Numerical study of MHD natural convection inside a sinusoidally heated lid-driven cavity filled with Fe3O4-water nanofluid in the presence of Joule heating

In the present contribution, the conjugate effect of Joule heating and Lorenz force acting on MHD natural convection and entropy generation inside a lid-driven cavity filled with Fe3O4-water nanofluid has been studied numerically. A sinusoidal temperature distribution on both vertical sides is considered, while the horizontal walls are kept adiabatic. The physical problem is represented mathematically by sets of governing partial differential equations and an accurate finite volume method is employed to solve the equations of flow and temperature fields. The study has been carried out for a wide range of Hartmann number Ha=0 to 50, Eckert number Ec=0.025 to 0.075, solid volume fraction ϕ=0 to 0.06, and phase deviation of temperature distribution γ=0 to π. The numerical results for cases with and without internal Joule heating are presented in terms of streamlines, isotherms, average Nusselt number, entropy generation, and Bejan number. The results show that the heat transfer rate reduces with the increase of either Hartmann or Eckert number. In the presence of Joule heating and for all phase deviations, the addition of ferrite nanoparticles to the base fluid improves the heat transfer rate. In addition, the total entropy generation increases with Hartmann and Eckert number as well as the solid volume fraction of nanoparticles.