Adiabatic Index Research Articles

Instability onset of Rayleigh-Bénard convection for diatomic rarefied gases: Effects of molecular interaction models and flow parameters

Studies on the stability of Rayleigh-Bénard convection in rarefied gases mainly focus on monatomic gases, whereas diatomic gases are the prevailing medium in actual flows. This paper conducts a study on the Rayleigh-Bénard convection stability of diatomic rarefied gases based on the Navier-Stokes (NS) equations modified with slip boundary conditions. We aim to elaborate the effects of different molecular interaction models and flow parameters (Knudsen number Kn, Froude number Fr, Prandtl number Pr, etc.). And several interesting phenomena have been discovered: (1) Compared with monatomic gases, the instability region of diatomic gases expands towards higher Knudsen numbers and smaller Froude numbers; (2) It is generally believed that increasing rarefaction leads to flow stabilization. However, we have found that in the case of small wave numbers within the scope of our research, the rarer the gas, the higher the growth rate, which contradicts traditional cognition; (3) Competition mechanism between buoyancy and gravity in the stability of Rayleigh-Bénard convection exists; (4) When considering the variations of Prandtl number and specific heat ratio with temperature, the relative deviation of the growth rate of the most unstable mode is significant.

Machine learning‐assisted analysis and prediction for the thermal effect of various working fluids in a vortex tube

AbstractWith the widespread application of vortex tube in various fields, it becomes essential to quantitatively explore the separation effect of different fluids (natural fluids, hydrocarbons, etc.) within the vortex tube and to promote its utilization. A new approach has been developed in this study to establish quantitative models for predicting the thermal effects of different fluids in a vortex tube. These models are based on both the macro properties of the working fluid and micro molecular descriptor through a molecular scale. A dataset of 11 numerical simulation results of hydrocarbons and hydrofluorocarbons refrigerants is employed. Three operating conditions, 10 property parameters, and 115 molecular descriptors are screened and identified using random forest feature analysis. Two types of models (micro and macro) have been developed by employing artificial neural network (ANN) modeling techniques. In the result, four key influencing fluid property parameters (the specific heat ratio γ, the multiplication of heat capacity and the molar weight cp·M, the kinematic viscosity ν, and the thermal conductivity λ) and nine molecular descriptors in affecting the thermal effect are identified and respectively chosen as the input in the macro and the micro ANN model establishment. Both types of developed models show a high correlation coefficient (R > .999) and a comparatively low mean square error (MSE). When R600 is employed in the validation, most of the relative error is less than 10%, suggesting both types of models can work effectively in predicting the thermal effect for other fluid. The findings contribute to a deeper understanding of the thermodynamic effect of vortex tubes and provide a valuable tool for selecting and optimizing working fluids in various applications.

Influence of modified gravity on self-gravitating stellar objects

This paper focuses on studying the self-gravitating spherical compositions enclosing anisotropic fluid distribution in the context of f(G,T) theory. The modified field equations representing anisotropic source are formulated, and then the MIT bag model equation of state is used to contribute the participation of bag constant. The mathematical equations are thoroughly computed using a quadratic f(G,T)=G2+ħT model (where ħ indicates the coupling parameter). We utilize the Finch-Skea ansatz to examine the compact objects Her X-I, Vela X-I, PSR J1614-2230, LMC X-4 and 4U1820-30. This solution facilitates in determining the behavior of physical factors, anisotropic source and energy constraints corresponding to the above-mentioned stars graphically. We construct the graphs by following two distinct values of the coupling parameter throughout. Some other important factors such as mass, redshift and compactness are also discussed. To examine the stable character, we use three strategies, i.e., causality condition, Herrera cracking approach and adiabatic index. Interestingly, for both the values of ħ, all the considered candidates signify the viable as well as stable behavior.

Influences of thermochemical non-equilibrium effects on Type III shock/shock interaction at Mach 10

Shock/shock interactions (SSIs) often lead to high thermal loads. To understand the influences of thermochemical non-equilibrium effects on the Type III SSI, four gas models based on the assumption of thermal perfect gas (TPG), thermal equilibrium chemical non-equilibrium gas (TECNG), thermal non-equilibrium chemical frozen gas (TNCFG), and thermochemical non-equilibrium gas (TCNEG) are employed to simulate the Type III SSI at Mach 10. The intersection of incident shock and bow shock is determined by dimensionless intercept of 0.05 and 0.1. It is found that the chemical non-equilibrium effects significantly lift up the impingement position of shear layer by reducing the standoff distance of bow shock. As a result, the peaks of wall pressure and heat flux calculated by TECNG and TCNEG model are higher than TPG and TNCFG model, respectively. Type IIIa SSI occur in the flows calculated by the TECNG and TCNEG model for the case with a dimensionless intercept of 0.1. The peaks of wall pressure and heat flux calculated by TECNG model are both over four times higher than those of TPG model. The thermal non-equilibrium effects slightly increase the standoff distance of bow shock and lower the impingement position of shear layer. In addition, the thermal non-equilibrium reduces the angle to the horizontal direction of shear layer by increasing the specific heat ratio.

