Thermal Entropy Research Articles

Compressive mechanical properties of thermal sprayed AlCoCrFeNi high entropy alloy coating

Atmospheric plasma spraying (APS) was used to deposit an AlCoCrFeNi high entropy alloy (HEA) coating on stainless steel substrate. The as-deposited coating was about 300 μm thick and the microstructure consisted of a nickel solid-solution matrix, together with a number of secondary phases/intermetallics. In addition, phase and splat boundaries were also prevailing. However, the extent of intermetallics and secondary phases were supressed, compared to other processing techniques (e.g., melting) of HEA, due to fast solidification in the APS process. In-situ micro-pillar compression was employed to evaluate the mechanical properties of the coating. The experimental results show that, mechanical properties of the coating in the cross-sectional direction (963.14 ± 28.58 MPa of yield strength and 1005.58 ± 22.08 MPa of compressive strength) is marginally higher than that of planar direction (802.33 ± 43.76 MPa of yield strength and 817.73 ± 43.84 MPa of compressive strength). The presence of secondary phases and/or intermetallics in the coating microstructure acts as a reinforcement medium to allow effective load bearing capacities of the coating. On the hindsight, phase and splat boundary areas are the ‘weakest link’, that acts as a slip/shear plan initiation site. The orientation of these phase/splat boundaries to that of direction of loading plays a significant role on the coating failure mode.

Thermo-fluidic and entropy generation analysis of MPCMS in straight, segmental, and rib-groove microchannel heat sinks: A numerical investigation

The efficient management of thermal systems is crucial for various technological applications, necessitating innovative cooling strategies to enhance performance and reduce entropy generation. Microchannels have emerged as a promising solution due to their high heat transfer rates and compact size. This study investigates the thermofluidic characteristics and entropy generation in straight, segmental, and rib-groove microchannels utilizing de-ionized water and microencapsulated phase change slurry (MPCMS) as working fluids. Employing numerical analysis, the investigation integrates a mixture model for the base fluid and micro-encapsulated phase change material (MPCM) using an equivalent heat capacity approach to incorporate the phase transition of the MPCM (composed of paraffin with a Ti shell). Operational parameters include an inlet fluid velocity ranging from 0.575 to 3.45 m/s, heat flux varying between 15 and 30 W/cm2, and MPCM volume fractions of 5% to 20%. The ANSYS Fluent Solver, a finite volume method using a multigrid solver, was used to control the simulation by species transport. Notably, segmental channels exhibit a notable decrease in wall temperature of 29.7% and 26.3% compared to straight and rib-groove channels, respectively, under constant heat flux and flow rate. However, the effectiveness of MPCM in enhancing thermal performance was greater in straight and rib-groove channels, surpassing segmental channels by 2.5% and 3.28%, respectively, under constant heat flux. On analyzing the irreversibility, segmental channels exhibit higher frictional entropy but lower thermal entropy generation due to the fin structure, resulting in an overall reduction in total entropy generation. Moreover, segmental microchannels, when utilizing MPCMS, demonstrate superior performance in reducing irreversibility by 60.66% and 49.6% compared to straight and rib-groove channels, respectively. Total entropy generation increases with higher velocity and heat flux, while it diminishes with higher MPCM concentration across all configurations.

Effects of longitudinal ventilation and GHEs on geothermal energy extraction and HRC in high geothermal tunnels

With the excavation of deep tunnels, the problem of high geothermal heat is becoming more and more prominent. However, high geothermal heat can be utilized as a renewable energy source. In order to effectively reduce thermal damage and utilize geothermal energy, it is necessary to study the effects of longitudinal ventilation and ground heat exchanges (GHEs) on the heat-regulating circle of the surrounding rock. In this study, an experimental platform was designed and constructed in a laboratory to test different geothermal heat exchanger flow rates and ventilation air velocities and to monitor the heat extraction from the geothermal heat exchanger, the ventilation heat extraction, and the temperature field of the surrounding rock. The experimental results show that when the temperature field tends to be stabilized, the flow rate and ventilation velocity of the GHEs are closely related to the temperature distribution of the surrounding rock. The initial heat storage and heat replenishment capacity of the enclosing rock have a great influence on the heat extraction efficiency. Ventilation has a great influence on the heat extraction efficiency of GHEs, and the optimal wind speed range is 1.5∼2 m/s considering the cooling and heat extraction efficiency. When the wind speed is less than 1.5 m/s, the heat extraction efficiency of GHEs can be improved, and the total heat transfer can be increased. When the wind speed is greater than 1.5 m/s, the situation is reversed. The thermal entropy theory for circular tunnels is not fully applicable to arched tunnels containing GHEs.

