The high permeability of the gas in the molten iron of the dripping zone of the blast furnace is a major factor in achieving the stable operation of a furnace with high productivity. Basic studies of the liquid flow behavior in a packed bed are necessary to grasp the effect of various operational changes on conditions in the dropping zone. Molten iron and slag together playa critical role in the lower zone, transporting mass and energy, while impairing and redistributing the gas flow. In turn, molten iron and slag undergo physical and chemical changes, and are redistributed radially as they descend to the hearth. In this research, mathematical formulations are derived for the gas and the liquid. The solid phase is fixed with constant porosity. The information for the molten iron and slag includes the hold-up, velocity, pressure, and information related to the areas of interaction between the gas and the liquid, and the solid and the liquid. Predictable results include the velocity, pressure and temperature distribution. Additional parameters include the packed particle size and the air blast rate.