International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

This paper talks about how we can use math to create better models based on actual compressor experiments. The goal? To bridge the gap between what we see happening in real life and what we can predict, ultimately helping us optimize HVAC systems for better performance.
Within these systems, parts like compressors, fans, and electrical components play crucial roles. Compressors, especially, are quite dynamic, especially in heat pump setups.
However, the problem is that manufacturers usually only give real-world data on how compressors perform, without detailed models for understanding how they work in different situations. Hopefully in this paper we will try to construct a detailed model in order to be able to evaluate a HVAC system without the necessity of real-world data. Also, we will evaluate two different mathematical models, two dimensional interpolation and approximation in order to see who perform better.

The article studies the mechanisms of energy exchange and transformations, which occur in a measuring instrument (probe) of an atomic force microscope (AFM) in the process of studying solid surfaces of materials. Mathematical modeling of the heating process of individual elements of the measuring unit of the atomic force microscope at the preparatory, final stages and the scanning stage of the surface under study was carried out. At the same time, such energy components of the processes occurring in the AFM control unit were taken into account. By minimizing the factors (heat dissipation due to friction of the probe on the surface), which negatively affect both the results of the monitoring and the condition of the probe and the surface, stable operation modes of the AFM are established. The solution of the equivalent thermal scheme of an atomic force microscope is presented, which confirms the adequacy of the mathematical models obtained.

The paper considers a way of the numerical solution of a system of partial differential equations describing the nonstationary flow of a viscous liquid along a vertical straight pipe of circular cross-section. The result obtained is not final, because the proposed approximation scheme is the simplest and provides only the first order of accuracy. Computer modeling has shown that such an approximation is suitable only for a small time interval.

In the paper a mathematical model of the non-stationary motion of a viscous liquid mixture through the vertical straight pipe of the circular cross section is proposed. During the model construction weak compressibility of the mixture is considered. The Navier-Stokes equations system is taken as a basis. Such model can be used in the description of oil motion in a vertical well.

In this paper the analytical solution of the differential equation, describing viscous incompressible liquid motion through straight round pipe, with one perturbation parameter is given. The perturbation is introduced into the equation through the disturbed viscosity, depending on the temperature. The solution of the corresponding differential equation is sought in the form of a series in the small parameter. Thus the flow reaction to the internal disturbance is studied. The solution, presented in this article, gives an opportunity to further studying the temperature impact on a viscous weakly compressible liquid motion through a pipe. This research may be of interest to the problems of hydrocarbons control flow through main pipelines.