The article evaluates the energy resources of the components of the environment and the prospects for their use on the redistribution with the creation of local zones of cooling and heating. The physical basis of the principle and systems of redistribution and transformations of energy resources of environments with coverage of the role of compensation processes is given. The use of closed energy circuits with intermediate energy sources, which are subject to phase transitions of evaporation and condensation, and data of energy potentials of ambient air, which are practically achievable for use on this basis, is proposed. The article shows the advantages of arranging systems for redistribution of thermal potentials based on the use of phase transitions of material media. Determination of energy balances of energy redistribution systems is carried out with the indication that in the end, such a method is the most energyefficient. Upon completion of technological tasks, local areas with different energy potentials and temperatures degrade in dissipation processes and transform to the level of environmental indicators. This means interfering with the environment only at the level of energy costs in compensation processes. The article shows the transition to secondary recovery systems of energy resources based on the use of primary energy sources in environmental transformations at the levels of increasing their energy potentials and providing phase transitions with appropriate mathematical formalizations. A regression analysis of the feasibility of using primary energy potentials is given. It is proved that in the heat pump due to the generated mechanical energy the heat return at the level of the lost one. The estimation of the general condition of processes at power effects is given. The offered air pump and system of realization of a refrigerating cycle are considered. The redistribution of energy potentials of natural, forcibly created environments or systems and the synthesis on this basis of powerful heat fluxes in combination with advanced control methods, allows you to control their values of thermodynamic parameters.
The physical parameters of the globe, relating to the magnetosphere, atmosphere, lithosphere, and hydrosphere, correspond to the conditions of existence of the entire biological world and human society. In this definition, the energy component is no less important than the material, despite its differences from the coordinates, seasons, or time of day. After all, even under the harsh conditions of the Arctic and Antarctic, the air levels are quite far from absolute zero. Moreover, this corresponds to areas of human habitation with air temperatures above 0 °C.
The existence of the Earth's hydrosphere and lithosphere is accompanied by energy potentials created by interactions on a planetary scale. At the same time, the stabilization of the energy balance in this interaction ensures the existence of the biosphere under the accepted conditions. From this point of view, the authors (
The properties of heat pumps provide (
A significant amount of modern research concerns the topic of opportunities for transformations of energy potentials. Research (
It should be noted that in the work of the authors (
The authors (
Therefore, the rational use of heat pumps with simultaneous heating and cooling of local areas is carried out based on exergy analysis. Here, the prototype heat pump operates in three main modes. The authors (
 the first – the heating mode which provides receiving of hot water with the use of heat available in ambient air;
 the second – the mode of cooling of cold water and heat removal to ambient air;
 in the third mode, hot water is supplied due to the heat taken away from the cold water.
Thus, the authors (
Recent advances in heat pump systems (GuoHua
Defined in the form of phenomenological analysis of thermodynamic efficiency of air heat pump using the energy potential of the environment in the heat supply system and redistribution of energy resources and prospects for use in the food industry.
The system of redistribution and transformations of energy resources of environments is considered. Theoretical and practical experience of thermodynamics specialists has allowed, among other things, to generalize the relationship between air heat capacity and temperature. Molar heat capacity at р = const, kJ / (kmol • K) is represented by the dependencies in the actual value in the interval 01000 °С:
and on average
Numerical values of heat capacities are given in
Table
Heat capacity of air.
Temperature, °C  Heat capacity  

Molar, kJ / (kmol • K)  Mass, kJ / (kg • K)  Volume, kJ / (m^{3} • K)  













0  29.073  20.758  29.073  20.758  1.0036  0.7164  1.2971  0.9261 
100  29.266  20.951  29.152  20.833  1.0061  0.7193  1.3004  0.9295 
200  29.676  21.361  29.299  20.984  1.0115  0.7243  1.3071  0.9362 
300  30266  21.951  29.521  21.206  1.0191  0.7319  1.3172  0.9462 
Estimation of energy potential in 1 m^{3} of air at a temperature of 303 K at a pressure of 1 bar, is:
Cooling this volume of air to 272 K means heat transfer Q to the receiver. At the same time, we note that the same volume of air at 30 °C or 243 K has a potential of 315.1953 kJ. Thus, technological opportunities for the redistribution of energy potentials open up prospects for their transformation and use, due to the second law of thermodynamics.
