Natural convection in a nano uid lled concentric annulus between an outer square cylinder and an inner elliptic cylinder

The lattice Boltzmann method is applied to investigate the natural convection ow of a nano uid in a concentric annulus between a cold outer square cylinder and a heated inner elliptic cylinder. In order to simulate the eective thermal conductivity and viscosity of nano uid, Maxwell-Garnetts (MG) and Brinkman models are used, respectively. This investigation is compared with other numerical methods and found to be in excellent agreement. Numerical results for ow and heat transfer characteristics are obtained for various values of the nanoparticle volume fraction, Rayleigh number and eccentricity. The results show that the minimum value of enhancement of heat transfer occurs at " = 0:95 for Ra = 105, but, for other values of Rayleigh number, is obtained at " = 0:65.