Algorithm for Processing Data on the Thermophysical Properties of Phosphorites by Solving the Inverse-Coefficient Heat-Conduction Problem

An algorithm is proposed to process experimental data to determine the thermophysical properties (specific heat capacity and thermal conductivity) of phosphorites by solving the inverse-coefficient heat-conduction problem, which reduces to programmable heating complicated by thermally activated endothermic reactions of dissociation of carbonates and control of the internal thermal state of a system with distributed parameters. Consideration is made of the problem of mathematical and computer modeling of a system for processing experimental data and generalizing the main dependences of the thermophysical properties in the operating temperature range of thermal-engineering equipment for the heat treatment of ore raw materials and the actual chemical-composition range of phosphorites. This problem is solved by solving the inverse-coefficient heat-conduction problem. The control parameters are thermal conductivity and specific heat capacity, which are the coefficients in the heat equation for a plate. The optimality criterion is the smallest deviation of the temperature distribution in the plate thickness obtained in a computational experiment from a given distribution. The optimization problem is solved by the sliding-tolerance method with optimization by the deformable-polyhedron method. The article presents the results obtained in computational experiments modeling phosphate raw materials. The obtained numerical results agree well with the results of physical experiments, which confirms the adequacy of our developed mathematical and computer models and the proposed algorithm for solving the inverse-coefficient heat-conduction problem.