Second Law Of Thermodynamics Research Articles

The Second Law of Thermodynamics and the Surface Characteristics of Dispersed Systems

The Second Law of Thermodynamics and the Surface Characteristics of Dispersed Systems

Automotive air-conditioning system thermal performance assessment: an experimental approach combining first and second laws of thermodynamics

Automotive air-conditioning system thermal performance assessment: an experimental approach combining first and second laws of thermodynamics

Equivalent Circuits for Exergy Flow in Thermodynamic Systems

Abstract The second law of thermodynamics explains the nature of all spontaneous processes, and it imposes a limit on the performance of all technologies, from heat engines to refrigerators. These limits are well described as early as Sadi Carnot's 1824 publication that established the field of thermodynamics; researchers later developed the concept of exergy, or the available work, that a thermodynamic system can produce when interacting with a specified environment. In this work, we describe a resistance analogy for thermodynamic systems, in which the need to remove entropy forces some amount of energy to leave the system as heat rejection. Specifically, it is the inverse temperature of the heat sink that resists energy flowing out of the system as heat rejection. An equivalent circuit can be drawn for any thermodynamic system, with energy flowing through different branches of the circuit. The different paths correspond to different energy and exergy flows, including the energy that must flow out of the system as heat rejection and, therefore, cannot contribute to the exergy content of the system. After establishing this equivalent circuit, it is applied to a natural gas combined cycle example problem, a desalination example problem, and a transient heating problem.

IGA Approximations of Elastic Interfaces and their Defects in an Elastic Medium with Couple Stress

AbstractThe objective of this work is to develop and implement a computational algorithm for calculating stress and couple-stress fields induced by bulk and interfacial line defects such as dislocations and generalized disclinations within phase/grain boundaries. The thermodynamic driving forces on line and planar defects, responsible for coupled plasticity and interface motion, fully coupled to stress, couple-stress and applied boundary conditions are also computed. A continuum approach for small deformations is considered following the formulation outlined in Acharya and Fressengeas (Continuum mechanics of the interaction of phase boundaries and dislocations in solids. In: Differential Geometry and Continuum Mechanics, pages 123–165, 2015), extended herein in the thermodynamics to accommodate physically necessary ingredients that arose in the modeling in Zhang and Acharya (J Mech Phys Solids 119:188–223, 2018), Zhang et al. (J Mech Phys Solids 114:258–302, 2018). Constitutive relations are derived from kinematics, balance laws and from the use of the second law of thermodynamics in global form. One of the challenges presented by this approach is the inclusion of couple stresses, Toupin (Arch Rational Mech Anal 17(2):85–112, 1964), and the consequent treatment of 4th order systems arising from the equations of balances of linear and angular momentum. In order to deal with these equations, the classical FEM approach is replaced by iso-geometric analysis (IGA), as proposed by Hughes et al. (Comput Methods Appl Mech Eng 194(39):4135–4195, 2005). Results on stress and couple stress fields of the various defects involved are computed. Further, the coupling of the dislocation density with the eigenwall allows for the capturing of the shear parallel to the grain boundary, which has been observed experimentally and through molecular dynamics.

Discretely Nonlinearly Stable Weight-Adjusted Flux Reconstruction High-Order Method for Compressible Flows on Curvilinear Grids

To achieve genuine predictive capability, an algorithm must consistently deliver accurate results over prolonged temporal integration periods, avoiding the unwarranted growth of aliasing errors that compromise the discrete solution. Provable nonlinear stability bounds the discrete approximation and ensures that the discretization does not diverge. Nonlinear stability is accomplished by satisfying a secondary conservation law, namely for compressible flows; the second law of thermodynamics. For high-order methods, discrete nonlinear stability and entropy stability, have been successfully implemented for discontinuous Galerkin (DG) and residual distribution schemes, where the stability proofs depend on properties of L2-norms. In this paper, nonlinearly stable flux reconstruction (NSFR) schemes are developed for three-dimensional compressible flow in curvilinear coordinates. NSFR is derived by merging the energy stable flux reconstruction (ESFR) framework with entropy stable DG schemes. NSFR is demonstrated to use larger time-steps than DG due to the ESFR correction functions, at the cost of larger error levels at design order convergence for equivalent degrees of freedom, while preserving discrete nonlinear stability. NSFR differs from ESFR schemes in the literature since it incorporates the FR correction functions on the volume terms through the use of a modified mass matrix. We also prove that discrete kinetic energy stability cannot be preserved to machine precision for quadrature rules where the surface quadrature is not a subset of the volume quadrature. This result stems from the inverse mapping from the kinetic energy variables to the conservative variables not existing for the kinetic energy projected variables. This paper also presents the NSFR modified mass matrix in a weight-adjusted form. This form reduces the computational cost in curvilinear coordinates because the dense matrix inversion is approximated by a pre-computed projection operator and the inverse of a diagonal matrix on-the-fly and exploits the tensor product basis functions to utilize sum-factorization. The nonlinear stability properties of the scheme are verified on a nonsymmetric curvilinear grid for the inviscid Taylor-Green vortex problem and the correct orders of convergence were obtained on a curvilinear mesh for a manufactured solution. Lastly, we perform a computational cost comparison between conservative DG, overintegrated DG, and our proposed entropy conserving NSFR scheme, and find that our proposed entropy conserving NSFR scheme is computationally competitive with the conservative DG scheme.

