, EMHD pumps, heat exchangers, biosensors, and liquid metal cooling systems. Understanding the interplay between electric and magnetic fields, which is vital for several industrial applications, serves as the driving force behind this study. The effects of nonlinear convection and Hall current are incorporated for the first time, contributing novel insights to the understanding of these phenomena. The analysis of the Hall effect is essential because of the applied magnetic and electric fields, while the induced magnetic field is ignored due to the high magnetic diffusivity condition. The impact of the nonlinear Boussinesq approximation makes it particularly suitable for high‐temperature conditions and ideal for modeling heating and cooling devices. In addition, geometric effects are analyzed by considering narrow, square, and wide‐shaped ducts. The formulated underlying equations are computed through the explicit central finite difference scheme (ECFDS) in Matlab R2023A. Computations have been performed for influencing parameters like as the Hartmann number, Brinkman number, nonlinear convection parameter, Grashof number, and Hall parameter. The study highlights the substantial influence of the nonlinear convection parameter, Hall parameter, and duct shape on flow behavior and thermal transport. Results indicate that the augmentation in the Hartmann number, Grashof number, nonlinear convection parameter, and Brinkman number augments the flow, whereas the flow rate declines with an elevation in the Hall parameter through ducts. An augmentation in the Hartmann number boosts the volumetric flow rate by 35% and about 95% rise in the Nusselt number at the cold wall of the duct. Additionally, the transition in the shape of the duct from narrow to wide elevates the volumetric flow rate and thermal transfer in the left wall of the duct. This study may play a vital role in optimizing and controlling the performance of heat exchanger devices.