Global Journal of Science Frontier Research, A: Physics and Space Science, Volume 23 Issue 1

created by nature itself. This is especially important due to the fact that many non-experts confuse efficiency with the heat transfer coefficient or the coefficient of performance, which may be distinguished by their units. Therefore, the use of power efficiency (24) not only reveals the unity of the laws of transformation of any forms of energy, but also allows us to propose a theory of the similarity of power plants of various types. VII. C onstruction of a T heory of S imilarity of P ower P lants A proper generalization of TIP to the processes of useful energy conversion in various machines allows us to propose a theory of the similarity of power plants [16]. This would complement the classical theory of heat engines by analyzing the relationship of thermodynamic efficiency (energy conversion efficiency) with productivity (based on power N ) and the operating mode of power and technological plants. As in the theory of similarity of heat transfer processes, the mathematical model of such systems includes, along with equations (22,23), the conditions for the uniqueness of the object of study. The latter contain boundary conditions determined in the case under consideration by the magnitude of the driving forces at the border with the energy source or object of work X i , X j , or by the magnitude of the fluxes J i , J j at these boundaries, and by the initial conditions. These latter are set by the magnitude of these forces X jo or fluxes J i in the initial mode, for example, at the "idle" of the installation (at J j = 0) , or in the "short circuit" mode J jk (at X j = 0) , as well as the coefficients L ij ( i , j =1,2) characterizing the transport properties of the system. These conditions make it possible to give the transport equations (22, 23) a dimensionless form Х j / Х j о +J j /J jk = 1. (26) and on its basis, propose a number of similarity criteria for power plants. One of them, which we called the load criterion, is composed of the boundary conditions set by the value of the forces X j , X jo or fluxes J j , J jk Ɓ =J j / J jk = 1– X j / X jo . (27) This criterion depends solely on the load of the installation and varies from zero in no-load mode ( J j = 0) to one in the “short circuit” mode ( X j = 0) Another criterion consists of the resistance coefficients R ij , the reciprocal of the conductivity coefficients L ij : Ф = R ij R ji / R ii R jj (28) This formula is similar in meaning to the ratio of reactive and active resistances, known in radio engineering as the “quality factor”, or “Q-factor” for short, of the circuit, and therefore is called the "criterion of the Q-factor" of the installation. Its value fluctuates from zero to infinity (0< Ф < ∞ ) , increasing as the "active" resistances (from the side of scattering forces) R ii and R jj decrease and the "reactive" resistances R ji (from the side of "heterogeneous" forces) increase. Like thermal resistances in the theory of heat transfer, they depend on the transport properties of the system, i.e., ultimately, on the design performance of the installation. Using these criteria in the expression for the power efficiency (24), it can be given the form of a criterial equation for the energy conversion process: η N = (1 – Ɓ )/ (1 + 1/ B Ф ). (29) Consequently, the efficiency of any energy converter under similar conditions ( Ɓ , Ф as above) is the same. It is expedient to call this provision the principle of similarity of power plants) [16]. This principle allows one to build a universal load characteristic of linear energy - converting systems (Figure 2) [16].Solid lines in the diagram show the dependence of the power efficiency η N of the installation on the load criterion B at different values of the quality factor Φ , and the dash-dotted line shows the dependence on the load of its output power N j.. Fig. 2 : Universal load characteristics of energy converters As can be seen in Fig. 2, in the absence of energy losses ( Ф = ∞ ) and the steady state of the process of its conversion ( B → 0), the efficiency of the installation reaches, as expected, unity. However, in all other cases the value of the power-based efficiency becomes zero twice, once in "idle" setting ( B = 0, J j = 0) and once in the "short-circuit" setting ( B = 1, X j = 0).This result is obtained by taking into account the energy consumption for the installation's own needs, as well as losses from irreversible energy exchange (including heat exchange) between the energy source and the working Energy (power) efficiency Relative power Relative load 0 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 0.1 0.3 0.5 0.7 0.9 0.5 1 3 5 10 20 50 Φ=∞ N / N max B η N 0.2 0.4 0.6 0.8 1.0 0.1 0.3 0.5 0.7 0.9 © 2023 Global Journals 1 Year 2023 14 Global Journal of Science Frontier Research Volume XXIII Issue ersion I VI ( A ) New Applications of Non-Equilibrium Thermodynamics