This document provides a comprehensive overview of the MFIX (Multiphase Flow with Interphase eXchanges) computer model, which is a general-purpose hydrodynamic model used to simulate chemical reactions and heat transfer in dense or dilute fluid-solids flows. The model is designed to assist in the design of industrial reactors by providing detailed information on pressure, temperature, composition, and velocity distributions. The report covers the hydrodynamic theory, including conservation equations, constitutive relations, and initial and boundary conditions. It also discusses the development of the model, its capabilities, and limitations. The hydrodynamic theory is based on the averaging approach and mixture theory approach, and it accounts for mass, momentum, energy, and species conservation. The document includes detailed equations for each phase and introduces concepts such as granular stress, fluid-solids momentum transfer, and heat transfer. The MFIX model is validated through comparisons with experimental data and has been applied to various industrial processes, including fluidized beds and fluid catalytic cracking. The report concludes with a discussion of the model's limitations and the need for expert users to interpret the results accurately.This document provides a comprehensive overview of the MFIX (Multiphase Flow with Interphase eXchanges) computer model, which is a general-purpose hydrodynamic model used to simulate chemical reactions and heat transfer in dense or dilute fluid-solids flows. The model is designed to assist in the design of industrial reactors by providing detailed information on pressure, temperature, composition, and velocity distributions. The report covers the hydrodynamic theory, including conservation equations, constitutive relations, and initial and boundary conditions. It also discusses the development of the model, its capabilities, and limitations. The hydrodynamic theory is based on the averaging approach and mixture theory approach, and it accounts for mass, momentum, energy, and species conservation. The document includes detailed equations for each phase and introduces concepts such as granular stress, fluid-solids momentum transfer, and heat transfer. The MFIX model is validated through comparisons with experimental data and has been applied to various industrial processes, including fluidized beds and fluid catalytic cracking. The report concludes with a discussion of the model's limitations and the need for expert users to interpret the results accurately.