Air is a mixture of gases. The composition of the air is not constant and varies depending on the area, region, and even the number of people around you. Air consists of about 78% nitrogen and 21% oxygen, the rest are impurities of various compounds. Its chemical formula is O2. Under normal conditions (temperature 0 °C, pressure 101.3 kPa) oxygen is in a gaseous state, with no mass of taste, odor, slightly heavier than air.
The flow temperature at the pump inlet and outlet was determined, after which the temperature value was averaged. Several thermocouples were used to measure the flow temperature in the middle of the pipeline. The data of the primary temperature transducers were fed to the ADC, converted into a digital signal, and entered into the PC. Data registration interval  10 s. Measurements were performed with chromelkopel thermocouples, measuring device brand Expert (manufacturer Ukraine).
At regular intervals, the surface temperature t was measured. The surface temperature of the module was determined by a thermocouple embossed into the surface. At regular intervals, the air pressure was measured. Measurements were performed with a manovacuummeter OBMV11006f (manufacturer Ukraine). The value of pressure in the tables of properties of water vapor was determined by its temperature.
The determination of ambient air parameters was done by using a psychrometer brand VIT2 (manufacturer Ukraine). There was a registration of air parameters, namely its temperature, humidity, moisture content, enthalpy. The measurement of these parameters was performed using the ADC module "Arduino" and a computer.
A digital humidity sensor SHT 10 was used to determine the parameters of the air coming from the pump. This allowed determining with high accuracy the characteristics of the air directly in the flow during the experiments. The program interface of the ADC converter is made in such a way that the change of air parameters from time to time is reflected in the form of graphical dependencies in the online mode. The use of such a scheme with the use of frequency control of the pump drive allowed to quickly intervening in the course of the experiment that simplifies its planning.
The fluid flow simulation was performed using ANSYS CFD generalpurpose computer software from ANSYS, Inc.
Software systems allow modeling and calculation of liquids and gases, heat and mass transfer processes, reacting flows. ANSYS CFD is fully integrated into the ANSYS Workbench environment, which is the basis of engineering modeling, it integrates all ANSYS tools and software.
The ANSYS Workbench environment provides general access to such tools as: communication with CADcomplexes, construction, and modification of geometry and calculation grid. The software package is widely used for modeling processes that take place in pumps, fans, compressors, gas, and hydro turbines, etc. The ANSYS CFDPost postprocessor, which is part of the software package, can be used to create highquality animations, illustrations, and graphics (
Theoretical modeling of conditions of creation and reproduction of processes of redistribution of energy potentials of environment and recovery of secondary resources based on provisions and laws of technical thermodynamics is used.
The research of the process was carried out according to the BoxBenken plan, which allows obtaining the maximum amount of objective information about the influence of factors with the help of the smallest number of experiments.
Processing of the obtained experimental data set was performed according to wellknown methods and statistical processing methods to obtain an empirical mathematical model:
using methods of correlation and regression analysis of the approximating function, which characterizes the influence of factors and their interaction on the optimization parameter, ie productivity.
Based on the constructed regression equation, the contribution of each independent variable to the variation of the studied dependent variable is determined, ie the influence of factors on the performance indicator.
The experimental data set was processed using the Statistica12 software package. The coefficients of the regression or approximating function equation, under the condition of orthogonality and symmetry of the planmatrix of the planned factorial experiment, were determined according to the standard method according to known dependences.
The obtained results were statistically processed using the standard Microsoft Office software package.
Theoretical and experimental research was performed fbased on the Problem Research Laboratory of the National University of Food Technologies. The study consisted of three parts. The first was to assess the energy potential of ambient air as the most accessible environment.
This part of the research is the basis for the creation of a modern air heat pump ( a patent of Ukraine 17167) with the implementation of phenomenological studies relating to the redistribution of heat fluxes based on the second law of thermodynamics using a closed circulating air circuit.
The second part of the study concerns the thermodynamic features of achieving phase transitions of water as the main filler of food industry environments with the development of mathematical formalizations and estimation of energy consumption in the processes of heating the liquid phase and entropy transformations.