A micropolar phase-field model for size-dependent electro-mechanical fracture

This article proposes a micropolar phase-field model for size-dependent brittle fracture in solids under electro-mechanical loading conditions. Considering displacement, micro-rotation, electric potential, and phase-field variable as the kinematic descriptors and employing the virtual power principle, we derive a set of coupled governing partial differential equations (PDEs) for size-dependent solids. Invoking the first and second laws of thermodynamics, we determine the constitutive relations for the thermodynamic fluxes. Carrying out the finite element implementation of the derived governing PDEs using the open-source Gridap package in Julia, we demonstrate the efficacy of the proposed phase-field model through a few representative numerical examples. Especially the importance of the proposed model in incorporating the effect of relative rotation, i.e., the difference between macro- and micro-rotation, on the response of solids under electro-mechanical loading is shown that may not be possible with the existing non-local models such as strain-gradient or couple-stress approaches. To capture the experimentally observed size effects in solids under electro-mechanical loading, the proposed model does not demand higher-order continuity of finite element shape functions, unlike a typically used strain gradient model. To demonstrate the efficacy of the proposed model, we have compared our results against demanding experimental and numerical benchmark results available in the literature. We provide a parametric study to unravel the effect of different micropolar material parameters on the electro-mechanical response of a brittle solid. Interestingly, the proposed micropolar model is less sensitive to the phase-field length scale than the conventional non-polar phase-field models.

The fate for the interior content of a Black Hole from one-quarter entropy area-law

In this paper we continue investigations concerning the physical nature of the black hole entropy. In particular, in order to depict massless excitations (gravitons) leading to the one-quarter entropy area law, we use a mechanical statistical approach. As a first result, we obtain that, starting with a radiation field, we cannot exactly obtain the one-quarter factor in entropy area law. In the aforementioned framework, the correct black hole entropy is obtained only in the case where the internal temperature Ti, proportional to the Bekenstein-Hawking one, is such that Ti→0. As a consequence, according to other similar proposals in the literature, only a kind of Bose Einstein condensate (BEC) can exactly support the black hole entropy.

Nonlinear generalized piezothermoelasticity of spherical vessels made of functionally graded piezoelectric materials

The present study investigates the thermoelastic response of a heterogeneous piezoelectric sphere under thermal shock loading. Boundary conditions as well as loading are considered as symmetric; thus, the response of the sphere is expected to be symmetric. All of the properties of the thick-walled sphere, including mechanical, electrical and thermal properties, are considered dependent on the radial position, except for the relaxation time, which is considered a constant value along the radius. The governing equations of the sphere have been derived under heterogeneous anisotropic assumptions. The general form of the second law of thermodynamics, which is nonlinear in nature, and is called nonlinear energy equation is used. The number of the established equations is three, which includes the motion equation, energy equation and Maxwell electrostatic equation of Maxwell. These equations are obtained in terms of radial displacement, temperature difference and electric potential. The energy equation is derived based on Lord and Shulman theory with a single relaxation time. In the next step, by introducing dimensionless variables, the governing equations are provided in dimensionless presentation. Then these equations have been discretized using generalized differential quadrature method. Also, in order to follow the solution of the equations in time domain, Newmark method has been used. Since the system of equations is nonlinear, Picard algorithm is applied as a predictor-corrector mechanism to solve the nonlinear system of equations. Then numerical results are presented to investigate the propagation of mechanical, thermal and electric waves inside the heterogeneous sphere and also their reflection from the outer surface of the sphere. By examining the results, it can be seen that mechanical and thermal waves propagate with a limited speed, while the speed of electric wave propagation is infinite.

