Heat treatment of the coal layer by microwave energy: an analytical study in conditions of heat removal of II and III order

Abstract

Relevance of the research is related to the necessity of scientific study of microwave exposure technology parameters for coal, especially when drying, at thermal treatment, burning intensification and others. Experiments show that use of microwave radiation help reduce harmful emissions from coal burning, increase energy efficiency, reduce process time, etc. For optimal conditions of microwave treatment it is very popular to search for theoretical approaches, in particular, the engineering practice requires analytical solutions for heat treatment of coal array, which was done in the study. The aim of the research is to develop strict analytic solutions of the problems of coal layer heating by microwave radiation under the heat removal of the II and III order, which allow carrying out the parametric analysis of microwave exposure and searching for the most advantageous modes of heating coal layer. Methods. The tasks of coal bed heating by microwave radiation with boundary conditions of the II and III order were set with a number of simplifications, such as persistence of thermal and electrical properties of the material, they are isotropy, one-dimensionality. This physical process itself is plane electromagnetic wave energy absorption and formation of heat sources in coal array, modeled on the Bouguer law. The energy equation in the form of Fourier in this case is considered independently of the Maxwell equations of electrodynamics. A new dependent variable was determined. It modifies the boundary conditions into homogeneous, and simplifies the search of solutions. As a result, the basic system of equations is divided into two subsystems, and the final solution was found making a superposition of these two sub-tasks. Results. The authors have found analytically strong dependences of temperature distribution over the cross section and time for carbon bed heated by microwave radiation, under heat removal of II and III order of boundary surfaces. These solutions are the basis for optimum parameters of microwave heating technology, a tool to reduce the spread of temperature field on the desired temperature distribution within the layer. They help determine quickly: maximum temperature inside a coal array, coordinates of its location, thermos-destructive voltage, limits of discharged heat fluxes and other.

Keywords

• the Fourier heat equation
• coal
• microwave energy
• the Buger law
• mixed boundary conditions
• thermal regime