The third part is devoted to the implementation of phase transitions with the assessment of the energy potentials of the secondary pair. This creates a basis for the implementation of regenerative processes by increasing the pressures and temperatures in the compensation processes and subsequent condensation to obtain a liquid phase of H2O in closed energy circuits.
In this article, we examine the first and second parts of the research, which substantiates our further direction of theoretically directed mathematical analysis.
Historically, humanity has received such opportunities after the creation of heat engines. In 1852, Lord Kelvin proposed new use of the heating machine for space heating. Kelvin called such a machine a heat pump, the task of which was to cool the cold outside air and transfer the received thermal energy at a higher temperature in the room. This unnatural process of heat transfer from a cold to a heated environment was carried out through the consumption of mechanical work. Each unit of mechanical work, brought to the ideal heat pump, before getting into the heated room "captured" 5 – 8 units of the heat of the outside air. Therefore, 427 k Gm of work at the inlet to the heat pump was converted into 6 – 9 kcal of heat at the outlet. The same kilocalorie formed by burning a certain amount of fuel is not supplemented by anything and remains one kilocalorie.
Burning some amount of fuel directly, bring in a heated room 1 kcal of heat. If the same amount of fuel will be burned in a heat engine, then only about 20%, equivalent to 85 kGm, will convert into mechanical work. If these 85 kGm are brought to the heat pump, it will provide 6 times more heat to the room, ie 6 • 85 = 510 kGm or 1,2 kcal. These ratios indicate the feasibility of using the primary energy potentials of the fuel in the circuit "heat engine  heat pump".
Thus, it is expedient to pay attention to equivalence in these thermodynamic transformations. Thus, the value of the coefficient of performance of heat engines is difficult or impossible to increase by 20%. In the heat pump due to the generated mechanical energy, heat returns to the level of lost.
software module (a) and General view of laboratory experimental setup (b).
Air heat pump.
Prerough control of the compressor shaft speed of the compressor of the appropriate diameter was set using commands from the motor control panel of the control multisystem control and reading device Altivar 71 using Power Suite software version 2.3.0. The technical capabilities of this device and software allow to smoothly change the speed of the motor shaft of the prototype laboratory installation in the range from 0 to 1300 rpm. The numerical value of the motor shaft speed (error within ± 1.5%) was recorded using a sensor type E40S610Z46L5, which is connected simultaneously to the rotor of the motor and the multisystem device.
Numerical data of energy costs and torque on the shaft of the electric drive depending on the load at a particular time of the experiment is displayed in the form of tabular data and graphical dependences on the PC monitor.
It is worth recalling that a heat pump is an installation that converts lowpotential natural thermal energy or heat from secondary lowtemperature energy resources into the energy of higher temperature potential, which is already suitable for practical use. The transformations take place in the reverse thermodynamic cycle, and the transfer of energy from the lower temperature level to a higher one is performed due to a certain amount of mechanical (electrical) energy, which is externally supplied to the heat pump compressor and its design.
The algorithm for conducting experimental studies of the air heat pump, formalized in the form of a the structural model scheme is shown in Figure
Scheme of the model of the planned experiment of the PFE 3^{3} type.
The total number of experiments e N one repetition was determined by the formula:
Where:
The experiments were performed in triplicate. The asymmetric planmatrix of the planned threefactor PFE 3^{3}type BoxBenkin experiment for three factors and three levels of factor variation had a total number of experiments equal to 27.
The independent variables were: the speed of the rotor of the compressor n_{k}, which was encoded by the index x_{1}, ie n_{k}; the diameter of the rotor of the compressor D_{k}, which is encoded by the index x_{2}, ie D_{k}; blade pitch T_{1}, encoded by the index x_{3}, ie T_{1}.
Structural model of a planned threefactor (
Thus, to study the performance of Q_{ke}, an approximate mathematical model in the form of a functional dependence was chosen.
When compiling the planmatrix of experiments, coded notations of upper (+1), lower (1), and zero (0) levels of variation by factors were introduced (
Surface response changes in productivity in the form of functionality.
The results of coding of variable input factors, the upper and lower level of variation of each factor, and the interval of its variation are given in Table.