Physical analysis of anisotropic compact stars in f(𝒬) gravity

The main objective of this study is to investigate the stability and viability of anisotropic compact stellar objects using the Krori–Burua solutions in [Formula: see text] gravity, where [Formula: see text] is a nonmetricity scalar that explains the gravitational effects. We use a static spherical metric in the inner region and Schwarzschild spacetime in the outer region of the Her X-I, SAX J 1808.4-3658 and 4U1820-30 compact stars to investigate their physical properties. By using observed values of the radius and mass of the considered compact stars, the unknown parameters are determined. We use a particular model of this theory to examine the behavior of energy density, pressure components, anisotropy, equation of state parameters and energy constraints in the interior of the proposed stellar objects. The Tolman–Oppenheimer–Volkoff equation is used to analyze the equilibrium state of these stars and causality condition, Herrera cracking method, adiabatic index methods are used to determine their stability. It is found that revolutionary technique sheds new light on the development of observationally accurate gravity model.

Large composite fermion effective mass at filling factor 5/2

The 5/2 fractional quantum Hall effect in the second Landau level of extremely clean two-dimensional electron gases has attracted much attention due to its topological order predicted to host quasiparticles that obey non-Abelian quantum statistics and could serve as a basis for fault-tolerant quantum computations. While previous works have establish the Fermi liquid (FL) nature of its putative composite fermion (CF) normal phase, little is known regarding its thermodynamics properties and as a result its effective mass is entirely unknown. Here, we report on time-resolved specific heat measurements at filling factor 5/2, and we examine the ratio of specific heat to temperature as a function of temperature. Combining these specific heat data with existing longitudinal thermopower data measuring the entropy in the clean limit we find that, unless a phase transition/crossover gives rise to large specific heat anomaly, both datasets point towards a large effective mass in the FL phase of CFs at 5/2. We estimate the effective-to-bare mass ratio m*/me to be ranging from ~ 2 to 4, which is two to three times larger than previously measured values in the first Landau level.

Relativistic model of anisotropic star with Bose–Einstein density depiction

In this article, we present a new model for anisotropic compact stars confined to physical dark matter (DM) based on the Bose–Einstein DM density profile and a bag model type equation of state (EoS). The obtained solutions are physically well-behaved and represent the physical and stable matter configuration by satisfying the energy conditions, causality conditions, and essential conditions on the stability factor and adiabatic index. The solutions supporting the matter sphere are in an equilibrium state by satisfying the generalized TOV equation. We also find the surface redshift, compactness parameter at the surface, maximum mass, and interestingly, all these values are under the desired range that makes our solution more physically viable. Here, the radially symmetric profiles of energy density, radial and transverse pressures are demonstrated.

A comprehensive study of Bardeen stars with conformal motion in f(G)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f({\\mathcal {G}})$$\\end{document} gravity

In this manuscript, we use the conformal killing vectors to solve the Einstein–Maxwell field equations in the background of modified f(G)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f({\\mathcal {G}})$$\\end{document} gravity. We consider the observational data for four different stars namely PSRJ1614-2230\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$PSR~J1614-2230$$\\end{document}, PSRJ1930+327\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$PSR ~J1930+327$$\\end{document}, CenX-3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Cen~X-3$$\\end{document} and VelaX-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Vela~X-1$$\\end{document} respectively. By using the data, we derive the physical parameters from the matching criteria using conformal killing vectors and the exterior Bardeen geometry. Furthermore, several physical properties of compact stellar structures are examined in order to achieve the physical validity and stability for considered models. The graphical analysis including energy density, pressure components, equation of state parameters, and energy conditions are examined. Moreover, the equilibrium conditions through Tolman–Oppenheimer–Volkoff equation and stability criteria through adiabatic index for the charged stellar structure study are investigated. It is worth noting that all of these compact objects are physically viable and stable under conformal motion in context of Bardeen geometry for two different models of f(G)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f({\\mathcal {G}})$$\\end{document} theory of gravity. Conclusively, the results show that f(G) gravity with Bardeen model may provide more massive stellar objects as compared to general relativity.

