•
•

## Bulletin of Gulistan State University

#### Abstract

Convective heat transfer processes in heat exchangers, which are widely used in industry, are characterized by partial differential equations. Ensuring the adequacy of mathematical models leads to the complication of particular differential equations for products and boundary value problems for them. Acad. A. Azamov and candidate of mathematical sciences M.A. Bekimov proposed a perfect mathematical model of the heat transfer process in rotary regenerative air heaters (RRAH) at thermal power plants in the form of discrete dynamic systems, which made it possible to control the operation mode of RRAH, calculate smoke and air temperature. A mathematical model of the heat transfer process occurring between hot gas flowing through an insulated tube was created using the method of creating a mathematical model of the convective heat transfer process in the form of discrete dynamical systems. An algebra of a special matrix is constructed, which is included in the created mathematical model, and new properties are studied. The article proposes two discrete models of the heat exchange process between a tube and a heat- exchange fluid (gas or liquid) passing through it. In the first model, the tube temperature is stationary. For that, the output is an explicit formula for the temperature of the effluent. In the second, the tube model is thermally insulated. In this case, a system of decomposed equations is compiled and a formula for the solution is obtained.

9

15

#### References

Prakash, Amit; Kumar, Manoj Numerical method for time-fractional gas dynamic equations. Proc. Nat. Acad. Sci. India Sect. A 89 (2019), no. 3, 559–570.

Koldoba, A. V.; Ustyugova, G. V. A difference scheme with a symmetry analyzer for equations in gas dynamics. (Russian) Mat. Model. 31 (2019), no. 7, 45–57.

Galanina, A. M.; Favorskiĭ, A. P. Numerical solution gas dynamic equations in Lagrangian variables. (Russian) Mat. Model. 24 (2012), no. 12, 119–123.

COinS