Journal articles: 'Numerical entropy production'

1

Puppo, Gabriella. "Numerical Entropy Production for Central Schemes." SIAM Journal on Scientific Computing 25, no. 4 (January 2004): 1382–415. http://dx.doi.org/10.1137/s1064827502386712.

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Mungkasi, Sudi, and Stephen Gwyn Roberts. "Numerical entropy production for shallow water flows." ANZIAM Journal 51 (April 9, 2011): 1. http://dx.doi.org/10.21914/anziamj.v52i0.3786.

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MUNGKASI, SUDI, and STEPHEN GWYN ROBERTS. "NUMERICAL ENTROPY PRODUCTION AS SMOOTHNESS INDICATOR FOR SHALLOW WATER EQUATIONS." ANZIAM Journal 61, no. 4 (October 2019): 398–415. http://dx.doi.org/10.1017/s1446181119000154.

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The numerical entropy production (NEP) for shallow water equations (SWE) is discussed and implemented as a smoothness indicator. We consider SWE in three different dimensions, namely, one-dimensional, one-and-a-half-dimensional, and two-dimensional SWE. An existing numerical entropy scheme is reviewed and an alternative scheme is provided. We prove the properties of these two numerical entropy schemes relating to the entropy steady state and consistency with the entropy equality on smooth regions. Simulation results show that both schemes produce NEP with the same behaviour for detecting discontinuities of solutions and perform similarly as smoothness indicators. An implementation of the NEP for an adaptive numerical method is also demonstrated.

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Mungkasi, Sudi, and Stephen Gwyn Roberts. "Numerical entropy production as smoothness indicator for shallow water equations." ANZIAM Journal 61 (May 6, 2020): 398–415. http://dx.doi.org/10.21914/anziamj.v61i0.14423.

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The numerical entropy production (NEP) for shallow water equations (SWE) is discussed and implemented as a smoothness indicator. We consider SWE in three different dimensions, namely, one-dimensional, one-and-a-half-dimensional, and two-dimensional SWE. An existing numerical entropy scheme is reviewed and an alternative scheme is provided. We prove the properties of these two numerical entropy schemes relating to the entropy steady state and consistency with the entropy equality on smooth regions. Simulation results show that both schemes produce NEP with the same behaviour for detecting discontinuities of solutions and perform similarly as smoothness indicators. An implementation of the NEP for an adaptive numerical method is also demonstrated. doi:10.1017/S1446181119000154

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Hou, Hucan, Yongxue Zhang, and Zhenlin Li. "A numerically research on energy loss evaluation in a centrifugal pump system based on local entropy production method." Thermal Science 21, no. 3 (2017): 1287–99. http://dx.doi.org/10.2298/tsci150702143h.

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Inspired by wide application of the second law of thermodynamics to flow and heat transfer devices, local entropy production analysis method was creatively introduced into energy assessment system of centrifugal water pump. Based on Reynolds stress turbulent model and energy equation model, the steady numerical simulation of the whole flow passage of one IS centrifugal pump was carried out. The local entropy production terms were calculated by user defined functions, mainly including wall entropy production, turbulent entropy production, and viscous entropy production. The numerical results indicated that the irreversible energy loss calculated by the local entropy production method agreed well with that calculated by the traditional method but with some deviations which were probably caused by high rotatability and high curvature of impeller and volute. The wall entropy production and turbulent entropy production took up large part of the whole entropy production about 48.61% and 47.91%, respectively, which indicated that wall friction and turbulent fluctuation were the major factors in affecting irreversible energy loss. Meanwhile, the entropy production rate distribution was discussed and compared with turbulent kinetic energy dissipation rate distribution, it showed that turbulent entropy production rate increased sharply at the near wall regions and both distributed more uniformly. The blade region in leading edge near suction side, trailing edge and volute tongue were the main regions to generate irreversible exergy loss. This research broadens a completely new view in evaluating energy loss and further optimizes pump using entropy production minimization.

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Golay, Frédéric. "Numerical entropy production and error indicator for compressible flows." Comptes Rendus Mécanique 337, no. 4 (April 2009): 233–37. http://dx.doi.org/10.1016/j.crme.2009.04.004.

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Mungkasi, Sudi. "An Accurate Smoothness Indicator for Shallow Water Flows along Channels with Varying Width." Applied Mechanics and Materials 771 (July 2015): 157–60. http://dx.doi.org/10.4028/www.scientific.net/amm.771.157.

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We extend the application of numerical entropy production, as a smoothness indicator, from conservation laws to balance laws. We aim to indicate the smoothness of solutions to the shallow water equations involving varying width, which are a system of balance laws. The numerical entropy production appears to be accurate to detect discontinuities. As a numerical test, a radial dam break is considered. We assume that there is a higher level of water inside a radial dam than water outside the dam wall. If the radial dam is totally broken, then water flows from inside to outside. The flow results in a solution having shock discontinuities. Finding the positions of the discontinuities is our interest. They are the positions where numerical solutions, such as those generated by a finite volume method, decrease their accuracy. Detecting the position of the discontinuity can help in the improvement of the numerical solution in terms of its accuracy. We obtain that the numerical entropy production is simple to implement but give an accurate detection. The discontinuity of the stage (free water surface) is clearly detected by large values of the numerical entropy production as the smoothness indicator.

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Brohi, Ali, Haochun Zhang, Kossi Min-Dianey, Muhammad Rafique, Muhammad Hassan, and Saadullah Farooqi. "Validation of accuracy and stability of numerical simulation for 2-D heat transfer system by an entropy production approach." Thermal Science 21, suppl. 1 (2017): 97–104. http://dx.doi.org/10.2298/tsci17s1097b.

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The entropy production in 2-D heat transfer system has been analyzed systematically by using the finite volume method, to develop new criteria for the numerical simulation in case of multidimensional systems, with the aid of the CFD codes. The steady-state heat conduction problem has been investigated for entropy production, and the entropy production profile has been calculated based upon the current approach. From results for 2-D heat conduction, it can be found that the stability of entropy production profile exhibits a better agreement with the exact solution accordingly, and the current approach is effective for measuring the accuracy and stability of numerical simulations for heat transfer problems.

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Masyagin, Victor Fedorovich, Ruslan Viktorovich Zhalnin, Marina Eugenievna Ladonkina, Olga Nikolaevna Terekhina, and Vladimir Fedorovich Tishkin. "Application of the entropic slope limiter for solving gas dynamics equations using the implicit scheme of the discontinuous Galerkin method." Keldysh Institute Preprints, no. 7 (2021): 1–18. http://dx.doi.org/10.20948/prepr-2021-7.