Exergy analysis in solid oxide fuel cells with different operating temperature and pore diameter

Solid oxide fuel cells (SOFC) provide energy production at high temperatures. In this study, the effect of operating temperature (873 K–1673 K) and pore diameter (4 μm–16 μm), which are important parameters determining the performance of solid oxide fuel cells, are investigated by energy and exergy analysis. Quadrupling the pore diameter increases the activation loss by 0.280 V under constant current density. Thermal efficiency, exergy dissipated, entropy production and exergy efficiency are calculated using energy and exergy analysis. The power density increases with increasing temperature. For example, at a current density of 3000 A/m2, increasing the operating temperature by 45 % from 873 K increases the power density by 3.79 times compared to the initial case. At the same current density, when the pore diameter is 4 μm and 10 μm, the power densities are 2659.64 W/m2 and 2253.46 W/m2, respectively. This is explained by the high cell losses at low temperatures. At a current density of 1000 A/m2, the exergy dissipated is 719.85 kW at an operating temperature of 973 K and 1030.07 kW at 873 K. At 1073 K operating temperature and 7 μm pore diameter, the maximum thermal and exergy efficiencies are 67.77 % and 61.72 %, respectively. Increasing the operating temperature from 873 K to 1273 K increases the thermal and exergy efficiency by 31.55 % and 28.39 % respectively. Increasing the pore diameter decreases the power density and causes a decrease in thermal and exergy efficiency. Increasing the pore diameter by 30 % at a current density of 7000 A/m2 results in a decrease in thermal and exergy efficiency by 5.1 % and 4.64 %, respectively. This research examines the effects of different temperatures and pore diameters in detail by considering the exergy analysis of the solid oxide fuel cell with a thermodynamic approach, unlike the numerical analysis studies concentrated on in the current literature.

Heat and mass transfer analysis of non‐miscible couple stress and micropolar fluids flow through a porous saturated channel

AbstractThis study examines the flow rate, Bejan number transportation, concentration distribution and thermal characteristics of an immiscible couple stress‐ micropolar fluids within a porous channel. The authors focus on the effects of heat radiation and an angled magnetic field on the thermal dispersion, concentration distribution and entropy formation of two different types of incompressible immiscible micropolar and couple stress fluids inside a porous channel. Here, the static walls of the channel are isothermal, and the pressure gradient in the flow domain's entrance zone is constant. In this flow problem, we tried to simulate thermal radiation in the energy equation by applying Rosseland's diffusion approximation. To solve the problem, the authors have used no‐slip conditions at the channel's immovable walls, a continuity of temperature profile, shear stresses, thermal flux, linear velocity, and micro‐rotational velocity over the fluid‐fluid interface. The equations that govern the flow of immiscible fluids are solved using a well‐defined methodology and both the temperature and flow field are then evaluated using a closed‐form solution. The mathematical results of the thermal distribution and flow velocity are used to derive the Bejan number distribution and the entropy generation number. Graphical discussions are used to illustrate the impact of different emerging factors on the model's flow and thermal properties, which describe the major impact of the proposed model. These variables involve the micropolarity parameter, Reynolds number, inclination angle parameter, radiation parameter, and Hartmann number. The outcomes of the present models are corroborated by previously established results available in the literature.

