Effects of MHD on Cu–water nanofluid flow and heat transfer by means of CVFEM

•Magnetic effect on natural convection heat transfer of Cu–water nanofluid is presented via Control Volume based Finite Element Method (CVFEM).•The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell–Garnetts (MG) and Brinkman models, respectively.•The calculations were performed for Hartmann number, Rayleigh number, nanoparticle volume fraction and inclined angle of elliptic inner cylinder.•A correlation of Nusselt number corresponding is also presented.•Comparison of present work is made with the existing literature.

In this study magnetohydrodynamic effect on natural convection heat transfer of Cu–water nanofluid in an enclosure with hot elliptic cylinder is investigated. The governing equations of fluid motion and heat transfer in their vorticity stream function form are used to simulate the nanofluid flow and heat transfer. Control Volume based Finite Element Method (CVFEM) is applied to solve these equations. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell–Garnetts (MG) and Brinkman models, respectively. The calculations are performed for different governing parameters such as the Hartmann number, Rayleigh number, nanoparticle volume fraction and inclined angle of inner cylinder. Also a correlation of average Nusselt number corresponding to active parameters is presented. The results indicate that Nusselt number is an increasing function of nanoparticle volume fraction, Rayleigh numbers and inclination angle while it is a decreasing function of Hartmann number. Also it can be found that increasing Rayleigh number leads to decrease heat transfer enhancement while opposite trend is observed with augment of Hartmann number.