An immersed boundary-lattice Boltzmann method for electro-thermo-convection in complex geometries

Abstract

Abstract An immersed boundary-lattice Boltzmann method for electro-thermo-convection in complex geometries is introduced in this paper. The modified governing equations with the additional source terms, including the Navier-stokes equations, the temperature field equation, the electric potential equation and the conservation equation of electric charge, are solved by the lattice Boltzmann method. Both Dirichlet-type and Neumann-type boundary conditions on curved boundaries are treated by the immersed boundary method. The numerical accuracy of the present method is verified by three simple cases with the curved boundary conditions. Moreover, the electro-thermo-convection problems with the prescribed wall temperature and wall heat flux for different geometric configurations are studied. The effects of the thermal Rayleigh number, the electric Rayleigh number, the aspect ratio and the Prandtl number on the streamlines, isotherms, charge density distribution and surface-averaged Nusselt number are investigated. The results indicate that increasing the electric Rayleigh number can enhance the heat transfer rate and change the flow field structure. The coexistence and competition of the buoyancy force and electric force can be also observed.