Total Entropy Research Articles

Numerical Investigation of Hybrid Nanofluid Natural Convection and Entropy Generation in a Corrugated Enclosure with an Inner Conducting Block

Current work deals with a numerical analysis of convective heat transfer and entropy generation inside a rectangular cavity with a corrugated bottom filled with MoS2–SiO2-water hybrid nanofluid. Here, a conducting solid body is attached to the top wall, and discrete heaters are attached to the bottom wall of the cavity. The numerical solutions of the governing equations are derived utilizing a higher-order compact (HOC) finite difference scheme and validated with the existing computational and experimental results. Present numerical results are then studied in detail, emphasizing isotherms, streamlines, and local entropy generation with respect to specific parameters like Rayleigh number (103 ≤ Ra ≤ 106), the volume percentage of nanoparticles (0% ≤ Φ ≤ 4%), the thermal conductivity of solid body (1.95 ≤ ks ≤ 16.00) as well as the aspect ratio of heater length (AR = 0.2, 0.4, 0.6, 0.8). The impacts of key factors on the Bejan number, average Nusselt number, and overall entropy generation are also investigated. The results show that an increase in the thermal conductivity of the solid body from 1.95 to 16.00 increases the average Nusselt number and total entropy generation by 9.17% and 40.07%, respectively, for AR = 0.2, Ra = 106, and Φ = 4%. In addition, the average Nusselt number and total entropy generation decrease by 59.11% and 61.99%, respectively, for ks = 16.00, Ra = 106, and Φ = 4% when the aspect ratio of heater length increases to 0.8.

Performance evaluation criteria based on the first and second laws of thermodynamics

Numerical simulations were conducted to investigate the correlation between assessments based on the total entropy generation rate criterion and the thermal resistance criterion in the context of evaluating heat transfer performance. This study focused on a parallel plate channel heat sink with the lower wall subjected to a constant heat flux, under various flow constraints. The flow was assumed to be laminar and fully developed. The energy equation was discretized using the control volume-based power law scheme, and the resulting algebraic equations were solved by the line-by-line method. Optimal channel heights which lead to minimize irreversibility and temperature difference between heated wall and inlet fluid temperatures were determined by both the total entropy generation rate and thermal resistance criteria under four distinct flow constraints: identical mass flow rate, identical inlet velocity, identical pumping power, and identical pressure drop. The investigation revealed a lack of significant correlation between the optimal channel heights derived from assessments based on the total entropy generation rate and thermal resistance. Consequently, the utilization of the total entropy generation rate criterion for evaluating heat transfer performance, based in the second law of thermodynamics, instead of the thermal resistance criterion, based in the first law of thermodynamics, was deemed inappropriate. The total entropy generation rate criterion was based on the minimization of the irreversibility and served as an indicator of heat transfer quality. As a recommendation, it is suggested that results obtained from both the total entropy generation rate and thermal resistance criteria for assessing heat transfer performance be presented separately for each specific application.

Irreversibility analysis for the EMHD flow of silver and magnesium oxide hybrid nanofluid due to nonlinear thermal radiation

Hybrid nanofluids were expressed by heat-transfer fluids into greater surface dispersion capabilities, stability and diffusion related for traditional nanofluids. The effort on the flow of volumetric entropy generation and convective heat transport of MHD hybrid nanofluid is considered. Hybrid nanofluid involves the field over the orderly stretchable surface for variable heat flux with the resistance of electric field. Effect on convective heating and nonlinear thermal radiation is again contained in the interpreted figure. Mathematical equations such as momentum, energy, conservation of mass and entropy were collected as conversion to governing partial differential equations by ordinary differential equations, utilizing similarity variables. An efficient finite element method (FEM) is used. Numerical calculations were accomplished for silver–magnesium oxide water (Ag-MgO/H2O) hybrid nanofluid and conventional silver water (Ag-H2O) nanofluid. The graphs were created by the temperature, velocity, and entropy profiles. to analyse the impact on governing parameters. These skin friction and heat transfer rates are analysed through regression analysis. The important allegation expressed by the hybrid Nanofluid has the best heat transfer rate, which is related to convectional nanofluid. Further, It raised the Brinkman number and Reynolds number and developed a total entropy of the structure.

