Local Thermal Equilibrium Assumption Research Articles

Calculation of thermodynamic properties and transport coefficients of Ar/N2–H2–Si plasma

Abstract 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.

Linear and weakly nonlinear analyses of double‐diffusive convection in porous media with chemical reaction using LTNE model

AbstractThe onset of convection in a horizontal porous layer with chemical reaction and local thermal nonequilibrium is investigated. The nondimensional governing equations have been solved using the normal mode technique, which results in an eigenvalue problem. The analytical expressions for both stationary and oscillatory Rayleigh numbers are obtained. The effect of different parameters has been investigated and presented. The amplitude equation is derived using weakly nonlinear theory. Nusselt number is calculated using an amplitude equation to investigate heat transport. When modeling a fluid‐saturated porous medium, previous research on double‐diffusive convection has uniformly operated under the assumption of local thermal equilibrium (LTE) between the fluid and solid phases at all points within the medium. This standard practice assumes a minimal temperature gradient between the phases at any given location. However, in practical scenarios involving high‐speed flows or significant temperature differentials between the fluid and solid phases, the LTE assumption proves insufficient.

Natural convection of water-based nanofluids in three-dimensional enclosures

The single-phase approach, in which nanofluids are treated as pure fluids assuming that the solid and liquid phases are in local thermal and hydrodynamic equilibrium, has been used with good results to simulate forced convection flows. Conversely, its extension to natural convection has revealed to be more problematic, as the obtained numerical results are substantially different from the experimental data, mainly due to the effects of the slip motion occurring between the suspended nanoparticles and the base liquid, whose consequent nonuniform distribution of the solid phase concentration can significantly affect both heat and momentum transfer. In the present article, a two-phase model based on a double-diffusive approach is proposed to study the natural convection flows of water-based metal oxide nanofluids inside cylindrical and rectangular enclosures heated and cooled at their opposite sides with the scope to reproduce a number of experimental data-sets available in the literature. Given the assumption of local thermal equilibrium between nanoparticles and host liquid, and considering the Brownian and thermophoretic diffusion as responsible for causing significant relative velocity between the solid and liquid phases, the governing equations are solved by a control-volume numerical method implemented using the open-source platform OpenFOAM (Open Field Operation and Manipulation). It has been found that the nanoparticle diffusion gives the major contribution to the decrease of the heat transfer rate red usually observed experimentally in natural convection flows of nanofluids inside differentially-heated enclosures. This means that a two-phase model, in conjunction with proper correlations for the evaluation of the nanofluid effective physical properties, must be necessarily enforced to obtain reliable results for many engineering applications.

Bubble-wall velocity in local thermal equilibrium: hydrodynamical simulations vs analytical treatment

We perform real-time hydrodynamical simulations of the growth of bubbles formed during cosmological first-order phase transitions under the assumption of local thermal equilibrium. We confirm that pure hydrodynamic backreaction can lead to steady-state expansion and that bubble-wall velocity in such case agrees very well with the analytical estimates. However, this is not the generic outcome. Instead, it is much more common to observe runaways, as the early-stage dynamics right after the nucleation allow the bubble walls to achieve supersonic velocities before the heated fluid shell in front of the bubble is formed. This effect is not captured by other methods of calculation of the bubble-wall velocity which assume stationary solutions to exist at all times and would have a crucial impact on the possible generation of both baryon asymmetry and gravitational wave signals.

Thermal lattice Boltzmann approach-based numerical study of nanofluid magnetohydrodynamic forced convection in a back-facing stepped porous channel

