Hydromagnetic flow of ferrofluid in an enclosed partially heated trapezoidal cavity filled with a porous medium

The flow and heat transfer in a trapezoidal cavity were investigated numerically. Water-based ferrofluid with Fe3O4 nanoparticles and porous medium with low Darcy number were chosen for the investigation. Both side walls were maintained at a constant cold temperature, the top wall was adiabatic, and the heater is placed at the bottom wall. The dimensionless governing equations are solved numerically using finite element method. A uniform magnetic field of strength B o was imposed. It is assumed that the magnetic Reynolds number is much smaller than the induced magnetic field so that it can be neglected when compared to the applied magnetic field. No slip boundary conditions were applied at the walls. The streamlines and isotherms were generated to explain the behaviour of dimensionless velocity and temperature inside the cavity. It is demonstrated that the magnetic field, thermal buoyancy, porous medium permeability and the length of the heating element play a crucial role in the enhancement of dimensionless average heat transfer rate.