  Natural convection is of great importance in many engineering applications.
This paper presents a smoothed particle hydrodynamics (SPH) method for natural
convection. The conservation equations of mass, momentum and energy of fluid
are discretized into SPH equations. The body force due to the change of density
in a temperature field is considered by the Boussinesq approximation. The
numerical method is validated by comparing numerical results with experimental
results from literature. The numerical and experimental results reach a good
agreement. Then the SPH method is applied to study the natural convection in a
horizontal concentric cylindrical annulus with Rayleigh number in the range of
10^2 to 10^7 and Prandtl number in the range of 0.01 to 10. In general, the
flow is stable at low Rayleigh number but unstable at high Rayleigh number. The
transition Rayleigh number from stable to unstable states is lower in the low
Prandtl number cases than in the high Prandtl number cases. Four different
convection states are identified in numerical simulations, namely, stable state
with 1 plume (SP1), unstable state with 1 plume (UP1), stable state with n (n >
1) plumes (SPN), and unstable state with n (n > 1) plumes (UPN). The SP1 and
UP1 states are observed for all Prandtl numbers, while the SPN and UPN states
are only observed at Pr = 0.1 and 0.01.
