Unsteady MHD forced convection over a backward facing step including a rotating cylinder utilizing Fe3O4-water ferrofluid

Abstract

Abstract In this paper, the unsteady magnetohydrodynamic forced convection of Fe 3 O 4 -water ferrofluids inside the backward facing step benchmark is investigated. A rotating cylinder with fixed dimensions is located inside the flow domain and one phase model is used to simulate the ferrofluid. The dimensionless governing equations are discretized using the Galerkin finite element method in space and the Crank-Nicolson scheme in time. The discrete system of equations in each time level is treated with the help of Newton’s method and the resulting linearized problems are computed using multigrid approach. Wide ranges of the governing parameters are considered such as the Hartmann number 0 ⩽ Ha ⩽ 100 , the magnetic field inclination angle 0 ° ⩽ γ ⩽ 90 ° , the angular velocity - 75 ⩽ Ω ⩽ 75 , the Reynolds number 10 ⩽ Re ⩽ 200 and the nanoparticle volume fraction 0 ⩽ ϕ ⩽ 0.15 . It is observed that the average Nusselt number and lift coefficient are enhanced by the increase in either nanoparticle volume fraction or Reynolds number, while the drag coefficient takes its minimum in case of the fixed cylinder ( Ω = 0 ). In addition, the lift coefficient takes its minimum at value of the magnetic field inclination angle equals π / 6 . Moreover, the electromagnetic force slowdown the ferrofluid flow but the drag coefficient is enhanced. Also, the average Nusselt number decreases with ratio 53.12% as the Hartmann number increases from 0 to 100.