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The ground source heat pump heating system is considered as one of the best solutions for the transition towards green heating under the continental climate conditions like Kazakhstan. In this paper, experimental and theoretical investigations were carried out to develop a ground source heat pump-based heating system under the weather conditions in Kazakhstan and to evaluate its thermodynamic performance. The water-to-water heat pump heating system, integrated with a ground source heat exchanger and used refrigerant R134a, was designed to provide hot water to meet the requirements for space heating. The predicted values of the coefficient of performance and the experimental results were found to be in good agreement within 6.2%. The thermodynamic performance of the system was also assessed using various environment-friendly refrigerants, such as R152a, R450A, R513A, R1234yf and R1234ze, as potential replacements for R134a. Although R152a is found to be a good alternative for R134a in terms of coefficient of performance and total equivalent warming impact, its flammability hinders its application. The heating system using refrigerants R450A, R513A, R1234yf and R1234ze shows 2-3% lower coefficient of performance than that of R134a. The highest exergy destruction is found to be attributed to the compressor, followed by the expansion valve, evaporator, and condenser. Considering their low flammability and low environmental impact, R450A, R513A, R1234yf and R1234ze are identified as valuable replacements for R134a.

We revisit the optimal performance of a thermoelectric generator within the endoreversible approximation, while imposing a finite physical dimensions constraint (FPDC) in the form of a fixed total area of the heat exchangers. Our analysis is based on the linear-irreversible law for heat transfer between the reservoir and the working medium, in contrast to Newton's law usually assumed in literature. The optimization of power output is performed with respect to the thermoelectric current as well as the fractional area of the heat exchangers. We describe two alternate designs for allocating optimal areas to the heat exchangers. Interestingly, for each design, the use of linear-irreversible law yields the efficiency at maximum power in the well-known form, $2\eta_{\rm C}^{}/ (4-\eta_{\rm C}^{})$, earlier obtained for the case of thermoelectric generator under exoreversible approximation, i.e. assuming only the internal irreversibility due to Joule heating. On the other hand, the use of Newton's law yields Curzon-Ahlborn efficiency., Comment: 7 pages, 5 figures

Thermostatics of CARNOT engines has been extended by more recent research based on endo-reversible model. Our model assumes exo-reversibility but endo-irreversibility to determine new upper-bound to thermomechanical conversion. We propose a functional expression of entropy production related to transformation cycle durations. This approach analyses the energy, entropy and power consequences. We introduce a new concept of entropy production actions that results in three optimums : maximum energy related to transformation durations, maximum energy associated with equipartition of entropy actions, optimal power for given period cycle., Comment: in French

According to harmonic analysis (Fourier analysis), any function $f(x)$, periodic over the interval $[-L, L]$, which satisfies the Dirichlet conditions, can be developed into an infinite sum (known in the literature as the trigonometric series, and for which, for reasons which will become evident in the course of this work, we will use the name of sinusoidal series), consisting of the weighted components of a complete biortogonal base, formed of the unitary function 1, of the fundamental harmonics $\sin(\pi x/L)$, even and $\cos(\pi x/L)$, odd ($2L$-periodic functions) and of the secondary harmonics $\sin(n\pi x/L)$ and $\cos(n\pi x/L)$ (periodic functions, with period $2L/n$, where $n\in \mathbb{Z}^+$, positive integers). The coefficients of these expansions (Fourier coefficients) can be calculated using Euler formulas. We will generalize this statement and show that the function $f(x)$ can also be developed into non-sinusoidal periodic series, formed from the sum of the weighted components of a complete, non-orthogonal base: the unit function 1, the fundamental quasi-harmonics $g(x)$, even and $h(x)$, odd ($2L$-periodic functions, with zero mean value over the definition interval) and the secondary quasi-harmonics $g_n(x)$ and $h_n(x)$ ($2L/n$-periodic functions), where $n\in \mathbb{Z}^+$. The fundamental quasi-harmonics $g(x)$ and $h(x)$ are any functions which admit expansions in sinusoidal series (satisfy Dirichlet conditions, or belong to $L^2$ space). The coefficients of these expansions are obtained with the help of certain algebraic relationships between the Fourier coefficients of the expansions of the functions $f(x)$, $g(x)$ and $h(x)$. In addition to their obvious theoretical importance, these types of expansions can have practical importance in the approximation of functions and in the numerical and analytical resolution of certain classes of differential equations.

The development of functions of real variables in Taylor and Frobenius series (whole series which are formed in nonorthogonal, nonperiodic bases), in sinusoidal Fourier series (bases of orthogonal, periodic functions), in series of special functions (bases of orthogonal, nonperiodic functions), etc. is a commonly used method for solving a wide range of ordinary differential equations (ODEs) and partial differential equations (PDEs).In this article, based on an in-depth analysis of the properties of periodic sinusoidal Fourier series (SFS), we will be able to apply this procedure to a much broader category of ODEs (all linear, homogeneous and non-homogeneous equations with constant coefficients, a large category of linear and non-linear equations with variable coefficients, systems of ODEs, integro-differential equations, etc.). We will also extend this procedure and we use it to solve certain ODEs, on non-orthogonal periodic bases, represented by non sinusoidal periodic Fourier series (SFN).

Even if not so ancient, the history of the heat engine efficiency at maximum power expression have been yet turbulent. More than a decade after the publication of the seminal article by Curzon and Ahlborn in 1975, one's rediscovered two older works by Chambadal and Novikov, both dating from 1957. Then, some years ago, the name of Yvon arose from a textual reference to this famous relation in a conference article published in 1955. Thanks to an historical study of French written books not anymore published for a long time, and since never translated in other languages, we bring to light in this paper that this relation was actually firstly proposed by Henri B. Reitlinger in 1929., Comment: 6 pages, 3 figures