Unsteady laminar magnetohydrodynamic forced convection and entropy generation inside a backward-facing step (BFS) porous channel with Cu-H2O nanofluid under a tilted magnetic field is numerically handled using a thermal lattice Boltzmann method (TLBM) with two distribution functions. The Darcy-Brinkman-Forchheimer (DBF) equations filled up with the energy equation (with local thermal equilibrium assumption) have been drawn up as the governing equations model. Their numerical solutions unveiled streamlines, Nusselt number, pumping power, performance index and entropy generation, and impacts of influential parameters (Hartmann number (Ha = 0; 10; 20; 100, 200), Darcy number (Da = 10−3; 10−2; 10−1), magnetic tilt angle (γ = 0, π∕4, π∕2), nanoparticles’ volume fraction (φ = 1 − 4%), medium porosity (ε = 0.6, 0.7, 0.8). The irreversibility analysis is also addressed to highlight the flow behavior. Regarding the validation of the modeling approach deemed, a consensus has been achieved with results available in the literature. Computations revealed that the volume fraction provides a fair performance rating with moderate pumping power. Likewise, the average Nusselt number, the average entropy generation, the pumping power and the performance index have a direct relationship with the Hartmann number, the nanoparticles volume fraction and the magnetic field tilt. Moreover, it can be stated the Cu-H2O nanofluid that seems worthwhile in terms of heat transfer efficiency compared to other examined nanofluids. Entropy generation due to the magnetic field was identified as the main source of irreversibility processes in all cases. Based on the outcomes, it is thought that applying a magnetic field can help minimize entropy generation in practical applications.

Melting performance analysis of finned metal foam thermal energy storage tube under steady rotation

The latent heat thermal energy storage (LHTES) technology based on solid-liquid phase change material (PCM) is of great significance for the efficient utilization of thermal energy. To address the issues of slow thermal response and non-uniform melting of the LHTES technology, a hybrid heat transfer enhancement method combined with finned metal foam and steady rotation is proposed in this work. An enthalpy-porosity model considering non-Darcy porous effects and mechanical rotation is established based on the local thermal equilibrium assumption and the fixed grid system. Four different structures (uniform metal foam, graded metal foam, finned metal foam with uniform porosity, and finned metal foam with graded porosity) are investigated firstly to identify the optimal structural arrangement under the same volume of PCM. Numerical results demonstrate that the LHTES units strengthened by the finned metal foam with graded porosity achieve the shortest melting time and largest thermal energy storage rate (TESR). The graded porous structure reduces thermal resistance, rotation enhances flow and heat transfer inside the container, and the fins expand the heat source area. Moreover, the effect of different fin types, graded porosities, and rotational speeds are further considered. The findings suggest that the increase of these three parameters does not correspond to better thermal performance; instead, there is an optimal value. Compared with the base case, the optimal configuration (fin length of 20 mm, fin width of 1.5 mm, porosity gradient of 2%, and rotational speed of 0.5 rpm) can shorten the melting time by 46.68%, increase the TESR and Nu by 74.06% and 69.02%, respectively. This paper validates the feasibility of the hybrid heat transfer enhancement method with finned metal foam and steady rotation, which can offer new insights into the engineering practice of the LHTES technology.

A novel numerical method to evaluate the heat transfer characteristics of complicated CICC structures

In this article, we propose a numerical model for calculating the external heat transfer coefficient between the bundle region and its wall for cables in conduit conductor (CICC). With the assumption of local thermal equilibrium, one macro equation describing the steady heat transfer on the cross section of the CICC can be obtained. A key parameter, the effective transverse thermal conductivity keff, which takes the contribution of both strands and flowing fluid into consideration, is introduced. To calculate the effective transverse thermal conductivity keff, we first obtain the true distribution of different phases (fluid, copper and superconducting material) on a cross section of CICC with the help of the image recognition technique. Based on this, the value of the effective transverse thermal conductivity keff can be calculated numerically. Due to the large difference among the component thermal conductivities (at 4.5 K, typical values of the thermal conductivity of liquid helium, superconducting material and copper are kHe=0.024Wm−1K−1, kNb3Sn=0.04Wm−1K−1 and kCu=708Wm−1K−1; and the maximal ratio of thermal conductivity can be as high as about 30,000), the high-performance finite analytical method (FAM) is recommended to calculate keff. After obtaining the effective transverse thermal conductivity keff of the bundle region, the heat transfer coefficient can be calculated directly by solving a simple Poisson equation under proper boundary conditions. Two case studies are performed, including the JT-60 Super Advanced (JT-60SA) CICC and the dual channel International Thermonuclear Experimental Reactor, Toroidal Field Performance Sample (ITER-TFPS). The calculated values of heat transfer coefficient are consistent with the experimental results, which verifies our proposed model.

