Mathematical modeling of microwave heating of products with central symmetry

[EN] Microwave heating is widely used in the energy, construction, forestry, chemical and food industries, etc. There are many publications that discuss the main mechanisms that occur during microwave heating. For a better understanding of these processes and the development of high-performance microwave installations, mathematical modeling is necessary. As a rule, nonlinear models that most adequately describe these phenomena use a numerical algorithm for calculations. The authors of this report are engaged in approximate analytical approaches for microwave heating and microwave drying of bodies, which, with a controlled decrease in accuracy, nevertheless allow you to display the main processes and evaluate such heating and drying parameters as: temperature and moisture distribution, heating time, drying speed, reaching maximum values, etc. In this work, we consider a model of microwave heating in the form of a ball with uniform irradiation of microwave energy in the conditions of radiation-convective interaction of the product with the environment. The absorption of the microwave inside the material is given by the law of the Bouguer. In this case, a number of simplifications were made: the electrophysical and thermophysical properties of the material are constant, the material is homogeneous in composition and properties.