Aspects of Developing an Innovative, Energy-Efficient, Low-Emission Co-Generator

Purpose. To develop a model and construct an experimental, innovative co-generator with high energy efficiency and low emissions. This involves developing a system that can efficiently generate both electricity and heat simultaneously while minimizing emissions, contributing to sustainability efforts, and addressing energy demands in a more environmentally friendly manner. Methodology. To achieve the goal, a system approach is utilized, enabling the selection of modelling types for the development of an experimental, cutting-edge co-generation system capable of efficiently producing both electricity and heat with superior energy efficiency and minimal emissions. For this purpose, the following steps were completed: processing and summarizing available literature and patent sources, analysing scientific and technical papers on the selection and application of modelling types in co-generation systems, and considering principles and individual approaches to input data formation for mathematical modelling. This process enables the selection of a mechanism and the creation of simulation models for effective energy production at various enterprises. Findings. Assessment is performed of the energy efficiency of the co-generator system under various operating conditions, comparing it with existing conventional methods of electricity and heat generation. Results are presented of performance testing to determine the system’s capability to simultaneously generate electricity and heat efficiently, considering factors such as output stability, load responsiveness, and overall reliability. Identification and evaluation are performed of innovative technologies and methodologies integrated into the co-generator design, highlighting their effectiveness in enhancing energy efficiency and reducing emissions. Insights into any operational challenges encountered during the construction, testing, and optimization phases, along with proposed solutions or improvements to solve these problems. The analysis of the overall environmental impact of deploying the co-generator showed potential benefits in terms of reduced greenhouse gas emissions and local air quality improvement. Originality. Using a combination of scientific approaches encompassing physics and heat transfer engineering, in accordance with the first law of thermodynamics, such as the conservation laws of energy and entropy, and principles of heat exchange employed to transfer heat between different mediums, gas kinetics have yielded values for the energy transformation coefficient, indicating qualitative characteristics of fuel thermolysis and power generation as the final product. Practical value. The results provide for developing a comprehensive model of an advanced co-generation system capable of efficiently producing both electricity and heat with superior energy efficiency and minimal emissions. It also entails determining the types of models for mathematical modelling at all management levels and establishing a new method for input data formation for both technologies and their subsystems, incorporating additional technological implementations.

Entanglement production through a cosmological bounce

In quantum cosmology, it is expected that the Big Bang singularity is resolved and the universe undergoes a bounce. We find that for Gaussian initial states, matter-gravity entanglement entropy rises rapidly during the bounce, declines, and then approaches a steady-state value following the bounce. These observations suggest that matter-gravity entanglement is a feature of the macroscopic universe and that there is no Second Law of entanglement entropy.

Thermal and hydrodynamic effects in variable geometry nanofluid transport with Thermo-Responsive liquid Composites: Dynamics of entropy generation

In this communication, the authors focused on energy loss during the flow of hybrid nanofluid in expanding/contracting channels. The goal is to determine how, in real-world applications, hybrid nanofluids can maximize energy efficiency and reduce entropy production, hence assisting in the development of more effective and sustainable thermal management systems. It is well documented that heat transfer is enhanced due to the presence of nanoparticles in a base fluid and hence decreases energy loss in the system. The second law of thermodynamics defines that heat transfer is not ideal; hence, entropy in a system always rises. Suitable measures can be taken to minimize energy loss. One method is to use a nanofluid, if multiple nanosized particles are used; it is named a hybrid nanofluid. In this communication, a comparative analysis of simple and hybrid nanofluids is provided. A mathematical model outlining the dynamics of the flow is provided. The upper plate acts as a porous plate that is contracting/expanding and through which coolant hybrid nanofluids enter the channel. The lower plate remains stationary and is heated externally. The equations governing the flow are converted into ordinary differential equations by employing the similarity transformation. These ODEs are then solved analytically to get the series solution by using HAM along with the given boundary conditions. The entropy equation is modelled using the Clausius Duhem inequality. Copper and silver nanoparticles are combined with water. The impacts of different dimensionless parameters on stream function, velocity profile, Nusselt number, entropy, and Bejan number are discussed, and their results are shown graphically.