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The paper presents the entropic slope limiter for solving gas dynamics equations using the implicit scheme of the discontinuous Galerkin method. It guarantees monotonicity of the numerical solution, non-negativity of pressure and entropy production for each finite element. The numerical method has been successfully verified using some well-known model gas-dynamic problems.

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Adeyinka, O. B., and G. F. Naterer. "Modeling of Entropy Production in Turbulent Flows." Journal of Fluids Engineering 126, no. 6 (November 1, 2004): 893–99. http://dx.doi.org/10.1115/1.1845551.

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This article presents new modeling of turbulence correlations in the entropy transport equation for viscous, incompressible flows. An explicit entropy equation of state is developed for gases with the ideal gas law, while entropy transport equations are derived for both gases and liquids. The formulation specifically considers incompressible forced convection problems without a buoyancy term in the y-momentum equation, as density variations are neglected. Reynolds averaging techniques are applied to the turbulence closure of fluctuating temperature and entropy fields. The problem of rigorously expressing the mean entropy production in terms of other mean flow quantities is addressed. The validity of the newly developed formulation is assessed using direct numerical simulation data and empirical relations for the friction factor. Also, the dissipation (ε) of turbulent kinetic energy is formulated in terms of the Second Law. In contrast to the conventional ε equation modeling, this article proposes an alternative method by utilizing both transport and positive definite forms of the entropy production equation.

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Yang, Fan, Zhongbin Li, Yiping Cai, Dongjin Jiang, Fangping Tang, and Shengjie Sun. "Numerical Study for Flow Loss Characteristic of an Axial-Flow Pump as Turbine via Entropy Production Analysis." Processes 10, no. 9 (August 26, 2022): 1695. http://dx.doi.org/10.3390/pr10091695.

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Low-head vertical axial-flow pump as turbine (PAT) devices play a vital part in the development of clean energy for hydropower in plain areas. The traditional method of evaluating the flow loss in hydraulic machinery is calculated by the pressure drop method, the limitation of which is that the location of the occurrence of large losses cannot be accurately determined. In this paper, entropy production theory is introduced to evaluate the irreversible losses in the axial-flow PAT from the perspective of the second law of thermodynamics. A three-dimensional model of the axial-flow PAT is established and solved numerically using the Reynolds time-averaged equation, and the turbulence model is adopted as Shear Stress Transport–Curvature Correction (SST-CC) model. The validity of the entropy production theory to evaluate the energy loss distribution of the axial-flow PAT is illustrated by comparing the flow loss calculated by the pressure drop and the entropy production theory, respectively. The entropy production by turbulent dissipative dominates the total entropy production in the whole flow conduit, and the turbulent dissipative entropy accounts for the smallest percentage of the whole conduit entropy production at the optimal working condition Qbep, which is 51%. The impeller and the dustpan-shaped conduit are the essential sources of hydraulic loss in the entire flow conduit of the axial-flow PAT, and most of the energy loss of the impeller occurs at the blade leading edge, the trailing edge, and the flow separation zone near the suction surface. The energy loss of the dustpan-shaped conduit results from the high-speed flow from the impeller outlet to dustpan-shaped conduit to form a vortex, backflow and other chaotic flow patterns. Flow impact, flow separation, vortex and backflow are the main causes of high entropy production and energy loss.

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Kollet, S. J. "Optimality and inference in hydrology from entropy production considerations: synthetic hillslope numerical experiments." Hydrology and Earth System Sciences Discussions 12, no. 5 (May 29, 2015): 5123–49. http://dx.doi.org/10.5194/hessd-12-5123-2015.

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Abstract. In this study, entropy production optimization and inference principles are applied to a synthetic semi-arid hillslope in high-resolution, physics-based simulations. The results suggest that entropy or power is indeed maximized, because of the strong nonlinearity of variably saturated flow and competing processes related to soil moisture fluxes, the depletion of gradients, and the movement of a free water table. Thus, it appears that the maximum entropy production (MEP) principle may indeed be applicable to hydrologic systems. In the application to hydrologic system, the free water table constitutes an important degree of freedom in the optimization of entropy production and may also relate the theory to actual observations. In an ensuing analysis, an attempt is made to transfer the complex, "microscopic" hillslope model into a macroscopic model of reduced complexity using the MEP principle as an interference tool to obtain effective conductance coefficients and forces/gradients. The results demonstrate a new approach for the application of MEP to hydrologic systems and may form the basis for fruitful discussions and research in future.

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Adeyinka, O. B., and G. F. Naterer. "Particle Image Velocimetry Based Measurement of Entropy Production With Free Convection Heat Transfer." Journal of Heat Transfer 127, no. 6 (June 1, 2005): 614–23. http://dx.doi.org/10.1115/1.1863272.

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Local entropy production rates are determined from a numerical and experimental study of natural convection in an enclosure. Numerical predictions are obtained from a control-volume-based finite element formulation of the conservation equations and the Second Law. The experimental procedure combines methods of particle image velocimetry and planar laser induced fluorescence for measured velocity and temperature fields in the enclosure. An entropy based conversion algorithm in the measurement procedure is developed and compared with numerical predictions of free convection in the cavity. The predicted and measured results show close agreement. A measurement uncertainty analysis suggests that the algorithm postprocesses velocities (accurate within ±0.5%) to give entropy production data, which is accurate within ±8.77% near the wall. Results are reported for free convection of air and water in a square cavity at various Rayleigh numbers. The results provide measured data for tracking spatial variations of friction irreversibility and local exergy losses.

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Li, Bo, Wen-Na Wei, Qing-Cui Wan, Kang Peng, and Ling-Ling Chen. "Numerical Investigation into the Development Performance of Gas Hydrate by Depressurization Based on Heat Transfer and Entropy Generation Analyses." Entropy 22, no. 11 (October 26, 2020): 1212. http://dx.doi.org/10.3390/e22111212.

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The purpose of this study is to analyze the dynamic properties of gas hydrate development from a large hydrate simulator through numerical simulation. A mathematical model of heat transfer and entropy production of methane hydrate dissociation by depressurization has been established, and the change behaviors of various heat flows and entropy generations have been evaluated. Simulation results show that most of the heat supplied from outside is assimilated by methane hydrate. The energy loss caused by the fluid production is insignificant in comparison to the heat assimilation of the hydrate reservoir. The entropy generation of gas hydrate can be considered as the entropy flow from the ambient environment to the hydrate particles, and it is favorable from the perspective of efficient hydrate exploitation. On the contrary, the undesirable entropy generations of water, gas and quartz sand are induced by the irreversible heat conduction and thermal convection under notable temperature gradient in the deposit. Although lower production pressure will lead to larger entropy production of the whole system, the irreversible energy loss is always extremely limited when compared with the amount of thermal energy utilized by methane hydrate. The production pressure should be set as low as possible for the purpose of enhancing exploitation efficiency, as the entropy production rate is not sensitive to the energy recovery rate under depressurization.