De Sitter Local Thermodynamics in f(R) Gravity

We consider the local thermodynamics of the de Sitter state in the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(\\mathcal{R})$$\\end{document} gravity. The local temperature, which is the same for all points of the de Sitter space, is \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T = H{\ ext{/}}\\pi $$\\end{document}, where H is the Hubble parameter. It is twice larger than the Gibbons–Hawking temperature of the cosmological horizon, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{T}_{{{\ ext{GH}}}}} = H{\ ext{/}}2\\pi $$\\end{document}. The local temperature is not related to the cosmological horizon. It determines the rate of the activation processes, which are possible in the de Sitter environment. The typical example is the process of the ionization of the atom in the de Sitter environment, which rate is determined by temperature \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T = H{\ ext{/}}\\pi $$\\end{document}. The local temperature determines the local entropy of the de Sitter vacuum state, and this allows to calculate the total entropy inside the cosmological horizon. The result reproduces the Gibbons–Hawking area law, which corresponds to the Wald entropy, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{S}_{{{\ ext{hor}}}}} = 4\\pi KA$$\\end{document}. Here, K is the effective gravitational coupling, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K = df{\ ext{/}}d\\mathcal{R}$$\\end{document}. In the local thermodynamic approach, K is the thermodynamic variable, which is conjugate to the Ricci scalar curvature \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{R}$$\\end{document}. The holographic connection between the bulk entropy of the Hubble volume and the surface entropy of the cosmological horizon supports the suggestion that the de Sitter quantum vacuum is characterized by the local thermodynamics with the local temperature \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T = H{\ ext{/}}\\pi $$\\end{document}. The local temperature \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T = H{\ ext{/}}\\pi $$\\end{document} of the de Sitter vacuum suggests that the de Sitter vacuum is locally unstable towards the creation of matter and its further heating. The decay of the de Sitter vacuum due to such processes determines the quantum breaking time of the space-times with positive cosmological constant.

Investigation of the performance of a parabolic trough collector outfitted with annular absorber tubes

The current work recommends a novel absorber tube for parabolic trough solar collectors. Annular absorber tubes with and without spiral tape have been investigated as an alternative to conventional absorber tubes. This work employs numerical analysis through the usage of CFD code. The pitch ratio (P/D), width ratio (W/D), and height ratio (H/D) of the spiral tape are each different. Within the annular absorber tube, these ratios have an impact on the performance of heat transfers, pressure drop, and entropy generation. The results reveal that an annular absorber tube without spiral tape has a higher Nu ratio than a conventional absorber tube. In an annular absorber tube with P/D = 1.4, the Nusselt number increases. In an annular absorber tube, the spiral tape thickness ratio has no effect. The average Nu ratio is 24.5% greater at a height ratio of 0.3 than it would be in an annular absorber tube without spiral tape. The annular absorber tube's spiral tape's pitch ratio, thickness ratio, and height ratio all generate less total entropy than a conventional absorber tube does. The wall temperature of the absorber tube with the lowest spiral tape pitch ratio decreases, which results in a reduction in the thermal stress on the absorber wall. On the other hand, spiral tape and an annular absorber tube have a higher friction ratio. It exceeds the friction ratio of the annular absorber tube without spiral tape by 41.7 times.