Entropy generation in radiative motion of tangent hyperbolic nanofluid in the presence of gyrotactic microorganisms and activation energy

In this work, entropy generation is optimized through the application of the second law of thermodynamics. The slip mechanisms, Brownian diffusions, and thermophoresis are elaborated using the tangent hyperbolic nanomaterial model. Magnetohydrodynamic (MHD) fluid is taken into consideration. To characterize the impact of activation energy, a unique model involving the binary chemical reaction is deployed. The effects of mixed convection that is nonlinear in nature, bioconvection, and Joule effect are all taken into consideration. The key partial differential equations (PDEs) are reduced into ordinary differential equations (ODEs) by utilizing appropriate similarity transformations and then solved numerically with the help of a built-in ‘bvp4c’ technique of MATLAB software. Varied flow parameters’ impacts on the nanoparticle volume concentration, entropy number, microorganism concentration, temperature, and velocity fields are analyzed using graphs. Various flow variables are taken into consideration to calculate the total rate of entropy generation. The obtained results show that concentration irreversibility, Joule effect irreversibility, viscous dissipation, and heat irreversibility all influence the entropy. The numerical outcomes were observed by fixing the physical parameters as 0.1<α<4.0, 0.1<M<1.2, 0.1<Nr<2.2, 0.1<Le<2.2, 0.1<Nb<0.4, 0.1<Nt<1.0, 2.0<⁡Pr⁡<5.0, and 0.1<Lb<2.0, as well as their impact on the momentum, thermal, concentration, and microorganism density profiles. From results, an increasing estimate of the variable representing chemical reaction indicates a decline in the concentration. The higher the chemical reaction variable, Hartmann number, and Weissenberg number, the higher the entropy number, while the Bejan number has a contrary behavior. Subsequently, all the outcomes are plotted in graphs and discussed in detail, when subjected to the involving physical quantities.

Rényi second laws for black holes

Hawking’s black hole area theorem provides a geometric realization of the second law of thermodynamics and constrains gravitational processes. In this work we explore a one-parameter extension of this constraint formulated in terms of the monotonicity properties of Rényi entropies. We focus on black hole mergers in asymptotically AdS space and determine new restrictions which these Rényi second laws impose on the final state. We evaluate the entropic inequalities starting from the thermodynamic ensembles description of black hole geometries, and find that for many situations they set more stringent bounds than those imposed by the area increase theorem.

Probing barrow entropy models with future event horizon as IR cutoff

We develop formulations for barrow holographic dark energy (BHDE) in both non-interacting and interacting scenarios within a cosmological framework, applying the conventional holographic principle. Model parameter constraints are determined through the Markov Chain Monte Carlo (MCMC) method, utilizing different datasets. The investigation excavates into the models' kinematic behavior, exploring the transition from deceleration to acceleration and tracking the evolution of the equation of state parameters. Further, these models can pretend the evolution of dark energy and matter in the Universe. Additionally, a thermodynamic analysis employing future event horizons is conducted, confirming the validation of the generalized second law of thermodynamics. The resultant of the BHDE models strongly suggests that the Universe is presently experiencing an accelerated phase attributed to dark energy.

On the principle of reciprocity in inelastic electron scattering.

In electron microscopy the principle of reciprocity is often used to imply time reversal symmetry. While this is true for elastic scattering, its applicability to inelastic scattering is less well established. From the second law of thermodynamics, the entropy for a thermally isolated system must be constant for any reversible process. Using entropy and statistical fluctuation arguments, it is shown that, while reversibility is possible at the microscopic level, it becomes statistically less likely for higher energy transfers. The implications for reciprocal imaging modes, including energy loss and energy gain measurements, as well as Kainuma's reciprocal wave model are also discussed.

Simulation-Based Design for Recycling of Car Electronic Modules as a Function of Disassembly Strategies

Modules (or parts) of a car are a complex functional material combination used to deliver a specified task for a car. Recovering all materials, energy, etc., into high-grade materials at their end of life (EoL) is impossible. This is dictated by the second law of thermodynamics (2LT) and thence economics. Thus, recyclability cannot be conducted with simplistic mass-based approaches void of thermodynamic considerations. We apply, in this paper, a process simulation model to estimate the true recyclability of various SEAT (Volkswagen Group) car parts within the EU H2020 TREASURE project. This simulation model is developed with 190 reactors and over 310 feed components with over 1000 reaction species in the 880 streams of the flowsheet. The uniqueness of the work in this paper is to apply the full material declaration (FMD) and bill of materials (BOM) of all 310 materials in the parts as a feed to the process simulation model to show the parts’ true recyclability. We classified all parts into categories, i.e., copper-rich, steel-rich and plastic-rich, to maximally recover metals at the desired material quality, as well as energy. Recyclability is understood to create high-grade products that can be applied with the same functional quality in these parts. In addition, disassembly strategies and related possible redesign show how much recyclability can be improved. Process simulation permits the creation of alloys, phases, materials, etc., at a desired quality. The strength of the simulation permits any feed from any End-of-Life part to be analyzed, as long as the FMD and BOM are available. This is analogous to any mineral and metallurgical engineering process simulation for which the full mineralogy must be available to analyze and/or design flowsheets. This paper delivers a wealth of data for various parts as well as the ultimate recovery of materials, elements, and energy. The results show clearly that there is no one single recycling rate for elements, materials, and alloys. It is in fact a function of the complexity and material combinations within the parts. The fact that we use a thermochemical-based process simulator with full compositional detail for the considered parts means full energy balances as well as exergy dissipation can be evaluated. This means that we can also evaluate which parts, due complex mixtures of plastics, are best processed for energy recovery or are best for material and metal recovery, with thermochemistry, reactor technology and integrated flowsheets being the basis.