Thermal-hydraulic investigation of liquid metal cross flow different arrangements of tube bundles under pulsating

The topic of this paper is to couple the passive and active approaches to enhance the heat transfer performance in the inline tube bundle heat exchanger. Firstly, the k-kl-ω turbulence model and Kays turbulent Prandtl number model are validated by liquid metal cross flow tube bundle experiments and rectangular groove pulsating flow experimental results. Then the numerical studies were carried out for pulsating velocity amplitude of 0.5, frequency of 10, and Re of 20,000 with transverse and streamwise pitch-to-diameter ratios of 1.5, 1.65, and 1.8. The introduction of pulsating flow effectively improves the turbulence characteristics between the tube bundles, especially at the first three rows, where the velocity fluctuation is enhanced by about 1.5–2 times. The tube heat transfer performances are all improved. The performance evaluation criterion (PEC) variation ranges from 1.04 to 1.32, which signifies that the introduction of pulsating flow can enhance the comprehensive heat transfer performance. The per unit flow rate thermal entropy generation decreased by about 9.7–33.3 %, in addition, a phase difference between the transient thermal entropy production and pulsating velocity was found. The correlation equations about Nu and f factor within the scope of this paper are presented.

Influence of rotating magnetic field on thermal field and entropy generation of a tube containing the nanofluid using mixture model

The thermo-fluidic properties and entropy generation in a tube comprising nanofluid under variable rotational magnetic field have not been studied earlier. In the current study, the influence of a rotating magnetic field is evaluated by using mixture model at four different pump power for three cases. A steady-state, Newtonian Ag/water nanofluid, incompressible, and 3D model have been supposed. The influence of pump power variation and using nanofluid are studied. Results indicated that by raising the pump power for three cases, the Nusselt number enhances, and Bejan number, the friction factor, and dimensionless temperature decreases. The rotating magnetic field for the Case III in comparison to the Case Ⅰ and Case Ⅱ at 60 W and 0.5 % volume fraction of nanofluid, enhanced the Nusselt number by 356.3 % and 12.42 %, respectively. In the presence of 0.5 % nanofluid at 60 W pump power, the friction factor increases by 103.5 % compared to Case Ⅰ, with the same fluctuations observed in Cases Ⅱ and Ⅲ. The maximum dimensionless temperature reached 0.575 for Case Ⅲ at a power of 30 W using water. A rotating magnetic field of 60 W raised PEC by 219.44 % and 261.11 % for Cases Ⅱ and Ⅲ, respectively, compared to Case Ⅰ.

Holographic thermal entropy from geodesic bit threads

The holographic bit threads are an insightful tool to investigate the holographic entanglement entropy and other quantities related to the bipartite entanglement in AdS/CFT. We mainly explore the geodesic bit threads in various static backgrounds, for the bipartitions characterized by either a sphere or an infinite strip. In pure AdS and for the sphere, the geodesic bit threads provide a gravitational dual of the map implementing the geometric action of the modular conjugation in the dual CFT. In Schwarzschild AdS black brane and for the sphere, our numerical analysis shows that the flux of the geodesic bit threads through the horizon gives the holographic thermal entropy of the sphere. This feature is not observed when the subsystem is an infinite strip, whenever we can construct the corresponding bit threads. The bit threads are also determined by the global structure of the gravitational background; indeed, for instance, we show that the geodesic bit threads of an arc in the BTZ black hole cannot be constructed.

Moving mirrors and event horizons in non-flat background geometry

Moving mirrors have been used for a long time as simple models for studying various properties of black hole radiation, such as the thermal spectrum and entanglement entropy. These models are typically constructed to mimic the collapse of a spherically symmetric distribution of matter in the Minkowski background. We generalize this correspondence to the case of non-trivial background geometry and consider two examples, the Schwarzschild—de Sitter black hole and the Bañados–Teitelboim–Zanelli (BTZ) black hole. In the BTZ case we were also able to show that this approach works for the spinning black hole which has only axial symmetry.

