Guangqi: A 2D Radiation Hydrodynamic Code with Realistic Equations of State

In order to check the assumption of local thermal equilibrium in a transient plasma with kTe ∼ 4 eV and Ne ∼ 1017 cm−3, the electron temperature has been determined by measuring both the spectral line intensity ratio of He II 4686 Å to He I 5876 Å, and the laser light scattered by the plasma. The former method is strongly dependent on the local thermal equilibrium assumption, whereas, the latter method is independent of this assumption. These measurements were made on incident and reflected shock waves produced in an electromagnetic T-tube which had been prefilled with helium or hydrogen to a pressure of 0.5−1.0 Torr. Within the experimental uncertainty of ± 15%, the two electron temperatures agreed, indicating that the assumption of local thermal equilibrium used in the spectroscopic temperature determination is a reasonable approximation. Validity criteria for local thermal equilibrium given by Griem are examined for these conditions.

A numerical study of the thermally induced response of two widely used glass-filled polymer composites has been performed. This study was conducted using a newly developed mathematical model, which, unlike previous models, does not include the idealized assumption of local thermal equilibrium existing between the solid matrix and product gas. Experimentally determined volumetric heat transfer coefficients were used to characterize the rate of energy transfer between the two phases within the tortuous pore network of each material. These coefficients were introduced into the model in the form of a Nusselt number/Reynolds number correlation developed in this study. The results of the present investigation include solid temperature, product gas temperature, pyrolysis mass loss, pressure, gas mass flux, gas-storage ratio, and expansion and volumetric heat-transfer coefficient profiles. Material composition and processing were used to compare and contrast these results. Of particular interest, the deviation from thermal equilibrium in one material has been predicted to be as high as 500 °C. A general discussion on the effect of the assumption of local thermal equilibrium is presented based on preliminary findings.

The validity of the local thermal equilibrium assumption in the periodic free convection channel flow is investigated analytically. Two cases are considered where in the first case transverse conduction in the solid domain is included while in the second case transverse conduction in the fluid domain is included. The periodic disturbance in the free convection flow is due to a periodic thermal disturbance imposed on the channel walls. The Darcy–Brinkman model is used to model the flow inside the porous domain. It is found that four dimensionless parameters control the local thermal equilibrium assumption in the first case and five parameters control the local equilibrium assumption in the second case. The criteria that secure the validity of the local thermal equilibrium assumption are derived.

The composition, thermodynamic properties and transport coefficients of Ar – H 2 – Si and N 2 – H 2 – Si plasma within a temperature range of 300–30 000 K and pressure range of 0.1–10 atm are calculated under the assumptions of local thermal equilibrium (LTE) and local chemical equilibrium (LCE). Taking Debye–Hückel corrections into account, the chemical equilibrium composition and thermodynamic properties of these two plasma systems are derived using the mass action law and classical statistical thermodynamics respectively. The transport coefficients, including viscosity, conductivity, and thermal conductivity, are calculated using the Chapman–Enskog (C–E) method extended to a third-order approximation (second-order for viscosity and heavy particle translational thermal conductivity). Some of the results have been compared with those of other researchers, and there is a good level of agreement. The slight difference arises from the selection of interaction potential. The final calculation reveals that the introduction of silicon vapor significantly alters the thermodynamic properties and transport coefficients of Ar / N 2 – H 2 – Si plasma, even at a small concentration of silicon vapor (1%), the effect on the electrical conductivity cannot be ignored. Furthermore, our calculation results provide the fundamental data for numerical simulations of magnetohydrodynamics (MHD) for the synthesis of silicon nanoparticles and silicon composites.