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Qasim, Muhammad, Zafar Ali, Umer Farooq, and Dianchen Lu. "Investigation of Entropy in Two-Dimensional Peristaltic Flow with Temperature Dependent Viscosity, Thermal and Electrical Conductivity." Entropy 22, no. 2 (February 10, 2020): 200. http://dx.doi.org/10.3390/e22020200.

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This study comprehensively explores the generalized form of two-dimensional peristaltic motions of incompressible fluid through temperature-dependent physical properties in a non-symmetric channel. Generation of entropy in the system, carrying Joule heat and Lorentz force is also examined. Viscous dissipation is not ignored, for viewing in-depth, effects of heat transmission and entropy production. The modeling of equations is tracked first in fixed and then in wave frame. The resultant set of coupled non-linear equations are solved numerically by utilizing NDSolve in Mathematica. Comparison between NDSolve and the numerical results obtained through bvp4c MATLAB is made for the validation of our numerical codes. The attained results are found to be in excellent agreement. The impact of control parameters on the velocity profiles, pressure gradient, heat transfer, streamlines and entropy production are studied and discussed graphically. It is witnessed that entropy production and heat transfer are increased significantly subject to the enhancement of Hartman number, Brinkman number and electrical conductivity parameter. Hence, choosing appropriate values of physical parameters, performance and efficiency of flow structure and system can be improved. The results reported provide a virtuous insight into bio energy systems providing a useful standard for experimental and extra progressive computational multiphysics simulations.

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Fuchs, Marco, Nico Lubos, and Stephan Kabelac. "Numerical Calculation of the Irreversible Entropy Production of Additively Manufacturable Off-Set Strip Fin Heat-Transferring Structures." Entropy 25, no. 1 (January 13, 2023): 162. http://dx.doi.org/10.3390/e25010162.

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In this manuscript, off-set strip fin structures are presented which are adapted to the possibilities of additive manufacturing. For this purpose, the geometric parameters, including fin height, fin spacing, fin length, and fin longitudinal displacement, are varied, and the Colburn j-factor and the Fanning friction factor are numerically calculated in the Reynolds number range of 80–920. The structures are classified with respect to their entropy production number according to Bejan. This method is compared with the results from partial differential equations for the calculation of the irreversible entropy production rate due to shear stresses and heat conduction. This study reveals that the chosen temperature difference leads to deviation in terms of entropy production due to heat conduction, whereas the dissipation by shear stresses shows only small deviations of less than 2%. It is further shown that the variation in fin height and fin spacing has only a small influence on heat transfer and pressure drop, while a variation in fin length and fin longitudinal displacement shows a larger influence. With respect to the entropy production number, short and long fins, as well as large fin spacing and fin longitudinal displacement, are shown to be beneficial. A detailed examination of a single structure shows that the entropy production rate due to heat conduction is dominated by the entropy production rate in the wall, while the fluid has only a minor influence.

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Afridi, M. Idrees, Muhammad Qasim, and Oluwole Daniel Makinde. "Minimization of Entropy Production in Three Dimensional Dissipative Flow of Nanofluid with Graphene Nanoparticles: A Numerical Study." Defect and Diffusion Forum 387 (September 2018): 157–65. http://dx.doi.org/10.4028/www.scientific.net/ddf.387.157.

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In this study we examined the entropy generation in the three-dimensional flow of nanofluid with graphene nanoparticles. Viscous heating function is added in the energy equation to study fluid frictional effects on entropy generation. The modeled equations are converted into ordinary differential equations using appropriate dimensionless quantities. Shooting technique is implemented to acquire numerical solutions. The numerical solutions are also obtained by using Matlab built-in boundary value solver bvp4c for the validation of our numerical code. The obtained results reveal that they are in good correlation. The obtained numerical results are represented by various graphs and illustrated in great detail.

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Ye, Sikun, Xiaojun Li, Zuchao Zhu, Linmin Li, and Tong Lin. "Numerical Study of the Energy Flow Characteristics of Multi-Stage Pump as Turbines." Processes 10, no. 12 (November 23, 2022): 2488. http://dx.doi.org/10.3390/pr10122488.

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Multi-stage pump as turbine (PAT) has a wider range of heads and application intervals compared to single-stage PAT. In our research, we have conducted experimental and numerical simulation studies on this issue. In this paper, based on experimental research, numerical simulation is applied to calculate the multi-stage PAT flow field. The flow characteristics of multi-stage PAT under different working conditions are studied using the entropy production theory. Finally, the Pearson correlation coefficient is used to evaluate the relationship between the hydraulic loss and entropy production of the impellers and guide vanes. The entropy production theory is used to determine the location where the multi-stage PAT energy loss occurs compared with the traditional pressure drop assessment method. The results show that the trend of the numerical simulation results is consistent with the experimental results. The energy loss in the multi-stage PAT is calculated combined with the impeller and guide vane which accounts for 69.1–73% of the total energy loss under all flow conditions. The total entropy production rate of each component under design flow conditions is listed in decreasing order: impeller, guide vane, front and back chamber, a balance disk, and inlet and outlet volute. The first stage component has a larger energy loss compared with the rest of the stages. The magnitude of energy loss is closely related to physical quantities such as flow field velocity and skin friction coefficient. Furthermore, the distribution of streamlines and vortex cores at the impellers reflects that flow domain stability increases from the first stage impeller to the fifth stage impeller. The correlation between entropy production and hydraulic loss was evaluated by the Pearson correlation coefficient. Therefore, using the entropy production theory can effectively identify the characteristics of the flow field and the location of energy losses. It provides a reference for the targeted optimization of multi-stage PAT.

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Guan, Hongyu, Wei Jiang, Jianguo Yang, Yuchuan Wang, Xinghai Zhao, and Junxue Wang. "Energy loss analysis of the double-suction centrifugal pump under different flow rates based on entropy production theory." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 234, no. 20 (April 15, 2020): 4009–23. http://dx.doi.org/10.1177/0954406220919795.