Numerical investigation of entropy generation and Magnetohydronamic natural convection in a porous square cavity with four embedded cylinders

In this study, we investigated buoyancy-induced convection in a permeable square hollow containing four embedded cylinders and subjected to a magnetic field using numerical methods. The finite element approach was used to solve the governing equations of the system as well as the initial and boundary conditions. We analyzed the effects of the emerging non-dimensional quantities on the flow pattern and thermal field, as well as entropy production, in relation to the thermophysical properties of the obstacles. In the limiting case, we compared our results with already published work and found outstanding concurrence. Our simulations revealed that increasing cylinder spacing leads to higher thermal entropy generation, while fluid friction irreversibility has the opposite effect. Additionally, the imposed magnetic field significantly suppressed temperature distribution and flow field, resulting in low thermal transmission within the cavity.

Sensible vs Nonsensible Work

As a science structured around entropy, classical thermodynamics is filled with inconsistencies. Beyond its mathematical implications, entropy possesses no clear universal lucidity. Entropy’s various interpretations tend to be application-dependent. Thermal entropy was devised in the 19th century by Clausius to enhance one’s understanding of the relationship between energy and work. The accepted theory of work done by expanding systems has been strictly expressed in terms of that expanding system’s parameters, which is non-sensible. A sensible second theorization of work will be discussed based on the facts that work is always external to the system performing that work and that an expanding system needs to lift the overlying atmosphere’s mass. These two different mathematical interpretations of work will be discussed, along with the cataclysmic implications for accepted thermodynamics. Occam’s razor points to sensible work, as presented herein.

Holographic timelike entanglement entropy from Rindler method* *Supported partially by the National Natural Science Foundation of China (12175008)

For a Lorentzian invariant theory, the entanglement entropy should be a function of the domain of dependence of the subregion under consideration. More precisely, it should be a function of the domain of dependence and the appropriate cut-off. In this study, we refine the concept of cut-off to make it applicable to timelike regions and assume that the usual entanglement entropy formula also applies to timelike intervals. Using the Rindler method, the timelike entanglement entropy can be regarded as the thermal entropy of the CFT after the Rindler transformation plus a constant , where c denotes the central charge. The gravitational dual of the 'covariant' timelike entanglement entropy is presented following this method.

Quantum entanglement on black hole horizons in string theory and holography

We compute the exact one-loop partition function of ℤN orbifolds of Euclidean BTZ black hole with the aim to compute the entanglement entropy of the black hole horizon in string theory as a function of the mass and spin of the black hole and the AdS3 radius. We analyze the tachyonic contribution to the modular integrand for the partition function known for odd integers N > 1 and show that it admits an analytic continuation resulting in a finite answer for the modular integral in the physical region 0 < N ≤ 1. We discuss the flat space limit and the relevance of this computation for quantum gravity near black hole horizons and holography in relation to the thermal entropy.

Effect of twisted rib on the hydrothermal performance and entropy generation behavior in minichannel heat sinks cooled by biologically synthesized Ag/water nanofluid

This numerical research study focuses on impacts of using twisted rib geometry on the hydrothermal performance and entropy generation characteristics of biologically synthesized Ag/water nanofluid flowing in heat sink ‌minichannels. To this end, twelve different twisted rib geometries (Case 1 to 12) were designed where the double-row ribs were twisted at the bottom and top portions with twist angles between − 45° and + 45°. To elucidate the cooling performance comprehensively, four different Reynolds numbers (Re = 500, 1000, 1500, and 2000) and four different nanoparticle concentrations (φ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\varphi \\hspace{0.17em}$$\\end{document}= 0%, 0.1%, 0.5%, and 1%) were included in the numerical computations. Results revealed that using twisted ribs significantly smoothen the fluid flow and reduces pressure drop remarkably depending on twist angles, nevertheless, it deteriorates the cooling performance. In Case 12, the convective heat transfer coefficient reduces by up to 15.8% at Re = 2000 and φ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\varphi$$\\end{document}=1%, compared to the base case. However, pumping power requirement is decreased by 43.9% in this case. Nanoparticle incorporation contributes to enhancement of convective heat transfer coefficient by up to 13.5% at the lowest Re. Frictional entropy generation considerably decreases (up to 31%) when twisted ribs are utilized. However, thermal entropy generation can increase up to 36%, due to ineffective cooling with twisted ribs. This work can be regarded as a first study in the field concerning the effects of top and bottom twist angles on hydrothermal performance and entropy generation in nanofluid-cooled mini-channel heat sinks.