A thermal model for nanosecond pulsed laser ablation of Cu in one dimension and in ambient gas, He at 1 atm, is proposed in which equations concerning heat conduction in the target and gas dynamics in the plume are solved. These equations are coupled to each other through the energy and mass balances at interface between the target and the vapor and also Knudsen layer conditions. By assumption of local thermal equilibrium, Saha–Eggert equations are used to investigate plasma formation. The shielding effect of the plasma, due to photoionization and inverse bremsstrahlung processes, is considered. Bremsstrahlung and blackbody radiation and spectral emissions of the plasma are also investigated. Spatial and temporal distribution of the target temperature, number densities of Cu and He, pressure and temperature of the plume, bremsstrahlung and blackbody radiation, and also spectral emissions of Cu at three wavelengths (510, 516, and 521 nm) are obtained. Results show that the spectral power of Cu lines has the same pattern as CuI relative intensities from National Institute of Standard and Technology. Investigation of spatially integrated bremsstrahlung and blackbody radiation, and also Cu spectral emissions indicates that although in early times the bremsstrahlung radiation dominates the two other radiations, the Copper spectral emission is the dominant radiation in later times. It should be mentioned that the blackbody radiation has the least values in both time intervals. The results can be used for prediction of the optimum time and position of the spectral line emission, which is applicable in some time resolved spectroscopic techniques such as laser induced breakdown spectroscopy. Furthermore, the results suggest that for distinguishing between the spectral emission and the bremsstrahlung radiation, a spatially resolved spectroscopy can be used instead of the time resolved one.

Purpose This study aims to numerically explore natural convection and latent heat transfer in a square porous cavity filled with a H2O/nano-encapsulated phase change material (NEPCM) mixture. Particular attention is paid to the influence of cavity geometry, block inclination and wall undulations on heat transfer and melting behavior. Design/methodology/approach This setup includes a central, inclined, heated elliptical block and features a corrugated cold wall. The dimensionless governing equations under the local thermal equilibrium (LTE) assumption are solved using the Galerkin-based finite element method. An exhaustive parametric analysis is conducted to evaluate the influence of main parameters, including Rayleigh number (103–106), Darcy number (10−5–10−1), Stefan number (Ste) (0.2–1), porosity (0.1–0.9), nanoparticle volume fraction (0%–5%), fusion temperature (0.05–0.95), block tilt angle (0° – 180°) and wall undulation shape (sinusoidal, triangular and rectangular). Selected validations were adopted to ascertain simulation accuracy and consistency. Findings It turned out that increasing specific settings is the keynote to improving or mitigating the average Nusselt number (Nuavg). The findings highlighted that higher Rayleigh and Darcy numbers, as well as porosity and nanoparticles’ volume fraction, improve the Nuavg, while a greater Ste mitigates thermal performance due to slower melting. An optimal fusion temperature is identified where latent heat absorption is maximized. Tilt angles close to 90° improve vortex formation and heat transfer efficiency. In terms of thermal performance, sinusoidal and triangular wall geometries outperform rectangular geometries, especially for low undulations. Furthermore, this numerical study seems germane to latent thermal energy storage systems. Research limitations/implications Future research could further explore thermal systems involving phase change and porous structures under additional factors, either by adding nanomaterials, encapsulating phase change materials, other boundary conditions or redesigning heat transfer surfaces to further improve their thermal performance. Practical implications The geometric configuration considered herein has practical applications in different engineering sectors, such as solar energy, waste heat recovery from building materials, advanced electronics, cooling technologies, fuel cells, mixing processes and even nuclear energy and many more. Originality/value To the best of the authors’ knowledge, this work is the first to provide new insights into the coupled effects of porous structures, latent heat storage and cavity geometry on the natural convection of H2O–NEPCM mixture in a cavity characterized by the Darcy–Brinkman model and the LTE assumption. The study of such a mixture in such a little-explored configuration revealed strong thermal interactions between conduction, convection and phase change. The obtained findings deal useful guidelines for the design of advanced passive cooling and high-efficiency latent heat energy storage systems.