The results of coding factors and levels of their variation.
Factors  Marking  Interval of variation  Levels of variation natural / coded  



natural  coded  


Speed of rotation, n_{k}¢,  X_{1}  x_{1}  100  100/1  200/0  300/+1 
Diameter D_{k}, m  X_{2}  x_{2}  0.04  0.12/1  0.16/0  0.2/+1 
Step T_{1}, m  X_{3}  x_{3}  0.03  0.05/1  0.08/0  0.11/+1 
Because during the experiments independent variable input factors, ie n_{k} are inhomogeneous, ie they all have different physical units and different orders of arithmetic numerical values of units, they were led to a single system of calculations by switching from the entered notation coded values to real (natural) values. Made a randomized plan matrix of the planned threefactor experiment type PFE 3^{3}.
After estimating the statistical significance of the coefficients of the regression equation and checking the adequacy of the mathematical model of the logarithmic function, we obtained a regression equation that characterizes the functional change in productivity in natural quantities (
With the probability level p = 0.95 and the value of the talpha criterion equal to 2.053, the following statistics were obtained: coefficient of multiple determination D = 0.893; multiple correlation coefficient R = 0.945; standard deviation of the estimate s = 0,150; Fisher's Ftest is 64,212. The coefficient D is significant with the probability level P = 1.00000. The regression equation (
According to the regression equation (
The dominant factors that have a significant functional impact on the increase in productivity Qke are the speed nk and diameter D_{k}, which is characteristic of the graphical interpretation of the response surface, and this is the regulation of energy potential, ie temperature.
Figure
The diagram of change of productivity Q_{ke} of the heat pump. Note: a, b, с – T1 = 0.05; 0.08 and 0.11 m.
Based on the graphanalytical analysis (Figure
Dependence of change in productivity Qe as a functional:а – Q_{k} = f_{Qk} (D) , 1, 2, 3 – in accordance, n_{k}= 100; 200; 300 rpm; b – Q_{k}= f_{Qk} (n _{k}), 1, 2, 3 – in accordance, T_{1} =0,05; 0,08; 0,11 m.
The discrepancy between the experimental values of the performance Q_{ke} of the pump obtained according to the regression equation (
Assessment of the general state of processes in energy effects.
This feature of energy transformations is based on the second law of thermodynamics with an indication of the need to use compensation systems by increasing the temperatures and pressures of energy sources in closed circuits.
An important advantage of the heat pump is that it implements "reverse" processes in the modes of heating and cooling of the premises as an ideal air conditioner.
The technical implementation of heat pumps and refrigeration machines based on the Carnot reverse cycle, which is the only achievement of humanity in the implementation of the principle of energy redistribution in existing parallel systems.
Returning to condition (3) we obtain an estimate of the heat flux dissipated from the cooling medium:
Where:
v– volumetric flow of the gas phase supplied to the evaporator as part of the heat pump, m^{3} / s;
Similarly, it is possible to determine the energy potentials of the liquid phases of lakes, rivers, seas and oceans, which are largely used.
The study (
Understanding this situation in a significant number of cases (
Another direction (
In cases of asynchronous situations, there is a need to use energysaving storage devices. However, the positive results for parallel system designs are quite achievable even in mechanical systems in which transients are generated. In this case, in addition to energy effects, it is possible to regulate the movement of machines with restrictions on total dynamic loads.
In the general list of processes that take place in food, chemical, microbiological and other technologies, there are mechanical, hydraulic, aerodynamic, thermal interactions or various combinations of them (Figure
During convection, heat is transferred during the mixing of cold and warm layers of liquids or gases, and therefore this process is inextricably linked with the mechanical motion of liquid and gas flows. Their theoretical basis relates to the relevant sections of hydro and aerodynamics, but the level of complexity, even for simple cases in mathematical formalizations, is so significant in combination with thermal processes that it has led to limitations in the relevant scientific interests. However, it is convection in heat transfer mechanisms in heating systems, technological devices, electric drives, brakes, compressors, refrigeration units, etc. in terms of significance that led to the development and solution of applied problems.