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The investigation of energy loss of pump is of great significance for energy conservation and structural optimization design. And traditional methods have great limitations in researching the distribution of energy losses. In this paper, the entropy production theory is utilized to analyze the energy loss of the double-suction centrifugal pump. The numerical simulation results verified by experiments indicate that the difference in total entropy production under different flow rates is mainly affected by the entropy production in the main flow region. Moreover, the entropy production of the volute has the greatest impact on the entropy production in the main flow region, and even the proportion of entropy production in the volute at 1.2 QD operating point reaches 96%. Besides, the Q-criterion is applied to study the morphology of the vortex core in the volute. In the volute inlet region, it is found that the stable double-vortex flow has a better flow field and less energy loss than the scattered wake vortex.

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Ogban, P. U., and G. F. Naterer. "Apparent Entropy Production Difference for Error Characterization in Numerical Heat Transfer." Journal of Thermophysics and Heat Transfer 34, no. 3 (July 2020): 659–68. http://dx.doi.org/10.2514/1.t5894.

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Ali Anwar Brohi, Hao-Chun Zhang, and Shahid Karim. "Numerical Analysis of Entropy Production during Hydrogen-Air Burner Combustion Process." Thermal Engineering 67, no. 5 (April 28, 2020): 304–13. http://dx.doi.org/10.1134/s0040601520050031.

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Hou, Hucan, Yongxue Zhang, Zhenlin Li, Ting Jiang, Jinya Zhang, and Cong Xu. "Numerical analysis of entropy production on a LNG cryogenic submerged pump." Journal of Natural Gas Science and Engineering 36 (November 2016): 87–96. http://dx.doi.org/10.1016/j.jngse.2016.10.017.

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Gassmann, Almut, and Hans-Joachim Herzog. "How is local material entropy production represented in a numerical model?" Quarterly Journal of the Royal Meteorological Society 141, no. 688 (July 14, 2014): 854–69. http://dx.doi.org/10.1002/qj.2404.

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Nishiyama, Akihiro, and Jack A. Tuszynski. "Nonequilibrium quantum electrodynamics: Entropy production during equilibration." International Journal of Modern Physics B 32, no. 24 (September 13, 2018): 1850265. http://dx.doi.org/10.1142/s021797921850265x.

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We study nonequilibrium processes of Quantum Electrodynamics (QED) with relativistic charged Bose fields. The aim is to describe thermal equilibration, based on the Klein–Gordon equation for background coherent fields and the Kadanoff–Baym (KB) equation including the leading-order (LO) self-energy of the coupling expansion (the Hartree–Fock approximation). We introduce a gauge invariant relativistic kinetic entropy current at the first-order in the gradient expansion of the KB equation and we show the proof of the H-theorem in d + 1 dimensions (d = 1, 2, 3) in the presence of nonzero background coherent fields. Finally, we present numerical simulation in 1 + 1 dimensions and aim to investigate whether decoherence of the system occurs or not. We find that equilibrium states are realized with remaining background coherent charged Bose and photon fields by preparing distributions of incoherent charged particles asymmetrically in frequency mode as initial conditions in the KB equation even if LO self-energy is present.

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Stucki, Jörg W., and Robert Urbanczik. "Entropy Production of the Willamowski-Rössler Oscillator." Zeitschrift für Naturforschung A 60, no. 8-9 (September 1, 2005): 599–9. http://dx.doi.org/10.1515/zna-2005-8-907.

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Some properties of the Willamowski-Rössler model are studied by numerical simulations. From the original equations a minimal version of the model is derived which also exhibits the characteristic properties of the original model. This minimal model shows that it contains the Volterra-Lotka oscillator as a core component. It thus belongs to a class of generalized Volterra-Lotka systems. It has two steady states, a saddle point, responsible for chaos, and a fixed point, dictating its dynamic behaviour. The chaotic attractor is located close to the surface of the basin of attraction of the saddle node. The mean values of the variables are equal to the (unstable) steady state values during oscillations even under chaos, and the variables are always non-negative as in other generalized Volterra-Lotka systems. Surprisingly this was also the case with the original reversible Willamowski-Rössler model allowing to compare the entropy production during oscillations with the entropy production of the steady states. During oscillations the entropy production was always lower even under chaos. Since under these circumstances less energy is dissipated to produce the same output, the oscillating system is more efficient than the non-oscillatory one.

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Puppo, Gabriella, and Matteo Semplice. "Numerical Entropy and Adaptivity for Finite Volume Schemes." Communications in Computational Physics 10, no. 5 (November 2011): 1132–60. http://dx.doi.org/10.4208/cicp.250909.210111a.

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AbstractWe propose an a-posteriori error/smoothness indicator for standard semi-discrete finite volume schemes for systems of conservation laws, based on the numerical production of entropy. This idea extends previous work by the first author limited to central finite volume schemes on staggered grids. We prove that the indicator converges to zero with the same rate of the error of the underlying numerical scheme on smooth flows under grid refinement. We construct and test an adaptive scheme for systems of equations in which the mesh is driven by the entropy indicator. The adaptive scheme uses a single nonuniform grid with a variable timestep. We show how to implement a second order scheme on such a space-time non uniform grid, preserving accuracy and conservation properties. We also give an example of a p-adaptive strategy.

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Chaudhuri, Arnab, Maxim Yu Khlopov, and Shiladitya Porey. "Effects of 2HDM in Electroweak Phase Transition." Galaxies 9, no. 2 (June 20, 2021): 45. http://dx.doi.org/10.3390/galaxies9020045.

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The entropy production scenarios due to the electroweak phase transition (EWPT) in the framework of the minimal extension of standard model, namely the two Higgs doublet model (2HDM), are revisited. The possibility of first order phase transition is discussed. Intense parameter scanning was done with the help of BSMPT, a C++ package. We perform numerical calculations in order to calculate the entropy production with numerous benchmark points.

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Eegunjobi, Adetayo Samuel, and Oluwole Daniel Makinde. "Inherent Irreversibility in a Variable Viscosity Hartmann Flow through a Rotating Permeable Channel with Hall Effects." Defect and Diffusion Forum 377 (September 2017): 180–88. http://dx.doi.org/10.4028/www.scientific.net/ddf.377.180.

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We investigate entropy production rate in a temperature dependent viscosity Hartmann flow with Hall current through a rotating permeable channel. It is assumed that fluid suction occurs at the upper wall and injection at lower wall. The nonlinear governing differential equations are obtained, analyzed and solved numerically using shooting technique together with Runge-Kutta-Fehlberg integration method. Velocity and temperature profiles obtained from the numerical solutions are then used to compute the skin frictions, Nusselt number, the entropy generation rate and the Bejan number. The germane results are presented and discussed quantitatively.

