Algorithm for the joint solution of heat and mass transfer equations and equations of the electromagnetic field during the drying with microwave radiation

A. M. Afanas'ev ; B. N. Siplivyi

Matematičeskaâ fizika i kompʹûternoe modelirovanie, no. 2 (2017), pp. 82-93

Résumé

The authors develop a numerical scheme allowing to find a joint solution to the equations of diffusion of heat and moisture, A.V. Lykov and Maxwell’s equations in electromagnetic drying of a sample with a flat geometry. Calculation scheme is based on two algorithms: a) for a given distribution of the dielectric constant the problem is to estimate the field density of electromagnetic losses, reflection coefficients and transmission; b) when there are electromagnetic losses of specified field density, the problem of calculation of fields of temperature and moisture content should be solved. The role of a bridge between these two algorithms performs the formula of Debye (it determines the dielectric permittivity of each of the two components of the mixture, the solid base and water, frequency and temperature) and mixing formula of Maxwell (on the basis of the Debye formulas for the solid base and water, it determines the dielectric permittivity of the mixture of these components as a function of frequency, temperature and moisture content). The calculation according to this scheme allows to take into account the reverse impact of distributions of temperature and moisture content at some point in time, on the distribution of absorbed electromagnetic energy in the same moment. Numerical experiment (drying the moist zeolite electromagnetic radiation in the microwave range), the results of which are in good agreement with available published experimental data.

Détail

Mots-clés : A.V. Lykov’s equations
Keywords: Maxwell’s equations, drying with electromagnetic radiation, initial boundary value problem, numerical methods, complex dielectric permittivity, the method of characteristic matrices.