Heat transfer assessment incorporated with entropy generation within a curved corner structure enclosing a cold domain

AbstractIn cold climates or winter countries, maintaining optimal room temperatures is essential for comfort and energy efficiency. Conventional square or rectangle‐shaped rooms often face challenges in achieving efficient heat transfer (HT) and uniform temperature distribution. To address these limitations, this study has been explored using curved corner cavities, varying their aspect ratio (AR = 1.0 and 0.5), and incorporating a circular shape cooler to enhance HT within the room. The curved corners promote better airflow circulation, creating a more efficient HT environment. The dimensionless governing equations and corresponding boundary conditions are solved numerically using the finite element method. This research aims to assess the optimized HT and entropy production within a curved corner cavity, varying their AR and enclosing a circular shape cooler to determine the most effective configuration for maximizing HT and energy efficiency in winter conditions. This study reveals that in the case without a cooler (WOC), the average Nusselt number () is higher in the curved rectangle cavity compared with the curved square cavity for all values. Using the curved square (AR = 1.0), increases by 191.86%, while with the curved rectangle (AR = 0.5), increases by 302.63% at . Additionally, in the case with a cooler (WC), is higher than the case WOC and , and an average total entropy increases for both the WOC and WC cases for all values. Transitioning from a square to a curved rectangle (AR = 0.5) WC, increases by 329.34% at . Furthermore, in the WOC case, the curved square cavity and, in the WC case, the curved rectangle show better energy efficiency and reduce environmental impact.

Large eddy simulation of the cavity shedding characteristics of ventilated cavitation around the underwater vehicle

Ventilated cavitation is utilized for reducing drag and improving the headway of underwater vehicles. The ventilated cavitating flow around the axisymmetric body is simulated using the Large Eddy Simulation (LES) method in this study. Three cavity morphologies with different ventilation rates (Cq) are observed: Foamy Cavity (FC), Continuous Transparent and Foamy Cavity (CTFC) and Super Cavity (SC). The cavity shedding characteristic of the three different cavity morphologies is revealed. For partial cavity, the periodic cavity shedding is dominated by the local high pressure, re-entrant jet and vortex. The distributions of the turbulent kinetic energy and the pulsation enstrophy exhibit different migration mechanisms during the cavity shedding. The energy characteristic is reflected by three terms of the entropy generation. And the entropy production rate by direct dissipation occupies a dominant position, accounting for about 80% of the total entropy production, while the entropy production rate by viscous dissipation only accounts for 4%. For super cavity, gas leakage is dominated by a re-entrant jet induced by the intense adverse pressure gradient. And the results also demonstrated the velocity and vorticity pulsations around the test body wrapped in a super cavity are not intense.

Evaluating hydraulic dissipation in a reversible mixed-flow pump for micro-pumped hydro storage based on entropy production theory

The promotion of renewables improves energy security but degrades the electricity quality and grid stability. This paradox can be resolved by enlarging the capacity of pumped hydro storage. Although high-head hydropower resources have been exhausted, untapped low-head resources are ideal alternatives and are utilized for micro-pumped hydro storage. Instead of the miniaturized pump-turbine or pump as turbine, we apply a low-head reversible mixed-flow pump (RMFP), which can efficiently fulfil both storage and generation requirements in microgrids without complicated guide vanes. To enhance the efficiency of the RMFP in two reverse directions simultaneously, high-hydraulic dissipation zones associated with deformed flows and unreasonable structural parameters must be investigated. This study introduces entropy production theory into computational fluid dynamics numerical simulation to evaluate hydraulic dissipation under the rated discharge in both pump and turbine modes of the RMFP. Refined mesh and validation from the energy characteristics experiment demonstrate the accuracy of the numerical scheme. The head loss assessed by the entropy Production method is compared with the predictions of the pressure drop method, and its precision exceeds 7%. In pump mode, entropy production in the volute constitutes the largest proportion (43%), followed by that in the runner (35%). However, in turbine mode, the largest proportion of the total entropy is generated in the runner (45%), followed by that in the draft tube (33%). The dissipation in the runner is bound up with the secondary flows over the blades. Backflow occurs on the suction surface near the leading edge; however, across different spans, flow separation occurs on the suction surface near the trailing edge. The requests for blade modification are opposite in pump and turbine modes. Significantly, hydraulic dissipation of the draft tube concentrates within its 0.5D2 segment upstream. The dissipation there is bound up with the transport of two types of vortex ropes. The originality lies in evaluating hydraulic dissipation and explaining the high-dissipation zone with the specific unsteady secondary flows in pump and turbine modes of an RMFP.