Local thermal equilibrium constraints for energy transport equations for thermal oil recovery processes

The mathematical framework of reservoir thermal simulators typically relies on the assumption of local thermal equilibrium (LTE) when modeling energy transport through porous media for petroleum engineering applications, including Thermal Enhanced Oil Recovery (TEOR) processes. The LTE presupposes instantaneous exchange of energy between the injected hot fluids and the reservoir's rock and fluids. Nevertheless, it is essential to acknowledge that LTE's validity becomes questionable in specific scenarios, potentially resulting in an overestimation of oil recovery, e.g., when high fluid velocities arise. Under such conditions, the local thermal non-equilibrium (LTNE) formulation may offer a more accurate representation of the energy transport physics. In this study, we present the physical constraints that must be satisfied for the application of two distinct mathematical formulations (1) the one-equation model for the fluids and rock as a whole (LTE is assumed), and (2) the two-equation model, one equation assigned to the fluids and another one to the rock (pseudo-LTNE is assumed). Such constraints were derived by examining conductive and convective heat transport properties via the theory of the method of volume averaging, specifically applied to an oil-water-gas-rock system at the pore scale. It was found that the one-equation model requires that 18 physical constraints to be satisfied, while the pseudo-LTNE model needs to fulfill 9 physical constraints. A sensitivity analysis was conducted based on factor upon which accumulation, conduction and convection constraint equations depend, aiming to identify the conditions under which LTNE occurs within the porous medium. These influencing factors encompass the characteristic time, the Peclet number, the presence of external heat sources, the distribution of phases at the pore-scale, and the disparity between rock and fluid properties. The combinations of these factors can induce the existence of local thermal non-equilibrium. One significant property is the heat transfer coefficient in the reservoir. We recommend that the pseudo-LTNE approach is reliable as long as the rock-fluid heat transfer coefficients are at least one order of magnitude larger than the fluid-fluid heat transfer coefficients (1000−10000W/(m3K)). Contrarily, the OEM should be employed only when the heat transfer coefficients surpass a threshold value of 10000W/(m3K). When injector and producer wells are hydraulically interconnected, resulting in heightened fluid velocities, it is encouraged the use of the two-equations model. The predictability and reliability of the energy models were verified by comparison of predicted oil recovery against data from laboratory experiments. The equations presented in this study consistently demonstrate their utility in assessing the reliability of energy transport models for TEOR scenarios.

Prediction and control of elevated temperatures within landfills under aeration and recirculation based on the thermal non-equilibrium model

Aeration is an effective approach to sustainable landfilling but may lead to elevated temperatures within landfills, resulting in landfill fires or explosions. Therefore, aeration is usually combined with leachate recirculation to control the elevated temperatures within landfills. To predict landfill temperatures during aeration and recirculation, a local thermal non-equilibrium model is developed considering the heat generation of biodegradation, the heat removal due to evaporation and leachate-gas flow, and the effects of the capillary. The solver is implemented in OpenFOAM based on the finite volume method and validated against a waste-column experiment and an in-situ aeration test. The simulation results demonstrate that the assumption of local thermal equilibrium will distinctly overestimate the temperature, maximally by 15 °C in the studied case. The model is then used to simulate a typical aerobic landfill unit to investigate the formation of explosive gas mixtures and elevated temperatures under different operating conditions. The simulation results of gas composition suggest that aeration will not result in explosive gas within landfills. A reasonable recirculation method for temperature control with corresponding operating parameters under a group of values of aeration pressure (2000–4000 Pa) and recirculation rate (0.0001–0.0008 m/s) are proposed, which can provide some guides for the design of an aeration and recirculation combined system. For a given total volume of added leachate, a higher recirculation rate does not always mean better cooling, and the cooling effect of continuous recirculation is better than that of intermittent recirculation.

