Abstract
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.
Highlights
Using the conditions for the uniqueness of the problem, we represent this system in the following dimensionless variables
We will find the solution of this system as the sum of the solution of a homogeneous problem and the solution with the inhomogeneous term taken into account: (, )= (, )+ (, )
+ ( ) ( ) + of inhomogeneous problem in the system [10-12], we find the constants: (
Summary
Using the conditions for the uniqueness of the problem, we represent this system in the following dimensionless variables. We will find the solution of this system as the sum of the solution of a homogeneous problem and the solution with the inhomogeneous term taken into account: ( , )= ( , )+ ( , ) The solution of a homogeneous problem in general: ( , ) = We substitute a general solution ( , ) =
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