An immersed boundary-lattice Boltzmann method for thermal and thermo-solutal problems of Newtonian and non-Newtonian fluids

An immersed boundary-lattice Boltzmann method is introduced that can be employed for different thermal and thermo-solutal problems of Newtonian and non-Newtonian fluids. The general macroscopic and mesoscopic equations are presented and discussed. It is shown and proved that the macroscopic equations are satisfied by the proposed lattice Boltzmann equations. This approach removes the limitation of the conventional lattice Boltzmann method in constitutive equations and boundary conditions. To validate the accuracy of the method, it is compared against several cases of complex geometries with curved boundaries for natural convection in enclosures. To demonstrate the ability of this method for the simulation of thermo-solutal flows of non-Newtonian fluids with curved boundaries, double diffusive natural convection of Carreau fluid between a square cylinder and two circular cylinders is investigated and results are reported. Next, double diffusive mixed convection of a Bingham fluid in a cavity with a curved boundary condition is studied.