Effects of bulk viscosity, heat capacity ratio, and Prandtl number on the dispersion relationship of compressible flows

Here, we present the variation of the dispersion characteristics of the three-dimensional (3D) linearized compressible Navier–Stokes equation (NSE) to bulk viscosity ratio, specific heat ratio (γ), and Prandtl number (Pr). The 3D compressible NSE supports five types of waves, two vortical, one entropic, and two acoustic modes. While the vortical and entropic modes are non-dispersive, the acoustic modes are dispersive only up to a specific bifurcation wavenumber. We illustrate the characteristics and variation of relative (with respect to the vortical mode) diffusion coefficient for entropic and acoustic modes and a specially designed dispersion function for acoustic modes with depressed wavenumber η=KM/Re, the bulk viscosity ratio, γ, and Prandtl number Pr of the flow. Here, K, M, and Re denote the absolute wavenumber of disturbances, Mach number, and Reynolds number of the flow, respectively. At lower wavenumber components, the deviation of the dispersion function from the inviscid and adiabatic case is proportional to η2 at the leading order, and the relative diffusion coefficients increase linearly with bulk viscosity ratio and γ while varying inversely with Pr. With the increase in the bulk viscosity ratio, the shape and extent of the dispersion function alter significantly, and the change is more substantial for higher wavenumber components. The relative diffusion coefficient for entropic and acoustic modes shows contrasting variation with wavenumber depending upon bulk viscosity ratio, γ, and Pr. We also show by solving linearized compressible NSE that relatively significant evolution and radiation of acoustic and entropic disturbances occur when the bulk viscosity ratio is close to the corresponding critical value of maximum bifurcation wavenumber. Based on this criterion, we have presented an empirical relation for estimating bulk viscosity ratio depending upon γ and Pr, giving the corresponding range for obtaining relatively significant disturbance evolution.

Charged anisotropic compact stellar models under gravitational decoupling scheme

The aim of this paper is to obtain new physically admissible exact anisotropic stellar models via gravitational decoupling technique. This will be done by taking Korkina and Orlyanskii model solution as a seed solution and extend it to an anisotropic domain via gravitational decoupling through the minimal geometric deformation (MGD) approach. We analyze the physical properties of four compact star models Her [Formula: see text] (Mass [Formula: see text], [Formula: see text][Formula: see text]km), LMC [Formula: see text] ([Formula: see text], [Formula: see text][Formula: see text]km), PSR [Formula: see text] ([Formula: see text], [Formula: see text][Formula: see text]km) and PSR [Formula: see text] ([Formula: see text], [Formula: see text][Formula: see text]km). We demonstrate the stability conditions of the obtained solution by plotting energy conditions, velocity of sound, adiabatic index and all the thermodynamic parameters and equilibrium conditions via TOV equation, etc. We found that the results are physically well behaved and also fulfill the requirement of stability criteria inside the anisotropic fluid sphere. We study the physical features of the solutions in detail, analytically and graphically for the four compact stars Her [Formula: see text], LMC [Formula: see text], PSR [Formula: see text] and PSR [Formula: see text]. Based on the results we realized that the extended gravitational decoupling technique is very effective for the analysis of the interior of the compact stellar structures.

Constructing traversable wormhole solutions in [formula omitted] theory

This paper aims to explore the viable and stable geometry of traversable wormholes in the framework of f(R,Lm) theory. For this purpose, we build a shape function using the Karmarkar condition that determines the geometry of the wormhole. The resulting shape function meets all the fundamental requirements and successfully establishes a connection between two asymptotically flat regions of the spacetime. We then formulate the field equations corresponding to two different models of this theory, representing static spherically symmetric anisotropic fluid distribution. We also check feasibility of the obtained wormhole solutions by graphically analyzing the behavior of null energy conditions. Finally, we examine the stability of these solutions through the speed of sound and adiabatic index criteria. We conclude that both our resulting models are well-agreed with the requirements needed for the existence of wormholes for chosen parametric values.