Numerical study on natural convection in a saturated non Darcian porous medium under radiation and entropy generation effects

This work focuses on analyzing fluid flow, generation of entropy, and heat transfer during natural convection in a cavity enclosed with a non-Darcian saturated porous medium. The influence of viscous dissipation and thermal radiation are considered. The Lattice Boltzmann method is adopted to simulate the governing equations. The study discusses the general effect of dimensionless parameters on the fluid structure interaction properties, entropy generation and the thermal field. The parameters investigated include the Grashof number, Eckert number, Rayleigh number, Forchheimer Resistance, inverse Darcy, radiation parameter, and Prandtl number. The combination of studying dimensionless parameters on non-Darcian porous medium, along with the consideration of thermal radiation, viscous dissipation, and entropy analysis, has made this research valuable and worth pursuing. The findings reveal that the areas of high entropy generation are primarily located along the walls (vertical) of the cavity. Moreover, it is observed that as the inverse Darcy and Forchheimer resistance increase, their effect on the average Nusselt number diminishes for varying parameters of radiation. As the Prandtl number increases, the isotherms cluster along the walls (vertical) of the porous cavity. With high Grashof values, convection becomes turbulent, and the temperature distribution becomes non-uniform. Additionally, the entropy caused by heat and fluid friction decreases as the Forchheimer resistance increases.

Feasibility of integrated numerical and Adaptive Neuro-Fuzzy Inference System models in predicting the thermophysical properties of unsteady coupled micropolar–Casson hybrid nanofluids

This article aims to probe postulated phenomena using a paired micropolar and Casson hybrid fluid over a rotating disk. The intension to design a numerical technique (Runge–Kutta fourth-order along with shooting technique) integrated Adaptive Neuro-Fuzzy Inference System (ANFIS) envisioned with a thermal and exponentially space-dependent heat source, nonlinear thermal radiation and entropy production is developed in this phase of work. To ensure that, a nonlinear partial differential equation set of equations has been transformed into an ordinary differential equation by using the proper self-similarity variables. The model's research results, with a few notable outliers, are mostly consistent with those from prior research that was merged into the dataset used to train the ANFIS model. With the impact of active factors, the results are esthetically exhibited for numerous profiles. This displays that with the rise in magnetic field and radiation, the velocity and temperature profiles increase sharply, resulting in a contradiction phenomenon with the decreasing electric field inputs. Also, tilting of vortex viscosity, spin gradient viscosity and microinertia density on the various microrotation components displays inclination. Moreover, ANFIS training was exploited to analyze the approximate solutions for specific scenarios, and the developed ANFIS was evaluated against a testing dataset to emphasize its performance. Due to their longer render, the nanoparticles exploited here are deemed suitable for use in bone implants, iodinated agents for blood imaging and red blood cell stimulation. Thus, the results of this study may be applied to therapeutic anemia therapies.

Circular Fluid Heating—Transient Entropy Generation

A technical issue with fluid flow heating is the relatively small temperature increase as the fluid passes through the heating surface. The fluid does not spend enough time inside the heating source to significantly raise its temperature, despite the heating source itself experiencing a substantial increase. To address this challenge, the concept of the multiple circular heating of air was developed, forming the basis of this work. Two PTC heaters with longitudinal fins are located within a closed channel inside housing composed of a thermal insulation material. Air flows circularly from one finned surface to another. Analytical modeling and experimental testing were used in the analysis, with established restrictions and boundary conditions. An important outcome of the analysis was the methodology established for the optimization of the geometric and process parameters based on minimizing the transient thermal entropy. In conducting the analytical modeling, the temperature of the PTC heater was assumed to be constant at 150 °C and 200 °C. By removing the restrictions and adjusting the boundary conditions, the established methodology for the analysis and optimization of various thermally transient industrial processes can be applied more widely. The experimental determination of the transient thermal entropy was performed at a much higher air flow rate of 0.005 m3s−1 inside the closed channel. The minimum transient entropy also indicates the optimal time for the opening of the channel, allowing the heated air to exit. The novelty of this work lies in the controlled circular heating of the fluid and the establishment of the minimum transient thermal entropy as an optimization criterion.

