Numerical Simulation of Thermomagnetic Convection in an Enclosure Using the Lattice Boltzmann Method

The application of the single relaxation time lattice Boltzmann method (LBM) is extended to the study of thermomagnetic convection in a differentially heated square cavity with an infinitely long third dimension. The magnetic field is created and controlled by placing a dipole at the bottom of the enclosure. The magnitude of the magnetic force acting on the ferrofluid is controlled by changing the electrical current through the dipole. In this study, the effects of combined natural convection and magnetic convection, which is commonly known as “thermomagnetic convection”, are analysed in what concerns the flow modes and heat transfer characteristics of a magnetic fluid (ferrofluid). This is a situation of considerable interest for cooling micro-electronic devices, when natural convection does not meet the cooling requirements, and forced convection is not viable due to the difficulties associated with pumping a ferrofluid.