Stellar structure modeling in Ricci-inverse gravity with Tolman–Kuchowicz spacetime

The primary objective of this research is to conduct an extensive investigation of stellar compact structures within the frame of the newly proposed Ricci-Inverse theory of gravity. The study utilizes the Tolman–Kuchowicz spacetime to explore these relativistic stars. In this work, we derive the modified field equations for a spherically symmetric line element with an isotropic matter distribution. To ensure physical validity, we consider appropriate expressions for the metric potentials i.e., ɛ=Br2+2ln(X) and ϑ=ln(1+ar2+br4). In order to determine the unknown parameters, we employ observational evidence from star models such as 4U1538−52, LMCX−4, EXO1785−248, 4U1820−30, and VelaX−1. Next, we examine and discuss the graphical behavior of several key parameters, including energy density and pressure, adiabatic index, equation of state, redshift function, and stability analysis. The observed behavior of these attributes aligns with accepted physical properties, and the emerging outcomes fall within the observed range. This demonstrates the viability of our proposed Ricci-Inverse gravity model.

Anisotropic compact stars admitting karmarkar condition in f(𝒬) theory

The major goal of this study is to examine the viability and stability of anisotropic compact stellar objects using the Karmarkar condition in [Formula: see text] gravity, where [Formula: see text] is a scalar of nonmetricity that explains gravitational effects. We consider a static spherical metric in inner and Schwarzschild spacetime in outer regions of the star to analyze the physical attribute of Vela [Formula: see text], SAX J 1808.4−3658, 4U 1608−52, PSR J0348+0432 and 4U 1820−30 compact stars. The unknown parameters are determined through observational values of the radius and mass of the considered compact stars. We take a specific model of this theory to evaluate the energy density, pressure elements, anisotropy, equation of state parameters and energy bounds in inner region of suggested stellar objects. The equilibrium position of these stars is examined through Tolman–Oppenheimer–Volkoff equation and their stability checked by Herrera cracking method and adiabatic index. We find more viable as well as stable compact stars in this modified theory.

Effect of Gas Type on Flow Characteristics in a Circuit Breaker under Cold Flow Scenario

This paper presents first stage of supersonic flow modelling in gas circuit breakers without an arc. Flow characterisation focused on shock and flow separation phenomenon. Velocity deceleration caused by shock will play a significant role in determining arc cooling performance and will impact thermal interruption capability. Gas properties such as specific heat ratio, density, and viscosity influenced the flow characteristics including shock location, strength and the flow separation process.

Experimental investigation on startup process of R290 air-source heat pump with different lubricants

The low density, small adiabatic index, and restricted charge of R290 result in different startup characteristics for R290 air-source heat pumps (ASHP) from that for HFCs ASHP. The research on the startup process of R290 refrigeration systems in the past has focused on system and compressor pressures, temperatures, changes in the bottom viscosity of the oil sump, and control strategies. There is a lack of research on the effect of lubricant types on the startup process, especially for R290 air-source heat pump. This paper experimentally measured and analyzed the changes in system temperatures and pressures as well as the changes in refrigerant concentration, concentration gradient, and mixture viscosity in the compressor oil sump during the startup process of R290 ASHP under different conditions, different startup types and with different lubricants. In addition, the oil discharge time, oil discharge, refrigerant mass in the compressor, and oil return time during the cold startup of LTH using PAG VG40 and MO VG100 were observed and clarified by installing transparent tubes and dismantling and weighing method. The experimental results showed that during the startup process, the mixture viscosity in the oil sump decreased and then increased, the refrigerant concentration increased and then reduced, and the refrigerant concentration gradient went from present to absent. The minimum viscosity was greater, the maximum concentration was smaller, and the low-viscosity duration was shorter for higher initial compressor temperature and with poorer miscible lubricants. PAG VG40 and MO VG100 showed good oil return performance.

Connection between Polytropic Index and Heating

The paper derives the one-to-one connecting relationships between plasma heating and its polytropic index, and addresses the consequences through the transport equation of temperature. Thermodynamic polytropic processes are classified in accordance to their polytropic index, the exponent of the power-law relationship of thermal pressure expressed with respect to density. These processes generalize the adiabatic one, where no heating is exchanged between the system and its environment. We show that, in addition to heating terms, the transport equation of temperature depends on the adiabatic index, instead of a general, nonadiabatic polytropic index, even when the plasma follows nonadiabatic processes. This is because all the information regarding the system's polytropic index is contained in the heating term, even for a nonconstant polytropic index. Moreover, the paper (i) defines the role of the polytropic index in the context of heating; (ii) clarifies the role of the nonadiabatic polytropic index in the transport equation of temperature; (iii) provides an alternative method for deriving the turbulent heating through the comparably simpler polytropic index path; and, finally, (iv) shows a one-component plasma proof-of-concept of this method and discusses the implications of such derived connecting relationships in the solar wind plasma in the heliosphere.

