A mathematic model based on the theory of interacting continua is developed to describe the complex liquid-solid two-phase flow with phase-change particles as encountered in non-thermal equilibrium melting of granular packed bed subject to horizontal, forced convection. The model is solved numerically using the SIMPLE method, in which the pressure correction based on two-phase mixture continuity equation is implemented. Conservation equations are solved in the entire computational domain including both the liquid-solid region and liquid-only region. It is ensured that the global mass, momentum, and energy of two phases are conserved. The local volume-averaged solid velocity and solid volume fractions are predicted as variables so that the moving and repacking of solid particles can be simulated. This is a step forward from the results published in the open literature where the assumptions of zero-relative motion of solid particles and constant porosity or the constant volume are often used. In addition, the model provides the detailed information about the motion of two phases and phase-change characteristics. Within the uncertainty, the simulation results agree reasonably with the available experimental data presented in Part I of this study [1]. (C) 2003 Elsevier Ltd. All rights reserved.