A mathematical model based on the continuum mechanic concept has been developed to describe the profile of solid particles in an industrial scale blast furnace with respect to the in-furnace conditions and its characteristics such as the shape and size of the deadman. The Navier-Stokes differential equation for multi-phase multi-dimensional space has been used to describe the behavior of existing phases. The surface stress tensor has been defined as an extra term and added to the Navier-Stokes equation to describe the particle-particle interactions. This extra term in the Navier-Stokes equation behave as a breaking force when the particles are sliding down. It is shown that the particles change their profile from a V-shape to a W-shape due to the characteristics of the deadman. Moreover, the velocity magnitude is higher at the outer surface of the deadman for higher grid-slabs in this region than the near-wall cells. However, the situation changes as solid particles moving to even lower level of grid-slabs at the outer surface of the deadman in comparison to near-wall cells. It has also been shown that an increase in the magnitude of the effective pressure reduces the velocity magnitude of descending particles.