Thermodynamics and stochastic thermodynamics of strongly coupled systems.

We further develop the strong-coupling theory of thermodynamics and stochastic thermodynamics for continuous systems, constructed in the previous work [Phys. Rev. Res. 4, 013015 (2022)2643-156410.1103/PhysRevResearch.4.013015]. A small system strongly interacting with a its environment, the dynamics of the system is assumed to be much slower than that of the bath. The system Hamiltonian is defined to be the Hamiltonian of mean force, whereas the system entropy is defined as the Gibbs-Shannon entropy. Equilibrium ensemble theories and thermodynamic theories are established for the system. Variations of three types of parameters are considered: (i) the system parameter λ which couples to the system and to the interaction, (ii) the bath parameter λ^{'} which couples to the bath only, and (iii) the temperature T=1/β. The work done to the system consists of three parts, proportional to dλ,dλ^{'}, and dβ respectively. The part proportional to dβ can be understood as the work done by the bath. As long as λ^{'} and β are not fixed, the work is not the change of total energy of the joint system. The differences between our strong-coupling equilibrium thermodynamics and the classical thermodynamics are discussed. The thermodynamic theory is promoted to the nonequilibrium level. Both the first and second laws of thermodynamics, as well as fluctuation theorems, are established for nonequilibrium processes. For processes with varying temperatures, fluctuation theorems cannot be expressed in terms of integrated work alone. Regardless of various subtleties, however, the stochastic thermodynamic theory is formulated in terms of system variables only, and dS-βd[over ¯]Q is the change of total entropy. Thermodynamic quantities of the system are related to those of the joint system, and the equivalence of theories at two levels of coarse-graining is explicitly demonstrated. Finally we show that there are infinite numbers of equivalent strong-coupling theories, each determined by its definition of system Hamiltonian. Our theory is distinguished by its maximal similarity with the weak-coupling theory.

New higher-order accurate super-compact scheme for three-dimensional natural convection and entropy generation

Exploring natural convection in three dimensions through numerical analysis has become essential for gaining a deeper understanding of this process compared to studying it in just two dimensions. This paper presents an enhanced analysis of three-dimensional (3D) natural convection phenomena within an air-filled cubical cavity, with a primary focus on heat transfer characteristics. The distinguishing feature of this research lies in the pioneering application of the newly developed higher-order accurate super-compact finite difference scheme to study 3D natural convection and entropy generation. This numerical method is renowned for its fourth-order spatial accuracy and second-order temporal accuracy. The super-compact scheme employs 19 grid points at the current time level (nth time level) while utilizing just seven grid points from the subsequent time level [(n+1)th time level. The flow is considered to be 3D, time-varying, laminar, and incompressible. First, the newly developed numerical code has undergone validation through quantitative and qualitative comparisons with existing results. Then, we analyze the flow phenomena and heat transfer dynamics within the cavity for various Rayleigh numbers (102≤Ra≤105) with a fixed Prandtl number (Pr = 0.71) by using this scheme. Various parameters such as local Nusselt numbers, averaged Nusselt numbers, local entropy, Bejan number, streamlines, and isotherm dispersion are studied in this work. It is found that as the Rayleigh number (Ra) increases, the Bejan number (Be) decreases, while the total entropy increases. When the Ra is less than or equal to 104, the Be remains above 0.5, indicating that irreversibility primarily arises from heat transfer. However, as we transition to Ra=105, the Be falls below 0.5, signaling that irreversibility is now predominantly driven by viscous effects. To the best of our knowledge, this research marks a pioneering effort by introducing the application of the higher order super-compact (HOSC) scheme for the examination of heat transfer within a 3D cubic cavity, thus endowing our work with a truly novel and pioneering character. It is worth mentioning that, before this study, there has been no precedent in the exploration of heat transfer using the super-compact scheme, thus endowing our work with a truly novel and pioneering character.

