Hard gluon evolution in warming medium

We describe the energy distribution of hard gluons travelling through a dense quark–gluon plasma whose temperature increases linearly with time, within a probabilistic perturbative approach. The results were applied to the thermalization problem in heavy ion collisions. In the weak coupling picture this thermalization occurs from “the bottom up”: high energy partons, formed early in the collision, radiate low energy gluons which then proceed to equilibrate among themselves, forming a thermal bath that brings the high energy sector to equilibrium. We see that, in this scenario, the dynamic we describe must set in around $$t \sim 0.5$$ t ∼ 0.5 fm/c after the collision in order to reach a fully thermalized state at $$t \sim 1$$ t ∼ 1 fm/c. We then look at the entropy density and average temperature of the soft thermal bath, as the system approaches (local) thermal equilibrium.

Natural Convection in Annulus Between Two Concentric Cylinders Partially Filled with Metal Foam Distributed with New Suggested Design

The investigation of natural convection in an annular space between two concentric cylinders partially filled with metal foam is introduced numerically. The metal foam is inserted with a new suggested design that includes the distribution of metal foam in the annular space, not only in the redial direction, but also with the angular direction. Temperatures of inner and outer cylinders are maintained at constant value in which inner cylinder temperature is higher than the outer one. Naiver Stokes equation with Boussinesq approximation is used for fluid regime while Brinkman-Forchheimer Darcy model used for metal foam. In addition, the local thermal equilibrium condition in the energy equation of the porous media is presumed to be applicable for the present investigation. CFD ANSYS FLUENT software package (version 18.2) is used as a solver to this problem. Various parameters are examined; Rayleigh number, Darcy number, and thermal conductivity ratio to study the effect of them on fluid flow and heat transfer inside the annuli space in the suggested design of metal foam layer. current model is compared with the available published results and good agreement is noticed. Results showed that as Rayleigh number increases the dominated of convection mode increases and Nusselt increases. Also, Nusselt is larger at the higher Darcy and thermal conductivity ratio. It was found that at Rayleigh of 106 and thermal conductivity ratio of 104 Nusselt reach its higher value which is 6.69 for Darcy of 0.1 and 6.77 for Darcy of 0.001. A comparison between this design and the traditional design was established for Darcy 0.001 and thermal conductivity ratio 102, and its showed a good enhancement in Nusselt number and the greatest enhancement percentage was 44% at Rayleigh equal 5*104 while the lowest percentage is 6% for Rayleigh equal106.

Thermal non-equilibrium of porous flow in a resting matrix applicable to melt migration: a parametric study

Fluid flow through rock occurs in many geological settings on different scales, at different temperature conditions and with different flow velocities. Depending on these conditions the fluid will be in local thermal equilibrium with the host rock or not. To explore the physical parameters controlling thermal non-equilibrium the coupled heat equations for fluid and solid phases are formulated for a fluid migrating through a resting porous solid by Darcy flow. By non-dimensionalizing the equations three non-dimensional numbers can be identified controlling thermal non-equilibrium: the Peclet number Pe describing the fluid velocity, the heat transfer number A describing the local interfacial heat transfer from the fluid to the solid, and the porosity ϕ. The equations are solved numerically for the fluid and solid temperature evolution for a simple 1D model setup with constant flow velocity. Three stages are observed: a transient stage followed by a stage with maximum non-equilibrium fluid to solid temperature difference, ∆Tmax, and a stage approaching the steady state. A simplified time-independent ordinary differential equation for depth-dependent (Tf – Ts) is derived and analytically solved. From these solutions simple scaling laws of the form (Tf – Ts) = f (Pe, A, ϕ, H), where H is the non-dimensional model height, are derived. The solutions for ∆Tmax and the scaling laws are in good agreement with the numerical solutions. The parameter space Pe, A, ϕ, H is systematically explored. In the Pe – A – parameter space three regimes can be identified: 1) at high Pe (> 1) strong thermal non-equilibrium develops independently of Pe and A; 2) at low Pe (< 1) and low A (< 1) non-equilibrium decreases proportional to decreasing Pe; 3) at low Pe (<1) and large A (>1) non-equilbrium scales with Pe/A and thus becomes unimportant. The porosity ϕ has only a minor effect on thermal non-equilibrium. The time scales for reaching thermal non-equilibrium scale with the advective time-scale in the high Pe-regime and with the interfacial diffusion time in the other two low Pe – regimes. Applying the results to natural magmatic systems such as mid-ocean ridges can be done by estimating appropriate orders of Pe and A. Plotting such typical ranges in the Pe – A regime diagram reveals that a) interstitial melt flow is in thermal equilibrium, b) melt channelling as e.g. revealed by dunite channels may reach moderate thermal non-equilibrium, and c) the dyke regime is at full thermal non-equilibrium.

