Thermal analysis of transient MHD ferrofluid flow and natural convection in a Porous cavity with a cylindrical barrier

The effects of Darcy, Rayleigh, and Hartmann numbers on the time-dependent ( 0 ≤ t ≤ 0.15 s e c o n d s ) This article investigates the ferrofluid flow behavior in a porous square cavity with a cylindrical barrier filled with 5 % iron oxide III ferroparticles (Fe3O4) and water (H2O) as the base fluid. The governing equations for the ferrofluid flow have been solved using Galerkin's finite element method. The boundary conditions are the cylindrical barrier, a part of the lower face of the cavity having a high temperature, the side faces of the cavity having a low temperature, and the remaining parts adiabatic. While observing the non-slip condition in all geometry surfaces, the square cavity, cylindrical barrier, and ferrofluid inside are under the magnetic field's influence. The range of Rayleigh numbers studied in the article is 10 3 ≤ R a ≤ 10 5 , Darcy number 10 − 5 ≤ D a ≤ 10 − 3 and Hartmann number H a = 20 , 100 , and finally, their effect on heat transfer and flow behavior has been investigated. The results show that increasing the Darcy number affected the velocity profiles in each Rayleigh and Hartmann number. Also, changes in ferrofluid velocity with respect to time according to different Rayleigh, Darcy, and Hartmann numbers were significant, while temperature changes with time were less compared to velocity changes with time.