Heating and melting of bulk lump materials

Porous materials, including bulk materials, are widely used for cleaning liquid and gaseous media from mechanical impurities, as heat insulating materials, working bodies in various technologies of mechanical engineering, power engineering, metallurgy, chemistry, petroleum chemistry, food industry, pharmacology, etc. The aim of the work is mathematical modeling of heat transfer in disperse bulk media, their melting, engineering assessment of a number of indicators essential in practice. A bulk disperse medium consisting of solid particles (lumps) of different shapes, sizes and composition, randomly arranged relative to each other, is considered. The article provides relationships for determining effective density, heat capacity, thermal conductivity, taking into account radiant heat transfer between particles (lumps) as applied to porous bulk materials. Using the obtained relationships, the model problem of heating and subsequent melting of the disperse medium under consideration is solved. The melting rate and the relaxation time during which the system consisting of melt and lumps comes to thermodynamic equilibrium are assessed. Though only one-dimensional thermal processes are considered in this paper, the proposed approach can be extended to two- and three-dimensional cases and applied for mathematical description of thermal behavior of nonmetallic porous materials. It is these materials that are mainly used for thermal insulation. Their behavior, especially in extreme, abnormal conditions is of great interest.