Numerical investigation of no-load startup in a high-head Francis turbine: Insights into flow instabilities and energy dissipation

The presented paper numerically investigates the internal flow behaviors and energy dissipation during the no-load startup process toward a Francis turbine. Passive runner rotation is implemented through the angular momentum balance equation accompanied by dynamic mesh technology and user defined function. Three phases of rotational speed are identified: stationary, rapid increase, and slow increase. Head exhibits a monotonic decrease, rapid rise and fall, and eventual fluctuation. Flow rate shows quasi-linear increase. The pressure fluctuations in the vaneless region are primarily dominated by the frequencies induced by Rotor-Stator Interaction and a broad frequency range below 50 Hz, and below 30 Hz in the draft tube. Runner inlet experiences positive to negative incidence angles, causing intense flow separation and unstable structures. Draft tube exhibits large-scale recirculation and evolving vortex structures. Energy loss analysis based on the entropy production method highlights the runner and draft tube as primary contributors. The energy loss within the runner exhibits an initial increase, subsequent decrease, and then a rise again during the stationary and rapid speed increase phases. While the draft tube shows a rapid increase during the phase of rapid speed increase. Turbulent fluctuations significantly contribute to entropy production loss, with trends matching total entropy production. Maximum energy loss locations correspond to runner inlet and draft tube wall, emphasizing the importance of unstable flow and vortex generation. This study establishes foundational insights into unstable hydrodynamics and energy dissipation modes during hydraulic turbine no-load startup, paving the way for further research.

Droplet coalescence kinetics: Thermodynamic non-equilibrium effects and entropy production mechanism

The thermodynamic non-equilibrium (TNE) effects and the relationships between various TNE effects and entropy production rate, morphology, kinematics, and dynamics during two initially static droplet coalescences are studied in detail via the discrete Boltzmann method. Temporal evolutions of the total TNE strength D¯* and the total entropy production rate can both provide concise, effective, and consistent physical criteria to distinguish different stages of droplet coalescence. Specifically, when the total TNE strength D¯* and the total entropy production rate reach their maxima, it corresponds to the time when the liquid–vapor interface length changes the fastest; when the total TNE strength D¯* and the total entropy production rate reach their valleys, it corresponds to the moment of the droplet being the longest elliptical shape. Throughout the merging process, the force contributed by surface tension in the coalescence direction acts as the primary driving force for droplet coalescence and reaches its maximum simultaneously with coalescent acceleration. In contrast, the force arising from non-organized momentum fluxes (NOMFs) in the coalescing direction inhibits the merging process and reaches its maximum at the same time as the total TNE strength D¯*. In the coalescence of two unequal-sized droplets, contrary to the larger droplet, the smaller droplet exhibits higher values for total TNE strength D¯*, merging velocity, driving force contributed by surface tension, and resistance contributed by the NOMFs. Moreover, these values gradually increase with the initial radius ratio of the large and small droplets due to the stronger non-equilibrium driving forces stemming from larger curvature. However, non-equilibrium components and forces related to shear velocity in the small droplet are consistently smaller than those in the larger droplet and diminish with the radius ratio. This study offers kinetic insights into the complexity of thermodynamic non-equilibrium effects during the process of droplet coalescence, advancing our comprehension of the underlying physical processes in both engineering applications and the natural world.

