Generalized mathematical model of the transfer processes in the enclosing structures of buildings, constructions, thermal and engineering networks

  • 1 Kazan State Power Engineering University, Russia


The problems of heat and moisture transfer, air permeability in single and enclosure constructions (EC) of buildings, facilities and heat, engineering and electrical networks under the influence of environmental factors and the work of heating, ventilation and air conditioning has been analyzed. A general definition of the problem taking into account the transfer processes of internal voluminous or local heat source (drainage) has been considered. A generalized mathematical model (MM) of unsteady heat and mass transfer process for bodies of different canonical form (half-plate, hollow cylinder and sphere) and their analogues has been developed. In particular cases of the mathematical model, the dependence of the physical characteristics of the (solid isotropic) medium, the boundary conditions parameters, the capacity of the mass substance transfer sources (drains) from the transfer potentials (temperature, moisture content) or the space-time continuum has been taken into consideration. The analytical solution of the generalized non-stationary and stationary heat and mass transfer problem under the general boundary conditions of different (first, second, third and mixed) kind on the outline of the researched area has been scrutinized. For constant system parameters of non-stationary transfer processes an algorithm for solving differential transfer equations using Fourier transformation with variable parameters of different kind of boundary conditions has been shown. For large-scale transitions, practical applications, parametric analysis of the solutions obtained, setting optimization and automation tasks for process control systems, the obtained MM, analytical and approximate solutions of direct transfer short circuits are given a criterion form convenient for these purposes.



  1. СНиП 23-02-2003. Thermal shielding of buildings. – М.: 2003. – 31p.
  2. Fokin K. F. Constructional heat engineering of the shielding parts of a building. М.: the AVOK-PRESS, 2006, 256 p.
  3. Bogoslovskiy V.N., 2006. Constructional thermophysics (thermophysical basis of heating, ventilation and air conditioning). Publishing house “Northwest AVOK”, 2006.–400 p.
  4. Hugo Hens. Building physics – Heat, Air and Moisture. – John Willey and Sons Limited. 2007. – 270 p
  5. Sadykov R.A. Theory of stationary non-linear transfer processes considering air permeability, condensation or evaporation vaporous liquid(article). KGASU news N3(17), 2011, pp. 268-276.
  6. Sadykov R. A. Calculation of thermo-technical characteristics of shielding constructions taking into account thermo diffusion and moisture filtration. // Materials of the International scientific and technical conference «Theoretical bases of heat and gas supply and ventilation», М.: МГСУ, 2005, pp. 53-57.
  7. Sadykov R.A. Modeling of heat and mass transfer in piecewise homogeneous media depending on physically coupled irreversible processes. // Materials of the XVI Minsk International Forum on Heat and Mass Transfer "MIF XVI", RB, Minsk, May 16-19, 2022, autumn section.
  8. Tikhonov A. N., Samarskiyi A. A. Equations of mathematical physics. M.: Science, 1996.-724 p.
  9. Kartashov E. M. Analytical methods of thermalconductivity of solid bodies.M.: High School, 2001. -550 p.
  10. Leontyev A.I. Heat and mass transfer theory. Publisher MGTU, 1997. – 683 p.
  11. Kudinov V.A., Kalashnikov V.V. , Kartashov E. М. and others. Heat and mass transfer and thermoelasticity in multilayered constructions. M.: Energoatomizdat, 1997. – 425 p.
  12. Demidovich B.P., Maron I.A., Shuvalova E.Z. Numerical methods of analysis. M.: Nauka, 1967, 368 p.
  13. Aramanovich I.G., Levin V.I. Equation of mathematical physics. M.: Nauka, 1969, 288 p.
  14. Tsoi P.V. Methods for calculating individual tasks of heat and mass transfer. M.: Energiya, 1971, 384 p.
  15. Polyanin A.D. Handbook. Linear equations of mathematical physics. M.: Fizmatlit, 2001, 576 p.
  16. Sharma J.N., Singh K. Partial differential equations for engineers and scientists. New Delhi: Narosa Publising house, 2000, 320 p.

Article full text

Download PDF