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 e ective 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.