Influence of cavitation on vortical structures and energy loss in a waterjet pump

Cavitation-induced vortex and energy loss are critical topics in the field of hydraulic machinery. Through a combination of experimental and numerical analysis, this paper investigates how blade loading affects vortical structures and energy loss during cavitation in a waterjet pump. The flow rate and cavitation conditions changed blade tip pressure loading, which significantly affected the trajectories of the primary tip leakage vortex cavitation and secondary tip leakage vortex cavitation. A considerable pressure gradient at the attached cavity closure region leads to a wall reentrant jet and a side-entrant jet, resulting in an attached vortex under the cavitation developing stage and severe stage. The development of the attached vortex leads to the shedding of attached cavities. Furthermore, the blade tip pressure difference loading significantly alters the distribution of tip leakage vortex and gives rise to a perpendicular leakage vortex (PLV). The PLV entrains the shedding cavities and forms a perpendicular cavitation vortex. These complex vortical structures induced by cavitation inevitably enhance enstrophy and lead to entropy production in the pump. The entropy production terms of viscous dissipation, turbulent dissipation, and the wall effect react differently to the development of cavitation. As the cavitation stages developed and became more severe, wall entropy production (S3) decreased. While turbulent dissipative entropy production S2 due to mixing losses occurring in the tip region increased sharply, which dominates the total entropy production S and results in an increase in S.

Adiabatic gas transport in the long flow channels

The paper present the determination of the state parameters of natural gas at the pipeline inlet based on knowledge of the pressure and temperature at the receiving point. Natural gas transport will be carried out through an offshore section of a transmission pipeline. The equations of the Fanno flow model will be used to describe the thermodynamic parameters of the gas in the flow lines. The mathematical equations of the flow mentioned above models have been derived from an analysis of the mass, energy and momentum balance equations. They also take into account the viscous friction forces in the transported gas. Based on the carried out calculations, changes in the Mach number, pressure and velocity of methane transported along the analysed pipeline were determined. In addition, the total entropy gain in the analysed methane flow was determined. The novelty of the calculations presented is the use of the Fanno flow model, which considers a realistic adiabatic gas flow. This is in contrast to the isothermal flow model, which assumes an unchanging temperature of the transported gas. In the case under consideration, the adopting model was possible because of the similar temperature values of the gas flowing in the pipeline and the corresponding temperature values of the surrounding seawater. The fundamental advantage of the Fanno flow model is that it satisfies the mass balance of the flowing gas in each cross-section. Thus, the product of the velocity and density of the gas in a pipeline of constant diameter assumes a constant value.

Effects of Hydrogen, Methane, and Their Blends on Rapid-Filling Process of High-Pressure Composite Tank

Alternative fuels such as hydrogen, compressed natural gas, and liquefied natural gas are considered as feasible energy carriers. Selected positive factors from the EU climate and energy policy on achieving climate neutrality by 2050 highlighted the need for the gradual expansion of the infrastructure for alternative fuel. In this research, continuity equations and the first and second laws of thermodynamics were used to develop a theoretical model to explore the impact of hydrogen and natural gas on both the filling process and the ultimate in-cylinder conditions of a type IV composite cylinder (20 MPa for CNG, 35 MPa and 70 MPa for hydrogen). A composite tank was considered an adiabatic system. Within this study, based on the GERG-2008 equation of state, a thermodynamic model was developed to compare and determine the influence of (i) hydrogen and (ii) natural gas on the selected thermodynamic parameters during the fast-filling process. The obtained results show that the cylinder-filling time, depending on the cylinder capacity, is approximately 36–37% shorter for pure hydrogen compared to pure methane, and the maximum energy stored in the storage tank for pure hydrogen is approximately 28% lower compared to methane, whereas the total entropy generation for pure hydrogen is approximately 52% higher compared to pure methane.

