Brinkman–Navier–Stokes flow under the influence of electric and magnetic fields

Importance of studying Brinkman–Navier–Stokes flow under the influence of electric and magnetic fields lies in its relevance to fundamental physical phenomena, its applications in various fields of science and engineering and its potential for technological advancements. The study of Brinkman–Navier–Stokes flow under the influence of electric and magnetic fields, along with additional factors such as Joule heating, fractional derivatives and convection, represents a multifaceted and challenging problem in fluid dynamics and applied mathematics. In this study, we explore the combined effects of Joule heating due to electric current passing through the fluid and fractional derivatives that describe nonlocal behaviors. The fractional formulation leads to a relaxation mechanism that exhibits delay and recollection of the fluid motion. The organization of direct temperature and concentration changes in MHD flow is made possible by this formalization. A finite difference/finite element method is used to calculate the flow dynamics issue and fractionally linked fields. The physical factors explain how the topic under examination is relevant.