The buoyancy-driven flow behavior of a lead-tin solution with immiscible tin particles in a rectangular container during a cooling process under both normal and microgravity conditions is studied using an Eulerian-Lagrangian approach. The continuum phase is simulated using the conservation of mass, momentum, and energy, and the motion of the particles dispersed in the liquid phase is predicted using the Lagrangian method where the trajectory of each particle is calculated based on Newton's second law of motion considering drag, buoyancy, Saffman lift, and the thermophoresis force. The effects of the dispersed particles on the fluid flow and heat transfer of the continuum phase are considered as volumetric body forces and heat sources, respectively. The simulation results show that heat transfer during the cooling process is dominated by heat conduction and the presence of the dispersed particle with a volume concentration of 15% does not have an appreciable influence on the temperature distribution. However, the behavior of the multiphase flow is very sensitive to the density ratio of tin particles to the lead-tin solution and the particle size. The upward sedimentation of the tin particles may lead to a flow pattern different from that of single liquid phase flow. However, the flow pattern with neutrally buoyant particles remains the same as the flow pattern for single-phase liquid flow, except with lower velocity magnitudes. Under microgravity, the motion of the particles and fluid is determined by the thermophoresis force. The effect of other parameters such as particle size is also presented.