Boundary Value Problems of Thermoelasticity for Porous Sphere and for A Space with Spherical Cavity

This article is concerned with the coupled linear quasi-static theory of thermoelasticity for porous materials under local thermal equilibrium. The system of equations is based on the constitutive equations, Darcy's law of the flow of a fluid through a porous medium, Fourier's law of heat conduction, the equations of equilibrium, fluid mass conservation and heat transfer. The system of governing equations is expressed in terms of displacement vector field, the change of volume fraction of pores, the change of fluid pressure in pore network and the variation of temperature of porous material. The present paper is devoted to construct explicit solutions of the quasi-static boundary value problems (BVPs) of coupled theory of thermoelasticity for a porous elastic sphere and for a space with a spherical cavity. In this research the regular solution of the system of equations for an isotropic porous material is constructed by means of the elementary (harmonic, bi-harmonic and meta-harmonic) functions. The basic boundary value problems (the Dirichlet type boundary value problem for a sphere and the Neumann type boundary value problem for a space with a spherical cavity) are solved explicitly. The obtained solutions are given by means of the harmonic, bi-harmonic and meta-harmonic functions. For the harmonic functions the Poisson type formulas are obtained. The bi-harmonic and meta-harmonic functions are presented as absolutely and uniformly convergent series.

Legitimacy of the Local Thermal Equilibrium Hypothesis in Porous Media: A Comprehensive Review

Local thermal equilibrium (LTE) is a frequently-employed hypothesis when analysing convection heat transfer in porous media. However, investigation of the non-equilibrium phenomenon exhibits that such hypothesis is typically not true for many circumstances such as rapid cooling or heating, and in industrial applications involving immediate transient thermal response, leading to a lack of local thermal equilibrium (LTE). Therefore, for the sake of appropriately conduct the technological process, it has become necessary to examine the validity of the LTE assumption before deciding which energy model should be used. Indeed, the legitimacy of the LTE hypothesis has been widely investigated in different applications and different modes of heat transfer, and many criteria have been developed. This paper summarises the studies that investigated this hypothesis in forced, free, and mixed convection, and presents the appropriate circumstances that can make the LTE hypothesis to be valid. For example, in forced convection, the literature shows that this hypothesis is valid for lower Darcy number, lower Reynolds number, lower Prandtl number, and/or lower solid phase thermal conductivity; however, it becomes invalid for higher effective fluid thermal conductivity and/or lower interstitial heat transfer coefficient.

Effect of concentric and eccentric porous layer on forced convection heat transfer and fluid flow around a solid cylinder

In this paper, heat transfer and fluid flow around a solid cylinder wrapped with a porous layer in the channel were studied numerically by computational fluid dynamics (CFD). The homogeneous concentric and eccentric porous medium round a rigid, solid cylinder are supposed at local thermal equilibrium. The transport phenomena within the porous layer, volume averaged equations were employed, however the conservation laws of mass, momentum and energy were applied in the channel. This current numerical analysis, the effects of eccentricity ( ), the variable diameter of porous layer (d=0.07,0.08,0.09), permeability, as well as the different Reynolds number and Darcy number on the heat transfer parameters and fluid flow was investigated. The main purpose of this study is analyzed and compared the heat flux of concentric and eccentric porous layer in Reynolds number range of 1 to 40 and Darcy numbers of to . It is found that with the decline of Darcy number, the vortex length is increased behind the solid cylinder surface. In addition, the heat flux rate of the cylinder is raised with the increase of Reynolds number. Finally, The results have demonstrated that with raising Reynolds and Darcy numbers, the increase of the average Nusselt numbers in the eccentric porous layer is higher than the concentric porous layer.