Thermodynamic mixing properties of disordered alkali feldspar solid-solution from Na–K partitioning and low-temperature calorimetry

The equilibrium partitioning of Na and K between alkali feldspar and NaCl–KCl salt melt was determined at 800 ∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^\\circ$$\\end{document}C, 850 ∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^\\circ$$\\end{document}C, 900 ∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^\\circ$$\\end{document}C, 950 ∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^\\circ$$\\end{document}C and 1000 ∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^\\circ$$\\end{document}C and close to ambient pressure. Four different natural gem-quality alkali feldspars with low degree of Al–Si ordering covering the range from orthoclase to high sanidine and with slightly different minor element concentrations were used as starting materials. The partitioning curves obtained for the four feldspars are indistinguishable indicating that Na–K partitioning independent of the differences of Al–Si ordering state and minor element concentrations existing amongst these feldspars. A sub-regular two parameter Margules type solution model was fitted to the partitioning data, and the excess Gibbs energy describing the thermodynamic non-ideality of the alkali feldspar solid-solution and the respective Margules parameters WgK\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W_{\ ext {g}\ ext {K}}$$\\end{document} and Wg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W_{\ ext {g}\ ext {Na}}$$\\end{document} including their temperature dependence expressed as Wg=Wh-TWs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W_g=W_h-TW_s$$\\end{document} were determined: WgK=19754±3140J·mol-1-T·2.33±2.67J·mol-1·K-1Wg=14916±4272J·mol-1-T·3.55±3.64J·mol-1·K-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} W_{\ ext {g}\ ext {K}}&= 19754 \\pm 3140 J\\cdot \\,\\,{\\hbox {mol}}\\,\\,^{-1} - T \\cdot 2.33 \\pm 2.67 J\\cdot \\,\\,{\\hbox {mol}}\\,\\,^{-1}\\cdot K^{-1} \\\\ W_{\ ext {g}\ ext {Na}}&= 14916 \\pm 4272 J\\cdot \\,\\,{\\hbox {mol}}\\,\\,^{-1} - T \\cdot 3.55 \\pm 3.64 J\\cdot {\\hbox {mol}}\\,\\,^{-1}\\cdot K^{-1} \\\\ \\end{aligned}$$\\end{document}The corresponding solvus has a critical temperature slightly above 650 ∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^\\circ$$\\end{document}C and is well comparable with earlier direct experimental determinations of the low-sanidine-albite solvus curve. Comparison of the vibrational excess entropy determined from low-temperature heat capacity measurements with the total excess entropy derived from the temperature dependence of the excess Gibbs energy yields a negative configurational contribution to the excess entropy pointing towards short-range Na–K ordering on the alkali site.

MHD free convective flow and entropy production of glycerin in a square domain with Joule heating and internal heat generation

This study inspects MHD free convective flow and entropy production inside a square domain (e.g., a nuclear reactor thermal cooling system) with Joule heating and internal heat generation. The left edge of the domain is set to a higher temperature than the right edge, and the top and bottom edges are insulated. The domain is filled with a heat-generating and electrically conducting fluid (glycerin) with fixed thermo-physical properties. This study has practical significance in many engineering applications, including nuclear reactor cooling systems, cooling electronics, designing solar thermal collectors, designing heat exchangers, etc. The primary objective of this study is to enhance heat transfer by examining optimal system characteristics. The Navier-Stokes and heat energy equations, which govern heat and fluid flow in the domain, are solved via the Galerkin finite element technique. Numerical simulation is performed over specific ranges of Rayleigh number (103 ≤ Ra ≤ 106), Joule heating parameter (0 ≤ J ≤ 7.31 × 10−9), Hartmann number (0 ≤ Ha ≤ 36.98), and volumetric heat generation coefficient (0 ≤ Δ ≤ 2) under laminar flow consideration. The parametric conditions for achieving the desired thermal performance can be controlled by determining the mean Nusselt number of the heated edge. Notably, heat transfer enhancement ensues with the simultaneous increment of Ra and Ha at a fixed Joule heating parameter. On the other hand, introducing internal heat generation reduces thermal performance inside the system, which has also been observed in terms of mean fluid temperature, total entropy production, and average Bejan number.