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Main, Ian G., and Mark Naylor. "Entropy production and self-organized (sub)criticality in earthquake dynamics." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, no. 1910 (January 13, 2010): 131–44. http://dx.doi.org/10.1098/rsta.2009.0206.

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We derive an analytical expression for entropy production in earthquake populations based on Dewar’s formulation, including flux (tectonic forcing) and source (earthquake population) terms, and apply it to the Olami–Feder–Christensen numerical model for earthquake dynamics. Assuming the commonly observed power-law rheology between driving stress and remote strain rate, we test the hypothesis that maximum entropy production (MEP) is a thermodynamic driver for self-organized ‘criticality’ (SOC) in the model. MEP occurs when the global elastic strain is near-critical, with small relative fluctuations in macroscopic strain energy expressed by a low seismic efficiency, and broad-bandwidth power-law scaling of frequency and rupture area. These phenomena, all as observed in natural earthquake populations, are hallmarks of the broad conceptual definition of SOC (which has, to date, often included self-organizing systems in a near but strictly subcritical state). In the MEP state, the strain field retains some memory of past events, expressed as coherent ‘domains’, implying a degree of predictability, albeit strongly limited in practice by the proximity to criticality and our inability to map the natural stress field at an equivalent resolution to the numerical model.

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Naterer, G. F., and C. D. Tokarz. "Entropy Based Design of Fuel Cells." Journal of Fuel Cell Science and Technology 3, no. 2 (August 30, 2005): 165–74. http://dx.doi.org/10.1115/1.2174065.

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This article aims to develop an entropy based method of systematically improving efficiency of fuel cells. Entropy production of both electrochemical and thermofluid irreversibilities is formulated based on the Second Law. Ohmic, concentration, and activation irreversibilities occur within the electrodes, while thermal and friction irreversibilities occur within the fuel channel. These irreversibilities reduce the overall cell efficiency by generating voltage losses. Unlike past studies, this article considers fuel channel irreversibilities within the total entropy production, for both solid oxide fuel cells (SOFCs) and proton exchange membrane fuel cells (PEMFCs). Predicted results of entropy production are shown at varying operating temperatures, surface resistances, and channel configurations. Numerical predictions are compared successfully against past measured data of voltage profiles, thereby providing useful validation of the entropy based formulation. The Second Law stipulates the maximum theoretical capability of energy conversion within the fuel cell. Unlike past methods characterizing voltage losses through overpotential or polarization curves, the entropy based method provides a useful alternative and systematic procedure for reducing voltage losses.

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Altazin, Thomas, Mehmet Ersoy, Frédéric Golay, Damien Sous, and Lyudmyla Yushchenko. "Numerical investigation of BB-AMR scheme using entropy production as refinement criterion." International Journal of Computational Fluid Dynamics 30, no. 3 (March 15, 2016): 256–71. http://dx.doi.org/10.1080/10618562.2016.1194977.

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Muhammad, Khursheed, T. Hayat, A. Alsaedi, and B. Ahmad. "Numerical study of entropy production minimization in Bödewadt flow with carbon nanotubes." Physica A: Statistical Mechanics and its Applications 550 (July 2020): 123966. http://dx.doi.org/10.1016/j.physa.2019.123966.

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Tadmor, Eitan. "Entropy stability theory for difference approximations of nonlinear conservation laws and related time-dependent problems." Acta Numerica 12 (May 2003): 451–512. http://dx.doi.org/10.1017/s0962492902000156.

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We study the entropy stability of difference approximations to nonlinear hyperbolic conservation laws, and related time-dependent problems governed by additional dissipative and dispersive forcing terms. We employ a comparison principle as the main tool for entropy stability analysis, comparing the entropy production of a given scheme against properly chosen entropy-conservative schemes.To this end, we introduce general families of entropy-conservative schemes, interesting in their own right. The present treatment of such schemes extends our earlier recipe for construction of entropy-conservative schemes, introduced in Tadmor (1987b). The new families of entropy-conservative schemes offer two main advantages, namely, (i) their numerical fluxes admit an explicit, closed-form expression, and (ii) by a proper choice of their path of integration in phase space, we can distinguish between different families of waves within the same computational cell; in particular, entropy stability can be enforced on rarefactions while keeping the sharp resolution of shock discontinuities.A comparison with the numerical viscosities associated with entropy-conservative schemes provides a useful framework for the construction and analysis of entropy-stable schemes. We employ this framework for a detailed study of entropy stability for a host of first- and second-order accurate schemes. The comparison approach yields a precise characterization of the entropy stability of semi-discrete schemes for both scalar problems and systems of equations.We extend these results to fully discrete schemes. Here, spatial entropy dissipation is balanced by the entropy production due to time discretization with a suffciently small time-step, satisfying a suitable CFL condition. Finally, we revisit the question of entropy stability for fully discrete schemes using a different approach based on homotopy arguments. We prove entropy stability under optimal CFL conditions.

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Muhammad, N. M., N. A. C. Sidik, A. Saat, Y. Asako, W. M. A. A. Japar, G. H. Musa, and S. N. A. Yuof. "Effect of corrugated minichannel variable width on entropy generation for convective heat transfer of alpha-Alumina-water nanofluid." Journal of Physics: Conference Series 2053, no. 1 (October 1, 2021): 012016. http://dx.doi.org/10.1088/1742-6596/2053/1/012016.

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Abstract Energy management and sustainability in thermal systems require maximum utilization of resources with minimal losses. However, it is rarely unattainable due to the ever-increasing need for a high-performance system combined with device size reduction. The numerical study examined convective heat transfer of an alpha-Alumina-water nanofluid in variable-width corrugated minichannel heat sinks. The objective is to study the impact of nanoparticle volume fractions and flow area variation on the entropy generation rate. The determining variables are 0.005 – 0.02 volume fractions, the fluid velocity 3 – 5.5 m/s and heat flux of 85 W/cm2. The numerical results show an acceptable correlation with the experiment results. The results indicate the thermal entropy production drop with an increase in nanoparticles volume fraction. Contrastingly, the frictional resistance entropy suggests the opposite trend due to the turbulence effect on the fluid viscosity. The induction of Alumina-Water nanofluid with enhanced thermal conductivity declined the entropy generation rate compared to water alone. The increase in width ratio by 16% between the cases translates to at least a 9% increase in thermal entropy production. The outcome of this study can provide designers and operators of thermal systems more insight into entropy management in corrugated heatsinks.