Effect of rotation on Brinkman-Bénard convection of a Newtonian nanoliquid using local thermal non-equilibrium model

Despite its widespread use, there are no universally established guidelines for determining when the local thermal equilibrium (LTE) assumption is applicable, leading to inconsistencies in porous media heat transfer modeling. To address this gap, this study conducted a comprehensive numerical analysis using critical parameters such as the flow rate, permeability, and thermal diffusivity ratio of hydrodynamic and thermal characteristics. Using the Darcy-Forchheimer-Brinkman model, simulations were conducted for a wide range of Reynolds numbers (1 to 1000), Darcy numbers (10<sup>-6</sup> to 10<sup>0</sup>), and thermal diffusivity ratios (10<sup>-3</sup> to 10<sup>3</sup>) to assess thermal behavior with both the LTNE and LTE approaches. The results indicated that, at low Reynolds numbers (Re ≤ 10), significant temperature differences existed between the solid and fluid phases, implying a dominant LTNE regime. However, as the Reynolds number increased beyond Re ≈ 100, enhanced convective effects facilitated better thermal coupling, validating the LTE assumption. The Darcy number significantly influenced thermal dispersion, with low Da (≤ 10<sup>-6</sup>) enhancing mixing and promoting LTE while high Da (≥ 10<sup>0</sup>) restricted thermal interaction due to boundary layer formation. The impact of the thermal diffusivity ratio was most pronounced at low Re, where a high value (≥ 10<sup>3</sup>) led to significant thermal disequilibrium due to the solid's high conduction capability relative to the fluid. However, at high Re (≥ 1000), convection dominated, making LTE applicable across a wide range of TDR values. By systematically mapping the LTE-LTNE transition across a broad parametric space, this study provides a novel framework for assessing the applicability of the LTE assumption.

The performance of solar updraft tower investigates numerically by comparing between two solar collectors with and without porous absorber flat plate. In this study, copper metal foam (10 and 40) PPI at the same porosity (0.9) are used as an absorber plate. The effect of the absorbing porous medium is studied to increase the air flow towards the updraft tower by tilting of the porous absorber at an angle (2° and 6°) from the horizontal line for (10 and 40) PPI and compared with the horizontal absorber flat plate. To simulate the physical quantities inside the porous medium, at steady state, symmetry, three dimensional, Darcy model and energy numerical model with local thermal equilibrium (LTE) assumption are adopted and numerical models is approximated by a RNG (Re-Normalization Group) k- ϵ turbulent model and discrete ordinates (DO) radiation model equations. The numerical study is analyzed by Fluent software package (version 18.2) to solve the governing equations. The results showed that the tilting of a porous absorber plate at an angle (2° and 6°) from the horizontal line lead to increase in the mass flow rate inside the solar updraft tower and the maximum performance is found by using 40 PPI at tilt angle 2°.The performance of solar updraft tower investigates numerically by comparing between two solar collectors with and without porous absorber flat plate. In this study, copper metal foam (10 and 40) PPI at the same porosity (0.9) are used as an absorber plate. The effect of the absorbing porous medium is studied to increase the air flow towards the updraft tower by tilting of the porous absorber at an angle (2° and 6°) from the horizontal line for (10 and 40) PPI and compared with the horizontal absorber flat plate. To simulate the physical quantities inside the porous medium, at steady state, symmetry, three dimensional, Darcy model and energy numerical model with local thermal equilibrium (LTE) assumption are adopted and numerical models is approximated by a RNG (Re-Normalization Group) k- ϵ turbulent model and discrete ordinates (DO) radiation model equations. The numerical study is analyzed by Fluent software package (version 18.2) to solve the governing equations. The results showed that the tilting of a porous absorber plate at an angle (2° and 6°) from the horizontal line lead to increase in the mass flow rate inside the solar updraft tower and the maximum performance is found by using 40 PPI at tilt angle 2°.

The local thermal equilibrium assumption in the transient natural convection channel flow is investigated numerically. The Darcy–Brinkman–Forchheimer model is used to model the flow inside the porous domain. The effect of different parameters on the validity of the local thermal equilibrium assumption is examined. It is found that the volumetric Nusselt number has the most significant effect on the local thermal equilibrium assumption.