Most of them concern the determination of heat transfer coefficients, which may depend on the thermal conductivity of the media, viscosity, density, heat capacity, kinematic parameters, and geometry of the media volumes. The effects of all these parameters are combined by the phenomenon of the boundary layer. The imaginary shirt creates the main barrier to heat transfer, which barriers that most effectively overcome in the modes of phase transitions of boiling and condensation due to the activation of heat transfer coefficients. An additional positive effect of the phase transition concerns the production of a coolant with a thermodynamic parameter supplemented by the heat of vaporization.
Phase transitions open additional possibilities of transformation of parameters of pressure and temperatures that allow overcome natural prohibitions which features are formulated by the second law of thermodynamics. In the classical definition, this is achieved by supplementing the closed or partially closed circuits with a
However, in addition to information on the creation of Lord Kelvin air heat pump with the transformation of energy potentials of air flows due to the relationship between pressure and temperature, we note the consequences of continuing attempts to create their modern structures, which we consider in this paper.
This applies to the development of the patent of Ukraine 17167 "Air heat pump" (Figure
The creation of initial energy potentials in such systems is carried out using primary energy sources. The latter in most cases relate to the resources of the generated vapor phase, electricity, energy of hydraulic systems, compressed air systems, or chemical energy of incoming raw materials. The presence of the latter is a constant factor in any technology, according to which the energy potential of recycled raw materials should be preserved as much as possible. However, the appropriate set of energymaterial transformations provide by the influences of external energy flows due to which the set temperatures of technological processing of environments are reached. It can be carried out without achieving the modes of phase transitions or with their implementation. Consider the transformation of the energy potentials of airflows due to the relationships between the design parameters of the pump and the process.
The potential of devices for increase of energy efficiency and intensification of processes of a mode of phase transitions and generation of steam, gas phase, or steamgas mixes is high enough. Development of new designs of heat exchangers, evaporators, the definition of rational modes of their operation is possible only based on the data received at comprehensive researches of the processes proceeding in devices.
It is expedient to refer to the peculiarities of the cycles of refrigeration units or heat pumps from the point of view of creating analogies for systems of industrial devices in which there are modes of phase transitions and generation of steam, gas phase, or steamgas mixtures. The existence of a closed circuit in the refrigeration cycle involves the combination of an evaporator as a steam phase generator (Figure
System of realization of a refrigerating cycle: 1 – the evaporator; 2 – compressor; 3 – capacitor; 4 – throttle; 5 – fan.
In the closed circulation circuit A of the refrigerant, phase transitions occur due to the supply of heat flow q0 from the cooling zone with circuit B and the removal of heat flow qk from the condenser in circuit C. Depending on the technological tasks, circuits B and C can be closed or open.
This leads to the conclusion that the total energy balance of circuit A is supplemented by the energy consumption
and the whole system in balance calculations must take into account power consumption in the circuits B and C. The decision of technical problems is achieved in one of the circuits B or C, or both simultaneously. It is important that the arrangement of energymaterial connections of circuits B and C following the evaporator and condenser can be realized due to convective air flows of the medium, which are formed in response to the existence of a gravitational field. This solution is present in the installation of most domestic and industrial refrigeration systems and systems.
Cooling and heating zones can exist as local, but in cases where they are open, it means that they are interconnected through the environment, and technical systems of refrigeration systems, heat pumps, and air conditioners
A scientifically based analysis of energy processes is essential for an active energysaving policy. Modern laws of thermodynamics (Annex 49 summary report IEA ECBCS. –Fraunhofer IBR. 2011) include the study of the properties of energy in its transformations in two approaches to efficient use: energy and exergy. Such approaches involve the use of two thermodynamic characteristics of energy  quantity and quality: quantity  in energy, both  in exergy.
Thus, the authors (
The magnitude of the work, as a quantitative measure of energy quality, is included in the equation of energy balance (First law of thermodynamics), and the condition of convertibility S gene ≥0  in the equation of entropy balance (Second law of thermodynamics). Therefore, the authors (
The calculation of authors (
Modeling and optimization of gas flow through the pipeline network by the authors (
Based on the above, the physical state of the system is determined by the values of two variables out of three, namely pressure, volume, and temperature.