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Cates, Michael E., Étienne Fodor, Tomer Markovich, Cesare Nardini, and Elsen Tjhung. "Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production." Entropy 24, no. 2 (February 9, 2022): 254. http://dx.doi.org/10.3390/e24020254.

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Many complex fluids can be described by continuum hydrodynamic field equations, to which noise must be added in order to capture thermal fluctuations. In almost all cases, the resulting coarse-grained stochastic partial differential equations carry a short-scale cutoff, which is also reflected in numerical discretisation schemes. We draw together our recent findings concerning the construction of such schemes and the interpretation of their continuum limits, focusing, for simplicity, on models with a purely diffusive scalar field, such as ‘Model B’ which describes phase separation in binary fluid mixtures. We address the requirement that the steady-state entropy production rate (EPR) must vanish for any stochastic hydrodynamic model in a thermal equilibrium. Only if this is achieved can the given discretisation scheme be relied upon to correctly calculate the nonvanishing EPR for ‘active field theories’ in which new terms are deliberately added to the fluctuating hydrodynamic equations that break detailed balance. To compute the correct probabilities of forward and time-reversed paths (whose ratio determines the EPR), we must make a careful treatment of so-called ‘spurious drift’ and other closely related terms that depend on the discretisation scheme. We show that such subtleties can arise not only in the temporal discretisation (as is well documented for stochastic ODEs with multiplicative noise) but also from spatial discretisation, even when noise is additive, as most active field theories assume. We then review how such noise can become multiplicative via off-diagonal couplings to additional fields that thermodynamically encode the underlying chemical processes responsible for activity. In this case, the spurious drift terms need careful accounting, not just to evaluate correctly the EPR but also to numerically implement the Langevin dynamics itself.

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Frizelle, G., and Y. Suhov. "The measurement of complexity in production and other commercial systems." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2098 (May 20, 2008): 2649–68. http://dx.doi.org/10.1098/rspa.2007.0275.

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The paper gives a review of three case studies of complexity of production systems in manufacturing and commercial industry and develops mathematical methods stemming from these studies. We use as measures of complexity various (long term) entropy rates that naturally emerge in the analysis of systems under consideration; in our case, the main focus is on (physical or virtual) queues and related phenomena. Consequently, a system is considered ‘more complex’ when its entropy rates are higher. The same principle is applied when different subsystems of a given system are compared with each other, identifying a ‘bottleneck’. The numerical values for entropy rates are determined in the course of observation and recording, subject to some simplifying assumptions. To enable us to make effective comparisons, we introduce various classifications of queue-related conditions in systems under investigation. We also discuss a number of practical issues that emerge here, including noise and data loss.

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Einav, Amit. "On Villani's conjecture concerning entropy production for the Kac Master equation." Kinetic & Related Models 4, no. 2 (2011): 479–97. http://dx.doi.org/10.3934/krm.2011.4.479.

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Spasojevic, Momcilo, Milovan Jankovic, and Damir Djakovic. "A new approach to entropy production minimization in diabatic distillation column with trays." Thermal Science 14, no. 2 (2010): 317–28. http://dx.doi.org/10.2298/tsci1002317s.

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Previous approach to direct numerical minimization of entropy production in diabatic distillation column in order to determine heat quantity to be exchanged at trays was based on temperatures on trays as control variables and it was applied only to simple binary columns. Also, previously developed theoretical models for determining optimal exchanged heat profile were determined only at such columns and while they were approximated they produced worse results than numerical minimum of entropy production. In this paper, as control variables for minimization, exchanged heat on the trays is used. It enables application to complex multicomponent diabatic columns. Ishii-Otto global method, based on model linearization and iterative solution by Newton-Raphson technique, is applied for solving column mathematical model. Needed thermodynamical properties for ideal systems are calculated using Lewis-Randall ideal solution model, and for non-ideal slightly polar systems they are calculated using Soave equation of state. Five direct methods are used for numerical optimization. Applied approach is successfully demonstrated at frequently used example of distillation of benzene and toluol mixture by using for these purposes specially written program. Simplex method appeared to be the most convenient optimization method for the considered problem.

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Rehman, Sohail, Hashim, Abdelaziz Nasr, Sayed M. Eldin, and Muhammad Y. Malik. "Entropy Minimization for Generalized Newtonian Fluid Flow between Converging and Diverging Channels." Micromachines 13, no. 10 (October 17, 2022): 1755. http://dx.doi.org/10.3390/mi13101755.

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The foremost focus of this article was to investigate the entropy generation in hydromagnetic flow of generalized Newtonian Carreau nanofluid through a converging and diverging channel. In addition, a heat transport analysis was performed for Carreau nanofluid using the Buongiorno model in the presence of viscous dissipation and Joule heating. The second law of thermodynamics was employed to model the governing flow transport along with entropy generation arising within the system. Entropy optimization analysis is accentuated as its minimization is the best measure to enhance the efficiency of thermal systems. This irreversibility computation and optimization were carried out in the dimensional form to obtain a better picture of the system’s entropy generation. With the help of proper dimensionless transformations, the modeled flow equations were converted into a system of non-linear ordinary differential equations. The numerical solutions were derived using an efficient numerical method, the Runge–Kutta Fehlberg method in conjunction with the shooting technique. The computed results were presented graphically through different profiles of velocity, temperature, concentration, entropy production, and Bejan number. From the acquired results, we perceive that entropy generation is augmented with higher Brinkman and Reynolds numbers. It is significant to mention that the system’s entropy production grew near its two walls, where the irreversibility of heat transfer predominates, in contrast to the channel’s center, where the irreversibility of frictional force predominates. These results serve as a valuable guide for designing and optimizing channels with diverging–converging profiles required in several heat-transfer applications.

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Waqas, Hassan, Faisal Fareed Bukhari, Taseer Muhammad, and Umar Farooq. "Thermal transport of hybrid nanofluids with entropy generation: A numerical simulation." International Journal of Modern Physics B 35, no. 21 (August 11, 2021): 2150218. http://dx.doi.org/10.1142/s0217979221502180.

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In this research, thermal radiation, entropy generation and variable thermal conductivity effects on hybrid nanofluids by moving sheet are analyzed. The liquid is placed by stretchable flat wall that is flowing in a nonlinear pattern. Thermal conductivity changes with temperature governed by thermal radiation and MHD is incorporated. Approximations of boundary layer correspond to a set of PDEs which are then changed into ODEs by considering suitable variables. The resulting ODEs are solved using the bvp4c method. The implication with considerable physical characteristics on temperature, entropy generation and velocity profile is graphically represented and numerically discussed. Entropy generation increases for increasing Reynolds number, velocity slip parameter, Brinkman number and magnetic parameter. Scientists have recently established a rising interest in the importance of nanoparticles due to their numerous technical, industrial and commercial uses. The provided insights can be used in extrusion application areas, macromolecules, biomimetic systems, energy production and industrial process improvements.

