Mathematical simulation of melted slag cooling by a system of metal balls

The problem of thermal conductivity in a sphere is solved analytically in unadjoined edge conditions in the case when the boundary conditions are a linear function of time. A computer model is constructed for the accumulating ability of the system of metal balls for a cyclic regime of cooling of a melted slag, which makes it possible to establish and analyze main features of operation of a slag processing unit due to thermal stabilization of its structure. The correctness of the developed computer model is verified by comparing the analytic and numerical solutions; the peculiarities of the numerical solution of the heat conduction equation for a ball, associated with unadjoined edge conditions are analyzed.