Variable magnetic field (VMF) effect on the heat transfer of a half-annulus cavity filled by Fe3O4-water nanofluid under constant heat flux

Highlights: • Effect of a variable magnetic field (VMF) on the natural convection is studied. • Fe₃O₄-water nanofluid in a half-annulus cavity is considered as the working fluid. • Finite element method using FlexPDE commercial code is applied on the problem. • Increasing the Hartmann number makes a decrease on the Nusselt number. In this paper, the effect of a variable magnetic field (VMF) on the natural convection heat transfer of Fe₃O₄-water nanofluid in a half-annulus cavity is studied by finite element method using FlexPDE commercial code. After deriving the governing equations and solving the problem by defined boundary conditions, the effects of three main parameters (Hartmann Number (Ha), nanoparticles volume fraction (φ) and Rayleigh number (Ra)) on the local and average Nusselt numbers of inner wall are investigated. As a main outcome, results confirm that in low Eckert numbers, increasing the Hartmann number make a decrease on the Nusselt number due to Lorentz force resulting from the presence of stronger magnetic field.