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ZHANG, Lixi, Gaopan CAO, and Zhengyang ZHANG. "Numerical simulation on heat transfer and entropy generation of impingement cooling on boss shaped surface." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 40, no. 2 (April 2022): 296–305. http://dx.doi.org/10.1051/jnwpu/20224020296.

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Using impingement jet to cool the external cavity of the end wall of the gas turbine guide blade is very effective for prolonging the service life of the gas turbine and ensuring its safety operation. In this paper, the numerical simulation method is used to study the impingement cooling heat transfer performance of the boss shaped surface in the external cavity of the end wall of the gas turbine guide blade, and the entropy generation of the impingement heat transfer process is analyzed. The results show that the average Nusselt number on the impingement target surface and the impingement hole surface increase with the increase of the Reynolds number of the impingement jet. When the Reynolds number is constant, the average Nusselt number of impingement target surface and impingement hole surface decrease with the increase of impingement target distance, but the cooling range on the impingement target surface increases and the heat transfer is more uniform. With the increase of the width of the boss shaped upper surface, the cooling range on the impingement target surface relatively decreases, and the average Nusselt numbers of the impingement target surface decreases and that of the impingement hole surface increases respectively. The heat transfer of the upper surface of the boss is better than that of the lower surface on both sides. The entropy generation in the process of impingement cooling mainly comes from the entropy production caused by viscous dissipation and the entropy flow caused by heat transfer. The entropy production in the flow vortex region is the main reason for the entropy generation. The research conclusions can provide basis and reference for optimizing the structural and operating parameters of boss shaped impingement cavity and improving its impingement heat transfer effect.

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Afanasyev, A. A., and O. E. Melnik. "Non-negative entropy production criteria for numerical simulations of flows in porous media." Computational Continuum Mechanics 6, no. 3 (2013): 328–35. http://dx.doi.org/10.7242/1999-6691/2013.6.3.37.

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Yu, An, Yifu Wang, Fei Song, Zongliang Li, and Qinghong Tang. "Numerical study of the entropy production characteristics in cryogenic liquid nitrogen cavitating flow." International Communications in Heat and Mass Transfer 133 (April 2022): 105963. http://dx.doi.org/10.1016/j.icheatmasstransfer.2022.105963.

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Zhao, Weidong, K. Julietraja, P. Venugopal, and Xiujun Zhang. "VDB Entropy Measures and Irregularity-Based Indices for the Rectangular Kekulene System." Journal of Mathematics 2021 (December 14, 2021): 1–15. http://dx.doi.org/10.1155/2021/7404529.

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Theoretical chemists are fascinated by polycyclic aromatic hydrocarbons (PAHs) because of their unique electromagnetic and other significant properties, such as superaromaticity. The study of PAHs has been steadily increasing because of their wide-ranging applications in several fields, like steel manufacturing, shale oil extraction, coal gasification, production of coke, tar distillation, and nanosciences. Topological indices (TIs) are numerical quantities that give a mathematical expression for the chemical structures. They are useful and cost-effective tools for predicting the properties of chemical compounds theoretically. Entropic network measures are a type of TIs with a broad array of applications, involving quantitative characterization of molecular structures and the investigation of some specific chemical properties of molecular graphs. Irregularity indices are numerical parameters that quantify the irregularity of a molecular graph and are used to predict some of the chemical properties, including boiling points, resistance, enthalpy of vaporization, entropy, melting points, and toxicity. This study aims to determine analytical expressions for the VDB entropy and irregularity-based indices in the rectangular Kekulene system.

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Spasojevic, Momcilo, Milovan Jankovic, and Damir Djakovic. "Entropy production minimization in a multicomponent diabatic distillation column." Thermal Science 24, no. 3 Part B (2020): 2256–66. http://dx.doi.org/10.2298/tsci181206284s.

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This work presents a procedure for direct numerical minimization of entropy production in a diabatic tray column with heat exchanged on the trays as control variables, as opposed to previously used procedures with temperature on the trays as control variables. The procedure, which had previously been demonstrated on a binary mixture, was in this work applied to a multicomponent mixture, with minor modifications. The procedure comprised the complex optimization method and the Ishii-Otto method for solving the equations of a column model based on the iterative Newton-Raphson technique with partial linearization of the equations. The desired separation of the components was realized by the addition of a penalty function to the goal function, i.e. entropy production in the column. The required thermodynamic characteristics were calculated by the Soave equation of state. As an illustration, an industrial debutanizer with five components was used whose data, obtained by simulation, were compared with the optimization results of a diabatic column with the same desired separation and number of trays. After the diabatic column optimization procedure, the value of 91.91 J/Ks was obtained as the best result for entropy production. According to the best solution, entropy production in the diabatic column was 23.2% lower than in the adiabatic column. The heat to be removed from the column increased by 24.7%, while the heat to be added to the column increased by 28.8%.

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Sivaraj, Chinnasamy, Vladimir E. Gubin, Aleksander S. Matveev, and Mikhail A. Sheremet. "Impacts of Uniform Magnetic Field and Internal Heated Vertical Plate on Ferrofluid Free Convection and Entropy Generation in a Square Chamber." Entropy 23, no. 6 (June 3, 2021): 709. http://dx.doi.org/10.3390/e23060709.

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The heat transfer enhancement and fluid flow control in engineering systems can be achieved by addition of ferric oxide nanoparticles of small concentration under magnetic impact. To increase the technical system life cycle, the entropy generation minimization technique can be employed. The present research deals with numerical simulation of magnetohydrodynamic thermal convection and entropy production in a ferrofluid chamber under the impact of an internal vertical hot sheet. The formulated governing equations have been worked out by the in-house program based on the finite volume technique. Influence of the Hartmann number, Lorentz force tilted angle, nanoadditives concentration, dimensionless temperature difference, and non-uniform heating parameter on circulation structures, temperature patterns, and entropy production has been scrutinized. It has been revealed that a transition from the isothermal plate to the non-uniformly warmed sheet illustrates a rise of the average entropy generation rate, while the average Nusselt number can be decreased weakly. A diminution of the mean entropy production strength can be achieved by an optimal selection of the Lorentz force tilted angle.