Experimental investigation on the validity of the local thermal equilibrium assumption in ablative-material response models

Thermal Protection Systems (TPS) material response models rely on the assumption of local thermal equilibrium (LTE) between the solid phase and the gas phase. This assumption was challenged and investigated by several authors but a sufficiently precise knowledge of heat transfer coefficients in TPS materials was lacking to reach final conclusions. The objective of this work is to contribute to filling this gap by providing a literature review of available data in other communities (thermal energy storage, heat exchangers) and by performing an experimental characterization of Calcarb, a commercial carbon preform used for manufacturing thermal protection systems. Heat transfer within Calcarb was studied experimentally in the Through-Thickness and in the In-Plane directions for Reynolds numbers of 1 to 4 - representative of the TPS application - using the transient single-blow technique. Numerical parameter estimation was performed using the Porous material Analysis Toolbox based on OpenFoam (PATO) and the Design Analysis Kit for Optimization and Terascale Applications (DAKOTA). The heat transfer coefficient hv is found to be greater than or equal to 108 W/(m3K) and the LTE assumption is shown to be valid in the conditions of the experiment. To assess the validity of the LTE assumption for other conditions, the above bound of hv may now be used in combination with a local thermal non-equilibrium model.

A Spectroscopic Thermometer: Individual Vibrational Band Spectroscopy with the Example of OH in the Atmosphere of WASP-33b

Individual vibrational band spectroscopy presents an opportunity to examine exoplanet atmospheres in detail, by distinguishing where the vibrational state populations of molecules differ from the current assumption of a Boltzmann distribution. Here, retrieving vibrational bands of OH in exoplanet atmospheres is explored using the hot Jupiter WASP-33b as an example. We simulate low-resolution spectroscopic data for observations with the JWST's NIRSpec instrument and use high-resolution observational data obtained from the Subaru InfraRed Doppler instrument (IRD). Vibrational band–specific OH cross-section sets are constructed and used in retrievals on the (simulated) low- and (real) high-resolution data. Low-resolution observations are simulated for two WASP-33b emission scenarios: under the assumption of local thermal equilibrium (LTE) and with a toy non-LTE model for vibrational excitation of selected bands. We show that mixing ratios for individual bands can be retrieved with sufficient precision to allow the vibrational population distributions of the forward models to be reconstructed. A fit for the Boltzmann distribution in the LTE case shows that the vibrational temperature is recoverable in this manner. For high-resolution, cross-correlation applications, we apply the individual vibrational band analysis to an IRD spectrum of WASP-33b, applying an “unpeeling” technique. Individual detection significances for the two strongest bands are shown to be in line with Boltzmann-distributed vibrational state populations, consistent with the effective temperature of the WASP-33b atmosphere reported previously. We show the viability of this approach for analyzing the individual vibrational state populations behind observed and simulated spectra, including reconstructing state population distributions.

Local thermal equilibrium analysis of complete phase change process inside porous diffuser using NanoFluids

This works implements an investigation on two-phase flow inside porous diffuser using Cu/water nanofluid instead of pure water. Interesting has been focused on how the using Cu/water affect the predictions of complete boiling process. Two-phase mixture model (TPMM), based on the assumptions of Local Thermal Equilibrium (LTE), has been converted to implement the actions of combining nano-fluid rather only water. The governing equations are solved by finite volume method. For the purpose of comparison, the solutions of temperature and liquid saturation, obtained employing Cu/water and only water as working fluid, have been displayed for a wide ranges of geometric parameters, operating parameters and properties of porous media to investigate impacts of using nanofluid. The findings illustrated that the adding Cu particle to water has a high influences on the heat diffusivity inside the diffuser as compared to the solutions of only water due to enhancing the axial diffusion. By employing Cu/water, the boiling and condensation fronts are considerably moved to downstream and upstream sections, respectively. The exit temperature is significantly reduced when utilizing Cu/water as compared to the only water solution. The findings of Cu/water show that the volume fraction of nano-fluid, operating conditions, geometric conditions and porous structure properties have large impacts on the locations of liquid and steam fronts. Accordingly, the nano-fluid is supposed as a safety key in the boiling applications since it improves the technique of heat transfer while simulating the complete boiling process.