Analysis of exergy and heat transfer in a tube fitted with flapped V-baffles

Vortex generator is a device that shows promise in generating streamwise vortices that can be utilized for boosting the rate of heat transmission inside a cooling/heating system with a relatively smaller penalty in terms of friction loss. The primary goal of the current research is to maximize the comparative Nusselt number ratio (Nu/Nu0) to be as large as possible to lower the size of the system while keeping thermal performance as high as feasible to save more energy. Thus, in the current study, the impacts of inserting the flapped V-baffle vortex generator (FBVG) on the thermal effectiveness improvement of a round tube were experimentally investigated. At a fixed attack angle (α = 60°) and baffle blockage ratio (BR = b/D = 0.3), the geometrical behaviors of FBVGs placed periodically along two edges of a straight tape were six different flap angles (θ = 0°, 25°, 35°, 45°, 65° and 90°) and three ratios of baffle pitches (P/D = PR = 2.0, 1.5, and 1.0). The current V-baffles, which were positioned on both tape edges, were designed to reduce friction loss caused by interrupting the central core flow when placed on both tape sides. The measurement results focused on the friction loss and thermal behaviors, including exergy and entropy analyses for Reynolds number from 4750 to 29,270. In the findings, the Nusselt number and friction factor of FBVG at θ = 0° and PR = 1 are, respectively, up to 5.6 and 35.24 times larger than those of the smooth tube. The entropy generation (S˙gen′) seems to decline as θ and PR increase, with the smallest S˙gen′ found at θ = 0° and PR = 1 for lower Re. The FBVG has the greatest exergy efficiency (ηEx) at θ = 0° and PR = 1. To find the true benefits of FBVG, its thermal performance is estimated and seen to reach a maximum at about 2.44 with NuR = 4.65 at θ = 45° and PR = 1. The optimal scenario at θ = 25° and PR = 1 was preferred, however, since it yielded the largest NuR = 5.42 at TEF = 2.39.

Free vibration for the thermo-magneto-electro-elastic (TMEE) nanobeams based on modified couple stress theory

Size-dependent vibration of thermo-magneto-electro-elastic (TMEE) nanobeams accounting for the thermal entropy is implemented. Modified couple stress theory is adopted, Euler-Bernoulli beam model and strain gradient theory are adopted. Free vibration of TMEE nanobeams is demonstrated, dispersion equation is depicted, and natural frequencies are evaluated. Effects of various parameters such as volume fraction, size-dependent parameter, thickness and length of the nanobeam are investigated. The conducted results perfectly match with the ones in existing literature, and the newly invented governing equation is rather compact, which can be easily used to efficiently estimate the natural frequencies of the TMEE nanobeams.

A novel design of double pipe heat exchanger with innovative turbulator inside the shell-side space

An innovative category of turbulators is implemented within the shell of a double pipe heat exchanger (DPHE). The impact of these turbulators on thermal performance and entropy generation is scrutinized through three-dimensional numerical simulations. Maintaining a constant Reynolds number of 500 for the fluid flowing within the shell, the tube's Reynolds number varies within the range of 3000 to 13,000. However, a simulation is performed with a shell-side/tube-side Reynolds number of 750/13000 to investigate the effects of shell-side Reynolds number on heat transfer. To enhance simulation accuracy, the thermophysical features of water, serving as the working fluid, are defined as temperature-dependent functions. Additionally, structured computational grids, featuring polyhedral cells forming the turbulators, are employed to discretize the solution domain. A notable concordance between the simulations' findings and existing experimental correlations is observed. The outcomes indicate that incorporating this turbulator type includes swirl flows, leading to a discernible enhancement in thermal performance. Specifically, for the case with three turbulators at Retube = 3000, the Nusselt number and pressure loss of the fluid flow within the shell show increments of 73% and 87%, respectively, compared to the conventional DPHE. The performance evaluation criterion (PEC) for the shell-side fluid attains a value of 1.41.