In this paper, the buoyancy-driven fluid flow and heat transfer in a square cavity with partially active side walls are investigated numerically. The top and vertical walls of the cavity are maintained at the relatively low temperature. The governing partial differential equations have been described in smoothed particle hydrodynamics formulations. The transport equations for a Newtonian fluid are solved numerically using smoothed particle hydrodynamics (SPH) method. The results indicate the relation among changes taking part in the heat source length, heat source location, Rayleigh number, maximum temperature and maximum value of stream function and velocities.