Developing and Studying a Model of Thermal Field within the Pyrolysis Regenerator Reaction Chamber

Abstract

The paper considers an approach to model the dynamics of heat propagation through homogeneous material within the pyrolysis regenerator reaction chamber with due account for the heaters located inside the chamber. The following ways to estimate thermal fields are considered: analytical solution (direct solution of Fourier partial differential equation), numerical solution (finite difference method, finite elements method), using equivalent circuits, computer simulation. It is shown that this dynamics is described by fractional-order differential equations. The form of the equations that specify the dependencies between the currents through the branches of the electrical circuit and the voltages at its nodes is just like the form of the equations that set the relations between the heat flux through a media and the temperatures of its certain points. Hence, the solution of the differential equation is replaced by simulation of time-domain operation of the electric circuit. Thermal conductivity schematic models are proposed for such space elements as the rod and the corresponding plane element, the column and the spatial region. These elements are used to simulate non-steady heat transfer through the medium. The schematic modeling validity is proved by means of special software performing classical finite element method.