Thermodynamic effects of gas adiabatic index on cavitation bubble collapse

In this paper, an improved multicomponent lattice Boltzmann model is employed to investigate the impact of the gas properties, specifically the gas adiabatic index, on the thermodynamic effects of cavitation bubble collapse. The study focuses on analyzing the temperature evolution in the flow field and the resulting thermal effects on the surrounding wall. The accuracy of the developed model is verified through comparisons with analytical solutions of the Rayleigh-Plesset equation and the validation of the adiabatic law. Then, a thermodynamic model of cavitation bubble composed of two-mixed gases collapsing near a wall is established to explore the influence of the gas adiabatic index γ on the temperature behavior. Key findings include the observation that the γ affects the temperature of the first collapse significantly, while its influence on the second collapse is minimal. Additionally, the presence of low-temperature regions near the bubble surface during collapse impacts both bubble and wall temperatures. The study also demonstrates that the γ affects maximum and minimum wall temperatures. The results have implications for selecting specific non-condensable gas properties within cavitation bubbles for targeted cooling or heating purposes, including potential applications in electronic component cooling and environmental refrigeration.

Adiabatic collapse of non-homogeneous self-gravitating gas cloud

In this letter, we find the critical mass of a self-gravitating, spherically symmetric gas cloud, above which the fluid, within the bubble, collapses. Our analysis departs from a non-homogeneous equilibrium density, satisfying the Boltzmann relation. A time scale is defined in terms of the adiabatic index of the gas. Subsequently, a sinusoidal perturbation around equilibrium is regarded, thereby leading to a dispersion relation of frequency with wavelength, which does not depend on geometrical curvature effects. Such a formulation clearly justifies that the collapse occurs much faster than predicted by the well-known Jeans approach. The equilibrium profiles of the density, gravitational field, and potential are obtained as functions of the spherical radius coordinate at marginal instability. Since our theory captures the essential physics of gravitational collapse, it can be used as the starting point for several advancements in galactic dynamics.

Similarity solutions for cylindrical shock wave in a self-gravitating and rotating gas under the influence of monochromatic radiation and azimuthal or axial magnetic field by using Lie invariance method

Abstract The group invariance technique is used to investigate the similarity solution of one-dimensional, unsteady motion of cylindrically symmetric shock waves propagating in a rotating, axisymmetric perfect gas permeated with an azimuthal or axial magnetic field, under the effect of monochromatic radiation, with or without self-gravitational effects. The density is considered to be varying with radiation flux moving through the gas. Considering the absorption coefficient to be variable and choosing different values for the arbitrary constants appearing in infinitesimal generators, all possible cases of similarity solutions with shock paths following the power law and exponential law are discussed in detail, and numerical solutions for both the power law and exponential law path is obtained. The effect of changes in the Alfven–Mach number, density exponent, adiabatic index, gravitational, and rotational parameters on shock formation and shock strength has been obtained for both the power law and the exponential law. Further, the effect of all these parameters on the behaviour of flow variables behind the shock is investigated in detail and the results are depicted graphically via figures. It has been found during the study that, the strength of the shock reduces considerably with an increase in the Alfven–Mach number, rotational parameter and adiabatic index, and it increases with increase in density index and gravitational parameter. Various computations involved in this article are carried out by using the MATLAB software.

Comprehensive analysis of relativistic embedded class-I exponential compact spheres in f(R, ϕ) gravity via Karmarkar condition

In this article, we use the prominent Karmarkar condition to investigate some novel features of astronomical objects in the f(R, ϕ) gravity; R and ϕ represent the Ricci curvature and the scalar field, respectively. It is worth noting that we classify the exclusive set of modified field equations using the exponential type model of the f(R, ϕ) theory of gravity f(R, ϕ) = ϕ(R + α(e β R − 1)). We show the embedded class-I approach via a static, spherically symmetric spacetime with an anisotropic distribution. To accomplish our objective, we use a particular interpretation of metric potential (g rr ) that has already been given in the literature and then presume the Karmarkar condition to derive the second metric potential. We employ distinct compact stars to determine the values of unknown parameters emerging in metric potentials. To ensure the viability and consistency of our exponential model, we execute distinct physical evolutions, i.e. the graphical structure of energy density and pressure evolution, mass function, adiabatic index, stability, equilibrium, and energy conditions. Our investigation reveals that the observed anisotropic findings are physically appropriate and have the highest level of precision.