Precise Measurements of CH Maser Emission and Its Abundance in Translucent Clouds

We present high-sensitivity CH 9 cm ON/OFF observations toward 18 extragalactic continuum sources that have been detected with OH 18 cm absorption in the Millennium survey with the Arecibo telescope. CH emission was detected toward 6 of the 18 sources. The excitation temperature of CH has been derived directly through analyzing all detected ON and OFF velocity components. The excitation temperature of CH 3335 MHz transition ranges from −54.5 to −0.4 K and roughly follows a log-normal distribution peaking within [−5, 0] K, which implies overestimation by 20% to more than 10 times during calculating CH column density by assuming the conventional value of −60 or −10 K. Furthermore, the column density of CH would be underestimated by a factor of 1.32 ± 0.03 when adopting local thermal equilibrium assumption instead of using the CH three hyperfine transitions. We found a correlation between the column density of CH and OH following log N(CH) = (1.80 ± 0.49) and log N(OH −11.59 ± 6.87. The linear correlation between the column density of CH and H2 is consistent with that derived from visible wavelengths studies, confirming that CH is one of the best tracers of H2 components in diffuse molecular gas.

Investigation of Shielding Effects on Picosecond Laser-Induced Copper Plasma Characteristics under Different Focusing Distances

In traditional laser-induced breakdown spectroscopy (LIBS) applications, the line intensity and analysis capability are susceptible to plasma shielding. To investigate the shielding effects on the characteristics of Cu plasma in air, a ~120-picosecond laser with a wavelength of 1064 nm was employed to produce plasma. The plasma temperature and electron density were calculated under the condition of local thermal equilibrium (LTE) and optically thin, while the relationships between the line intensity, plasma temperature and electron density were analyzed. Moreover, the LTE condition was validated by the McWhirter relation, plasma relaxation time and diffusion length, and the optically thin condition was observed through the variation in line intensity. The results indicated that when the focal point was below the target surface, the plasma shielding was the weakest, and the highest line intensity could be obtained. In addition, there was a positive correlation between the increased plasma temperature and the degree of shielding effect. When the focal point was above the target surface, the high-irradiance pulse directly broke down the free air and produced a shock wave. Under the high pressure of the over-heated shock wave, the line intensity, plasma temperature and electron density increased again. This study provides an important insight into the experiments and applications of picosecond LIBS.

Comparison of Numerical Models of Flow and Heat Transfer Through Porous Medium in a Vertical Channel

Porous medium modelling technique has opened up ways for number of numerical studies to investigate the performance of many devices that involve heat exchanging process. Such modelling technique not only avoids huge cost and time as compared to experimental analysis but also makes computationally less time-consuming as in case of numerical simulation by exact geometry modelling of porous materials. In this regard the present paper analyses two different thermal models namely local thermal equilibrium model and local thermal non equilibrium model along with two different flow models namely Darcy flow model and Darcy extended Forchheimer model. Suitability of the mentioned models in predicting heat transfer through metal foam and wire mesh porous medium is examined subjected to variations in structural aspects of the porous medium that could be primarily represented by variation in porosity and pore density. For this purpose, a vertical channel subjected to constant heat flux capable of housing porous medium reported in literature is numerically modelled and air flow is numerically simulated through the channel. A variety of structural configuration (combination of different porosity and pore density) of the mentioned porous media are considered and among the mentioned flow and thermal models, best suited models for predicting flow and heat transfer through such medium are identified with appropriate justifications. It is revealed from the present study that, Darcy-Forchheimer and LTNE models are best suited to predict flow and heat transfer through porous media than the basic Darcy and LTE models.

Measuring the Thermal De-Broglie Wavelength in Laser-produced Plasma of different Samples of Writing Inks Elements Using LIBS Spectroscopy

In this paper, the technique of laser pulse breakdown spectroscopy (LIBS) under the influence of the pulse Nd:YAG laser of 1064nm wavelength and with a pulse time of 10ns was used on different samples of writing ink models. In this work, the de-Broglie wavelength was measured. After calculating the electron temperature and assuming the local thermal equilibrium conditions (LTE), and using a spectral detector model (View spectra 2100) within the spectral range (200nm-900nm), the results after performing the analysis showed differences in the D-Broglie thermal wavelength of the plasma. The formation and temperature of the electron, which can be applied in plasma spectroscopy processes in many sciences, including the field of forensic evidence, to detect forgery in documents and documents.