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Sadiki, Amsini, Senda Agrebi, and Florian Ries. "Entropy Generation Analysis in Turbulent Reacting Flows and Near Wall: A Review." Entropy 24, no. 8 (August 10, 2022): 1099. http://dx.doi.org/10.3390/e24081099.

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This paper provides a review of different contributions dedicated thus far to entropy generation analysis (EGA) in turbulent combustion systems. We account for various parametric studies that include wall boundedness, flow operating conditions, combustion regimes, fuels/alternative fuels and application geometries. Special attention is paid to experimental and numerical modeling works along with selected applications. First, the difficulties of performing comprehensive experiments that may support the understanding of entropy generation phenomena are outlined. Together with practical applications, the lumped approach to calculate the total entropy generation rate is presented. Apart from direct numerical simulation, numerical modeling approaches are described within the continuum formulation in the framework of non-equilibrium thermodynamics. Considering the entropy transport equations in both Reynolds-averaged Navier–Stokes and large eddy simulation modeling, different modeling degrees of the entropy production terms are presented and discussed. Finally, exemplary investigations and validation cases going from generic or/and canonical configurations to practical configurations, such as internal combustion engines, gas turbines and power plants, are reported. Thereby, the areas for future research in the development of EGA for enabling efficient combustion systems are highlighted. Since EGA is known as a promising tool for optimization of combustion systems, this aspect is highlighted in this work.

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Rehman, Rabia, Hafiz Abdul Wahab, Nawa Alshammari, Umar Khan, and Ilyas Khan. "Aggregation Effects on Entropy Generation Analysis for Nanofluid Flow over a Wedge with Thermal Radiation: A Numerical Investigation." Journal of Nanomaterials 2022 (September 24, 2022): 1–10. http://dx.doi.org/10.1155/2022/3992590.

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The current study investigated the formation of entropy in a nanofluid flow in a wedge with thermal radiation and convective boundary conditions. Nanoparticle aggregation is also taken into consideration. The rate of heat transmission of a water-based aggregated fluid over a wedge has been investigated due to the effects of thermal radiation. A set of nonlinear differential equations governs the flow process, and these are numerically solved using a helpful approach called the Runge-Kutta-Fehlberg scheme. This method starts by breaking down the equations into a collection of first-order equations. The RK method then solves those equations. The effects on flow and heat transmission are studied using graphical analysis. Entropy generation and Bejan number changes are also graphically displayed, and the results are discussed in detail. These equations’ answers were also incorporated into a dimensionless entropy generating equation. According to the findings, raising the radiation parameter and decreasing boundary convection minimize entropy generation, while nanoparticles boost entropy production.

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Tahir, Madeeha, Ayesha Naz, Muhammad Imran, Hasan Waqas, Ali Akgül, Hussein Shanak, Rabab Jarrar, and Jihad Asad. "Activation energy impact on unsteady Bio-convection nanomaterial flow over porous surface." AIMS Mathematics 7, no. 11 (2022): 19822–45. http://dx.doi.org/10.3934/math.20221086.

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<abstract> <p>Nanofluid is an advanced technology to enhance heat transportation. Additionally, the thermal conductivity of nanofluids is high therefore, they are more useful for heat transportation. Evaluation of entropy generation has been a helpful technique for tackling improvements in thermal features because it provides information that cannot be obtained via energy analysis. For thermodynamic irreversibilities, a good approximation is the rate of entropy generation. As a result of a reduction of entropy production, energy transport infrastructure has become more efficient. This study aims to analyse the bioconvective flow of nanofluid flow through a stretching sheet in the occurence of gyrotactic motile microorganisms. A magnetised nanomaterial model with thermophoretic and Brownian diffusion properties is analysed. The impacts of activation energy, temperature dependent and exponential base heat source are investigated in this analysis. The entropy generation of the system is also observed for nanofluid flow. The mathematical model is developed as partial differential equations. The governing equations are reduced to a dimensionless system of ordinary differential equations by applying similarity transformations. The ODEs are tacked numerically with the aid of shooting scheme in commercial software MATLAB. For graphical and numerical results of flow controlling parameters versus subjective fields, the commercial software MATLAB tool bvp4 is used with the shooting scheme. The novelty of this analysis computes numerical computation of bioconvective nanofluid flow with temperature-dependent and exponential base heat source investigated. Furthermore, the consequence of thermal radiation and entropy of the system is considered. The porous medium with activation energy is also taken into consideration. The results show that the velocity field is reduced with increased bioconvection Rayleigh number. The thermal field is increased via an exponential space-based heat source. The concentration is reduced via Lewis number. the microorganisms profile declines for larger bioconvection Lewis number. The Brinkman number Br, magnetic and permeability characteristics all showed a rising trend when plotted against the entropy production rate.</p> </abstract>

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Wang, Y., W. Xu, H. Yin, Y. Zhang, and H. S. Dou. "Numerical study on the influence of pre-swirl angle on internal flow characteristics of centrifugal pumps." AIP Advances 12, no. 4 (April 1, 2022): 045019. http://dx.doi.org/10.1063/5.0085903.

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The effect of inlet pre-swirl on the performance of a centrifugal pump is studied by numerical simulation. The governing equations are Navier–Stokes equations and the shear stress transport k–ω turbulence model. The numerical results show that the optimal operating point moves from the low flow region to the high flow region as the pre-swirl angle shifts from positive to negative. It is found by contours of Omega–Liutex that the positive pre-swirl angle is able to weaken the vortex on the blade suction and reduce the energy dissipation. On both the 0.5Q0 and 1.2Q0 operating conditions, the proportion of entropy production loss in the impeller and volute is about 60% and 30%, respectively. As the pre-swirl angle changes from negative to positive, the entropy production loss in the inlet and outlet pipes increases slowly, and the entropy production loss in the volute and impeller shows a decreasing trend and the peak area of entropy loss moves toward the outlet. Under the four pre-swirl angles, the main frequency is always the passing frequency of the blade. The pre-swirl angle affects the pressure fluctuation at the main frequency but has little effect at the secondary frequency. The change in velocity pulsation amplitude in the impeller in the positive pre-swirl angle is smaller than that in the negative pre-swirl angle. As a result, for the positive pre-swirl angle, the turbulent kinetic energy density in the impeller is low, and the energy loss is low, compared with negative pre-swirl. Under the low flow condition (0.5Q0), the change in velocity pulsation amplitude in the inertial range of the energy spectrum under negative pre-swirl is greater than that under positive pre-swirl.

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Journal articles on the topic 'Numerical entropy production'

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