The ironmaking blast furnace is the most efficient reactor for extracting iron from iron ore. Iron ore consists of iron oxides and in the blast furnace the iron oxides are reduced to iron and melted before it is transformed into steel in the steel plant. The lowest part or hearth of an ironmaking blast furnace plays no doubt the most important role in the making of hot metal, the primary product of a blast furnace: molten, unrefined iron. The hearth is the location where the final reactions take place, which determine the hot occur at places where usually large refractory degradation occurs in a blast furnace. It is shown that a distribution of hot metal entering the hearth has a large impact on flow in the hearth. Although not all aspects of the modelling worked well, it is shown that these methods show a computational workable route for modelling large particle systems. metal quality, but also where wear of the protective refractory lining is the main reason for a major, lengthy and costly maintenance stoppage once every 10 to 20 years. In the hearth, hot metal flows through the bed of packed coke particles, the deadman, toward a tap hole in the wall of the hearth. The particles of the coke bed exhibit a particle size distribution, which determines the permeability for liquid flow in the packed bed. The permeability is not uniformly distributed and this determines the flow distribution in the hearth. It is the flow of hot metal which dissolves the carbon of the coke particles, resulting in a change in packing of the coke bed and degrades the refractory lining of the hearth. The process conditions in the hearth make it near to impossible to monitor and predict these processes. Using mathematical modelling as a tool, insight is gained in understanding the process of dissolution of coke bed particles and the impact on the packing of the coke bed as well as the hot metal flow inside the hearth. In this thesis population balance modelling and particle-packing modelling are used to model the effect of dissolving particles on the packing of a packed bed. The model is linked with a CFD model of a simplified blast furnace hearth, and the resulting packed bed porosity is used to calculate the effects on hot metal flow in the hearth. The ensuing effects on coke dissolution rate and flow in the CFD model is demonstrated. This approach of simultaneously calculating the distribution of the deadman porosity, caused by dissolution, and the ensuing hot metal flow is an unique and new aspect in blast furnace hearth modelling. Results of dissolution experiments, in water, with spherical benzoic acid particles in a packed bed, validate the results of the dissolution and packing model. It is also shown that the packing model is also suited for modelling packed coke beds. This thesis shows that population balance modelling is well suited to model systems with a large number of particles, especially in the case of calculating the evolution of the particle size distribution of dissolving particles. CFD results in this thesis demonstrate that large coke dissolution rates and high flow rates occur at places where usually large refractory degradation occurs in a blast furnace. It is shown that a distribution of hot metal entering the hearth has a large impact on flow in the hearth. Although not all aspects of the modelling worked well, it is shown that these methods show a computational workable route for modelling large particle systems.@en