It is known that the physical state of the system is determined by the values of two variables out of three, namely pressure, volume, and temperature. There is a functional connection between these three parameters. In what follows, we will consider the pressure p and the volume v as independent variables, and then we will display this relationship in the form:
The set of values of p and v determines the position of a point on the plane pv. Each such point corresponds to a certain value of temperature T (Figure
Dependence of p = p (v) in thermodynamic transformations parameters.
Differential
is a complete differential. By changing the state of the system from the parameters at point A to the parameters of point B, the temperature at point B can be determined in the form:
Determining the values of the work performed by the system as a result of changing its state during the transition of parameters from point A to point B and, considering the process inverse, we reflect the dependence:
The graphical interpretation of the given integral is the plane under the transition curve on the pv diagram. Since the transition from point A to point B can be done with different trajectories, it means that these areas will be different. Their area is to some extent determined by the design parameters and speed of the drive. It follows that the value of W depends on not only the coordinates of points A and B, but also on the selected transition trajectories. It is logical to assume that the amount of heat perceived in this transition of the system also depends on that, but the difference between the amount of perceived heat Q and energy W does not depend on the shape of the transition trajectory. The conclusion about the constancy of the difference Q – W, which corresponds only to the state of the system at points A and B, indicates a change in the internal energy u:
In another form, expression (
For the case of a closed trajectory from point A we obtain a curvilinear integral from du, then we have:
The written curvilinear integral is called the circulation and is denoted by a symbol
Where:
Bringing the heat flux Q to the medium means corresponding changes in the value of entropy. The latter is determined only by the variables that characterize the physical state of the system, and in the transition from point A to point B changes in entropy do not depend on its trajectory.
Where:
dQ_{B} – the amount of heat passing through the system boundaries during the reverse process.
In the elementary process we have:
Replacement of values dQ i dW provided (12) leads to the form
in which there are point functions and complete differentials.
Integration (16) leads to the value of u as a function of the variables s and v in the form:
or, disclosing condition (17), write:
and by comparison with condition (16) we obtain:
If condition (19) is known for a mass of any homogeneous liquid, then the parameters T, p and u can be calculated for any physical state of the medium, which is determined by the independent variables s and v. Therefore, the performance of the heat pump sets the value of the internal energy
The paper (
Therefore, the calculation of the temperature field of a lowpotential energy source in the zone of influence of the compressor rotor diameter and the blade pitch reduced to solving the equation of nonstationary thermal conductivity.
In a cylindrical coordinate system characteristic of a heat pump, the equation has the form (
Therefore, the calculation of the temperature field of a lowpotential energy source in the zone of influence of the compressor rotor diameter and the blade pitch reduced to solving the equation of nonstationary thermal conductivity. In a cylindrical coordinate system characteristic of a heat pump, the equation has the form (
Where:
t – the ambient temperature, °C;
τ – hour, s;
a – thermal conductivity, m^{2}/s;
r is the radial coordinate, m;
θ is the polar angle (the angle between the radius vector r and the x axis).
This is a threedimensional problem, but given the shape and length of the rotor relative to the radius of impact, as well as the heterogeneity of the blades, it can be reduced to twodimensional with a sufficient degree of accuracy. For this problem statement, taking into account the symmetry of the temperature field, it is proposed to make a simplified solution, provided that τ>; 0 до rр< r< rк (
Where:
rр – average rotor radius, m;
r_{к} – radius of the contour of influence, m.
Simplifying the task by switching from a threedimensional to a twodimensional model eliminates heat flow along the rotor axis. However, the heat flow in the vertical direction, despite its small orders, must be taken into account due to its continuity in time, even when the heat pump is stopped. To solve the problem, we introduce an amendment that compensates for bulk sources and heat fluxes (environment). Then equation (2.2) will take the following form (
Where:
t – ambient temperature, °C;
r – time, s;
a – thermal conductivity, m^{2} /s;
r – is the radial coordinate, m;
qvsources and heat runoff due to heat fluxes of the environment and heat release through the surface, W / m^{3};
c – heat capacity, J / (m^{3} • °C).