Generalized Itô’s lemma and the stochastic thermodynamics of diffusion with resetting

Abstract Methods from the theory of stochastic processes are increasingly being used to extend classical thermodynamics to mesoscopic non-equilibrium systems. One characteristic feature of these systems is that averaging the stochastic entropy with respect to an ensemble of stochastic trajectories leads to a second law of thermodynamics that quantifies the degree of departure from thermodynamic equilibrium. A well known mechanism for maintaining a diffusing particle out of thermodynamic equilibrium is stochastic resetting. In its simplest form, the position of the particle instantaneously resets to a fixed position x 0 at a sequence of times generated from a Poisson process of constant rate r. Within the context of stochastic thermodynamics, instantaneous resetting to a single point is a unidirectional process that has no time-reversed equivalent. Hence, the average rate of entropy production calculated using the Gibbs–Shannon entropy cannot be related to the degree of time-reversal symmetry breaking. The problem of unidirectionality can be avoided by considering resetting to a random position or diffusion in an intermittent confining potential. In this paper we show how stochastic entropy production along sample paths of diffusion processes with resetting can be analyzed in terms of extensions of Itô’s formula for stochastic differential equations (SDEs) that include both continuous and discrete processes. First, we use the stochastic calculus of jump-diffusion processes to calculate the rate of stochastic entropy production for instantaneous resetting, and show how previous results are recovered upon averaging over sample trajectories. Second, we formulate single-particle diffusion in a switching potential as a hybrid SDE and develop a hybrid extension of Itô’s stochastic calculus to derive a general expression for the rate of stochastic entropy production. We illustrate the theory by considering overdamped Brownian motion in an intermittent harmonic potential. Finally, we calculate the average rate of entropy production for a population of non-interacting Brownian particles moving in a common switching potential. In particular, we show that the latter induces statistical correlations between the particles, which means that the total entropy is not given by the sum of the 1-particle entropies.

Study of cosmic evolution admitting thermodynamic analysis

This article examines the cosmic evolution in the framework of symmetric teleparallel theory, characterized by the function of non-metricity scalar (Q)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\mathcal {Q})$$\\end{document}. We use the e-folding number and reconstruction method with a suitable parametrization of the scale factor to obtain the functional form of symmetric teleparallel theory. Using this reconstructed model, we examine the behavior of different cosmographic parameters to demonstrate the bouncing scenarios of the cosmos by considering the contraction and expansion phases of cosmos before and after the bouncing point, respectively. It is found that the null energy condition is violated which shows that the singularity issue can be resolved in this extended theoretical framework. Moreover, we observe that the acceleration occurs near the bouncing point and the reconstructed model aligns with the current cosmic expansion. Finally, we check the validity of second law of thermodynamics in the bouncing framework of our model.

Computational Foundations for the Second Law of Thermodynamics

Computational Foundations for the Second Law of Thermodynamics

Rethinking Loss of Available Work and Gouy-Stodola Theorem

Abstract Exergy represents the maximum useful work possible when a system at a specific state reaches equilibrium with the environmental dead state at temperature To. Correspondingly, the exergy difference between two states is the maximum work output when the system changes from one state to the other, assuming that during the processes, the system exchanges heat reversibly with the environment. If the process involves irreversibility, the Guoy-Stodola theorem states that the exergy destruction equals the entropy generated during the process multiplied by To. The exergy concept and the Gouy-Stodola theorem are often used to optimize processes or systems, even when they are not directly connected to the environment. In the past, questions have been raised on if To is the proper temperature to use in calculating the exergy destruction. Here, we start from the first and the second laws of thermodynamics to unambiguously show that the useful energy loss (UEL) of a system or process should equal to the entropy generation multiplied by an equivalent temperature associated with the entropy rejected out of the entire system. For many engineering systems and processes, this entropy rejection temperature can be easily calculated as the ratio of the changes of the enthalpy and entropy of the fluid stream carrying the entropy out, which we call the state-change temperature. The UEL is unambiguous and independent of the environmental dead state, and it should be used for system optimization rather than the exergy destruction.