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 convectionow of a nanouid in a concentric annulus between a cold outer square cylinder and aheated inner elliptic cylinder. in order to simulate the eective thermal conductivity andviscosity of nanouid, maxwell-garnetts (mg) and brinkman models are used, respectively.this investigation is compared with other numerical methods and found to be in excellentagreement. numerical results for ow and heat transfer characteristics are obtained forvarious values of the nanoparticle volume fraction, rayleigh number and eccentricity. theresults show that the minimum value of enhancement of heat transfer occurs at = 0:95for ra = 105, but, for other values of rayleigh number, is obtained at = 0:65.