Design method based on a new slip-diffusion parameter of centrifugal pump for multiple conditions in wide operation region

Centrifugal pumps are widely used in industrial production, agricultural irrigation, water transportation, energy storage pump station and ocean engineering, and the development prospect of centrifugal pump is to work in a wide operation region with high efficiency. In this work, the achievement of high-efficiency operation for multiple conditions in a wide operation region is strenuously realized by a new design method from the perspective of flow mechanism analysis and theoretical derivation. A new dimensionless slip-diffusion parameter Φ on consideration of the slip effect and diffusion effect in impeller is proposed. On the basis of the new parameter Φ, a new design method of centrifugal pump is established to improve the pump efficiency for multiple conditions in a wide region. Two centrifugal pumps with different specific speeds of 102 and 127 are designed to validate the proposed design method. When the slip-diffusion parameter Φ ≈ 0.677, the centrifugal pump can achieve the maximum average efficiency for multiple conditions. For Φ < 0.677, the pump efficiency rapidly drops at the high flow rate region. For Φ > 0.677, the pump efficiency rapidly drops at the low flow rate region. Two centrifugal pumps are numerically simulated to obtain the flow pattern, and the entropy production method is used to analyze the relationship between flow field and energy performance of the pumps. Entropy production mainly appears at the blade suction side and the impeller outlet. For different flow rates, the total entropy productions of pumps with Φ ≈ 0.677 are always the minimum.

Underpinnings behind the magnetic order-to-disorder transition and property anomaly of disproportionated insulating samarium nickelate

Perovskite nickelates (RNiO3), as benchmark materials for exploring underlying physics of phase transitions in strong correlated systems, are well-known for their rich structural characteristics and physicochemical properties. Understanding phase transition from the spin-ordered antiferromagnetic (AFM) state to the spin-disordered paramagnetic (PM) state of RNiO3 requires accurate models at finite temperatures. Here, we investigate the underpinning physics behind the property anomaly and AFM-to-PM transition in samarium nickelate (SmNiO3) using a thermodynamic zentropy approach, which depicts the temperature-dependent total entropy for a system of interest via a nested formula through integration of quantum mechanics and statistical mechanics. The SmNiO3 displays the ground-state of AFM insulator as well as the PM metal and PM insulator at elevated temperatures. It turns out that the magnetic configurational entropy induced by competition among different spatially fluctuating polymorphous spin configurations, contributes to the specific-heat anomaly and the phase transition of SmNiO3 from AFM to PM state. The predicted Néel temperature of 241±25 K for SmNiO3 is in satisfactory agreement with the experimental value. Unlike empirical interpretations in literature, the present work indicates that the magnetic order-to-disorder transition in SmNiO3 is associated with the magnetic configurational entropy due to thermal mixture of multiple spin configurations at elevated temperatures, which can be quantitively captured by the first-principles based thermodynamic zentropy approach.

Inhomogeneous flow model of natural convection, entropy generation, and heatlines visualization in wavy I‐shaped enclosure with rectangular heater

AbstractThe present investigation is on examination of the natural convection and entropy generation considering the heatlines visualization of nanofluid I‐shaped enclosure with two corrugated walls considering inner rectangular heater of three different heights. The influence of Brownian motion along with thermophoresis had been implemented using Inhomogeneous two‐phase model of nanofluid. The governing equations were solved numerically using COMSOL software. Influence of Rayleigh number , Buoyancy ratio number , Lewis number , heater length . The results indicate that the influence of Lewis number on heat transfer bettering is stronger at high Rayleigh number while its impact is negligible at a lower value of Rayleigh number (conduction mode). In addition, the total entropy generation gets its highest value at Lewis number . Bejan number, fluid flow strength and heat rate increase as the rectangular heater height increases. Also, higher heat transfer augmentation is taken when the heater height is while increasing the heater height to leads to more total entropy generation. The impact of heater height on total entropy generation is highly affected by Rayleigh number as increasing the heater height from into , total entropy generation increases by at while it increases by at .