MHD natural convective flow of [formula omitted] ferrofluids in an inclined partial open complex-wavy-walls ringed enclosures using non-linear Boussinesq approximation

Abstract

In the current contribution, a numerical investigation of natural convection with nonlinear Boussinesq approximation is considered for a ferrofluid flows inside an inclined, and partial open cavity. The vertical walls of the cavity are wavy where the aperture part lies in the right one. The left wall is considered to be uniformly heated whereas the remaining parts of the cavity are adiabatic. The nonslip boundary condition is assumed for all the boundaries except the aperture part where the directional do-nothing boundary condition is introduced to ensure the theoretical studies which leads to a conservative kinetic energy. The problem is modeled and the resulting partial differential equation system, after converting it to a non-dimensional form using a suitable transformation variables, is solved based on the Galerkin finite element method. The entropy generation analysis is presented for the local entropy generation due to heat transfer, local entropy generation due to fluid friction as well as their contribution to Bejan number. An intensive computation is carried out for wide ranges of the governing parameters namely; the Rayleigh number Ra, Hartmann number Ha, nanoparticle volume fraction ϕ, amplitudes of the two superimposed sinusoidal functions αi, non-linear Boussinesq parameter ξ, length of the aperture BR and its position bR. The obtained results are shown in terms of the streamlines, isotherms, local entropy generation due to heat transfer, local entropy generation due to fluid friction contours as well as average Bejan and Nusselt number. Over all, most of the governing parameters have a significant impacts in the flow and heat transfer rate as shown in the discussion section.