Mathematical Modeling
Vol. 9 (2025), Issue 2, pg(s) 45-46

MATHEMATICAL MODELLING OF TECHNOLOGICAL PROCESSES AND SYSTEMS

Field-free calculation of heat and mass transfer flows with short-term contact of phases

  • 1 Kazan State Power Engineering University, Kazan, Russia
  • 2 Moscow State University of Civil Engineering, Moscow, Russia

Abstract

Calculation of thermal diffusion and filtration fluxes at the interface by “traditional” methods requires preliminary determination of the potential values (concentration, moisture content, temperature, pressure) in the four-dimensional space of events. Such methods for solving boundary value problems, which provide “extra” information for technical calculations, are usually very laborous and require the use of numerical methods that are not always convenient in engineering practice. The proposed fieldless calculation method allows one to determine on the boundary of the region the gradients from the transfer potentials and, consequently, energy and material flows in the form of a known functional of the potentials at the interface at their short-term contact directly on the matrix of transfer coefficients of the formalized boundary value problem. This method uses the fractional index differentiation operation (fractional differentiation) and is convenient for solving limiting boundary value problems, i.e. when the characteristic size of the contacting phases in the boundary conditions of boundary value problems tends to infinity or the time of their interaction tends to zero.

Keywords

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