| Summary: | This work is dedicated to the search for the exact analytical dependences of microwave heating due to absorption of a plane electromagnetic wave by coal layer with asymmetric and non-uniform heat dissipation conditions I and III kind. Some of simplifications have been made, such as one-dimensional problem, uniformity and isotropic coal material, and the constancy of the electrical properties of thermal coal during heating of microwave radiation. This has led to the fact that the Maxwell’s task is solved separately from the Fourier’s task, and a heat source generated in the carbon layer is subject to Bouguer law. For the system of equations of heat transfer has been found a new dependent variable, which is to simplify the search for a final solution. All this has given the possibility of finding rigorous analytical solution of the problem of microwave heating of the coal layer in the presence of asymmetric and inhomogeneous boundary conditions I and III kind.
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