The paper (
Therefore, the set of factors: background temperature of low potential energy source (t_{fon}, °C), ambient temperature, heat runoff (qv, W), thermophysical characteristics, the intensity of incident solar radiation, are the basic data in the calculations. The set of factors: background temperature of low potential energy source (t_{fon}, °C), ambient temperature, heat runoff (qv, W), thermophysical characteristics, the intensity of incident solar radiation, are the basic data in the calculations.
Execution of the technical and economic analysis is reduced to the definition of the temperature of the heat carrier selected from the heat pump that in turn, is defined by the created temperature. The second feature is the need to assess the operating conditions of the heat pump in the worst, in terms of the coefficient of thermal transformation, conditions. This corresponds to the time period of completion of the heating (cooling) cycle.
The known similarity criteria do not fully reflect the studied phenomena, in connection with which the following dimensionless complexes are proposed in the research work: relative heat flux (Q), modified dimensionless temperature (Θ), and criterion Fo.
The temperature field of a lowpotential energy source is described by a dimensionless function (
Where:
Fo –Fourier criterion,
Θ – dimensionless temperature,
Q – relative heat flux.
Considering the active load on the rotor with blades, which perturbs the temperature field factor, we propose to introduce the relative heat flux (Q), which is accepted in the research work to calculate the formula:
Where:
q _{na} – specific heat flux per unit area of the rotating rotor with blades, heat load on the pump in a certain period of operation, W / m^{2};
q_{fon} – background heat flux (specific, per unit area of the environment), W / m^{2}
The operating parameters of the heat pump depend on the difference between the generated temperature and the ambient temperature.
The Fo criterion was formed by a known formula (
Where:
а  thermal conductivity coefficient equal to а =λ/сρ m^{2}/s;
λ  thermal conductivity, W / m ˚С;
ρ – air density, kg / m^{3};
с_{p}  heat capacity of air, J / (kg × °С);
τ  characteristic time of change of external conditions, s; rр  characteristic body size (rotor radius), m.
The complex nature of the mutual influence of the defining parameters does not allow to formalize an unambiguous solution, in connection with which the traditional approach to the type of criterion equation as a static dependence is used. The generalizing equation for singlestream operation can be described as a regression:
Where:
k_{1,2 ... n} – determining factors.
The results of the calculations are well approximated by secondorder polynomials. Applying the methods of statistical processing, the criterion equation is obtained:
The results of the calculation of the temperature at the outlet of the partition as a function of the defining parameters in the dimensionless form are presented in Figure
The results of the calculation of the function from the defining parameters.
The process of supplying and discharging heat to a lowpotential energy source is a function of time and space. The temperature field is formed by the design parameters of the pump. Analysis of performance data and these formed temperature fields showed the predominance of heat flux in the radial direction and a small amount of heat flux in the axial direction. Nevertheless, due to the design, the formation of heat flow and heat dissipation from the circuit are stabilizing factors that provide a quasistationary state.
The phenomenological analysis of the materials given in researches allows noting perspective directions of use of the closed power circuits in the following list:
 Technologies of redistribution of energy potentials of the environment based on heat pumps, refrigeration units, and air conditioners;
 Recuperative transformations of heat fluxes of industrial environments based on thermodynamic connections between pressures and temperatures of gas and steam phases;
 Technologies of creation and transformations of steam, gas, and steamgas streams with the application of modes of adiabatic phase transitions;
 Creation of technologies based on use of dynamic systems in which continuous processes of heating, endurance, and cooling of streams of environments for use of primary potentials in the closed system without initial streams with the subsequent compensation of losses in the environment with the subsequent transition to dynamic modes are realized;
 In cooling systems of environments in large volumes of technological devices based on the use of cooling jackets or external heat exchangers, an important disadvantage is the gradual reduction of temperature differences on heat exchange surfaces and restrictions on heat recovery. Avoidance of such shortcomings is associated with the transition to a dynamic system with constant temperature differences.
According to the results of theoretical and experimental studies, taking into account thermodynamic analysis, the temperature field of a potential energy source, the main rational parameters of the heat pump rotor are set. So, diameter  0.2 m; step of the first turn of the blade  0.11 m; step increment  0.03 m; the number of blades that are installed between one a pair of adjacent turns  4 pcs; rotor speed  300 rpm.

This research received no external funding.
The authors declare no conflict of interest.
This article does not contain any studies that would require an ethical statement.