\n We present calculations of quasi-equilibrium sequences\nof irrotational binary neutron stars based on realistic equations of state (EOS) for the whole neutron star interior. Three realistic nuclear EOSs of various softness and\nbased on different microscopic models have been joined with a recent\nrealistic EOS of the crust, giving in this way three different\nEOSs of a neutron-star interior. Computations of quasi-equilibrium\nsequences are performed within the Isenberg-Wilson-Mathews\napproximation to general relativity. For all evolutionary sequences,\nthe innermost stable circular orbit (ISCO) is found to be given \nby mass-shedding limit (Roche lobe overflow). \nThe EOS dependence on the last orbits is found to be quite important:\nfor two $1.35~M_{\\odot}$ neutron stars, the gravitational wave frequency at the ISCO (which\nmarks the end of the inspiral phase) ranges from 800 Hz to \n1200 Hz, depending upon the EOS. Detailed comparisons with 3rd order\npost-Newtonian results for point-mass binaries reveals a very good agreement until hydrodynamical effects (dominated by high-order functions of frequency) become important, \nwhich occurs at a frequency ranging from 500 Hz to 1050 Hz, \ndepending upon the EOS.\n \n \n

The assumption of local thermal equilibrium (LTE) between solid and fluid phases commonly is used for studies of heat transfer in saturated soil and is valid for a wide range of conditions. However, for certain conditions, the heat transfer process may give rise to local thermal nonequilibrium (LTNE) in which adjacent solid and fluid phases have different temperatures. This note presents the results of a numerical study of the validity of the LTE assumption for one-dimensional heat transfer in a saturated soil layer with fluid flow. For the conditions investigated, the LTE assumption holds for soil with particle sizes smaller than the gravel range. For soil with particles sizes in the gravel range and larger, the LTE assumption may be valid or invalid, depending primarily on fluid discharge velocity, with higher fluid velocity values more likely to produce LTNE conditions.

Under the assumption of local thermal equilibrium, a numerical algorithm is proposed to find the equation of state for laser-induced plasmas (LIPs) in which chemical reactions are permitted in addition to ionization processes. The Coulomb interaction in plasma is accounted for by the Debye–Huckel method. The algorithm is used to calculate the equation of state for LIPs containing carbon, silicon, nitrogen, and argon. The equilibrium reaction constants are calculated using the latest experimental and ab initio data of spectroscopic constants for the molecules $$\hbox {N}_2, \hbox {C}_2, \hbox {Si}_2, \hbox {CN}, \hbox {SiN}, \hbox {SiC}$$ and their ions. The algorithm is incorporated into a fluid dynamic numerical model based on the Navier–Stokes equations describing an expansion of LIP plumes into an ambient gas. The dynamics of LIP plumes obtained by the ablation of SiC, solid silicon, or solid carbon in an ambient gas containing $$\hbox {N}_2$$ and Ar is simulated to study formation of molecules and molecular ions.

Heavy-quark (HQ) transport coefficients have been estimated for a viscous quark–gluon plasma (QGP) medium, utilizing a recently proposed quasi-particle description based on a realistic QGP equation of state (EoS). Interactions entering through the EoS significantly suppress the temperature dependence of the drag coefficient of QGP, compared to those of an ideal relativistic system of quarks and gluons. The inclusion of shear and bulk viscosities through the corrections to the thermal phase space factors of the bath particles alters the magnitude of the drag coefficient; the enhancement is significant at lower temperatures. In the competition between the effects of the EoS and dissipative corrections through phase space factors, the former eventually dictate how the drag coefficient would behave as a function of temperature and how much it quantitatively digresses from the ideal case. The observations suggest a significant impact of both the realistic EoS and the viscosities on the HQs transport at Relativistic Heavy Ion Collider and Large Hadron Collider collision energies.

The validity of the local thermal equilibrium assumption in the periodic forced convection porous channel flow is investigated analytically. Closed form expressions are presented for the temperatures of the fluid and solid domains and for the criterion that ensures the validity of the local thermal equilibrium assumption. It is found that four dimensionless parameters control the local thermal equilibrium assumption. These parameters are the porous domain void fraction ∈, the volumetric Biot number Bi, the dimensionless frequency ω, and the solid-to-fluid total thermal capacity ratio CR. The criterion that secures the validity of the local thermal equilibrium assumption within 5% error, is found to be...