Validity of Local Thermal Equilibrium Assumption for Heat Transfer in a Saturated Soil Layer

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.

Islands in the fluid: islands are common in cosmology

We discuss the possibility of entanglement islands in cosmological spacetimes with a general perfect fluid with an equation of state w. We find that flat universes with time-symmetric slices where the Hubble parameter vanishes always have islands on that slice. We then move away from such slices, considering still universes with a general perfect fluid. Under the local thermal equilibrium assumption, the comoving entropy density sc is constant. As a result, the conditions for an island become an inequality between the energy density (or Hubble parameter) and the temperature at some time of normalization. The consequences are that islands can exist for practically all fluids that are not radiation, i.e. w ≠ 1/3. We also discuss the ramifications of our results for universes with spatial curvature. Finally, we show that islands occur in the Simple Harmonic Universe model which has no classical singularity at the background level, in contrast to all previous examples where islands occurred only in space-times with singularities.

Simulating Nanofluid Forced Convection Flow by Thermal Lattice Boltzmann Approach

Improving heat transfer using nanofluids has proven to be a promising option with many practical applications. However, the behavior of particles conveying energy for thermal transport depends closely on the dimensions of systems and channels where the flow evolves. Thereby, any fine thermal analysis should lean on a mesoscale approach applied at a microscale level. To this end, the multi-distribution functions–thermal lattice Boltzmann method has been taken to deal with convective heat flow and entropy generation in a channel with isothermal top–bottom walls and filled with a nanofluid (Cu/water). It was extended to simulate the flow governed by the Brinkman–Forchheimer Darcy model using the local thermal equilibrium assumption. The effects of nanoparticles’ volume fraction, Darcy number, porosity, heat capacity ratio and thermal conductivity ratio on heat transfer, entropy generation, average Nusselt number, and Bejan number are investigated. Among the salient results, it can be stated that the nanoparticles’ volume fraction increases heat transfer and entropy generation, but such a propensity can be affected by the porous medium permeability used. To sum up, the findings confirm the potential of the multi-distribution functions–lattice Boltzmann formalism to tackle forced nanofluid flows with heat transfer in porous media.

Experimental evidence for local thermal non-equilibrium during heat transport in sand representative of natural conditions

When modelling heat transport in hydrogeological systems, a standard assumption is local thermal equilibrium (LTE), which implies that the porous medium temperature at the interface between the solid and fluid instantaneously reaches equilibrium. Few studies have investigated the validity of the LTE assumption and its violation, also known as local thermal non-equilibrium (LTNE), as well as its impact on the accuracy of heat transport models. While the theoretical conditions under which LTNE occurs in natural groundwater flow have recently been revealed, these have not yet been experimentally verified. We examined the applicability of the LTE assumption by conducting systematic laboratory experiments using eight distinct flow velocities (Reynolds number, Re < 0.37) through sand (0.76 mm grain size), injecting both heat and solute as tracers and observing the response at multiple points downstream. Theoretical heat transport parameters were calculated from solute tracer experiments by applying a retardation factor, and the results were subsequently compared to the actual parameters estimated from heat tracing. Our experimental results confirm that the LTE assumption can be violated under natural groundwater flow conditions, and that LTNE impacts thermal dispersion coefficients more significantly than thermal front velocities. The largest differences between the predicted and estimated thermal transport parameters were 112% and 13% for the dispersion coefficients and velocities, respectively. Our results demonstrate that LTNE effects need to be considered in heat transport modelling especially when analyzing thermal dispersion coefficients.

Validation of the Local Thermal Equilibrium Assumption for Free Convection Boundary Layer Flow Over a Horizontal Cylinder Embedded in an Infinite Saturated Porous Medium

Validation of the Local Thermal Equilibrium Assumption for Free Convection Boundary Layer Flow Over a Horizontal Cylinder Embedded in an Infinite Saturated Porous Medium

Validation of the Local Thermal Equilibrium Assumption for Free Convection Boundary Layer Flow Over a Horizontal Cylinder Embedded in an Infinite Saturated Porous Medium

Validation of the Local Thermal Equilibrium Assumption for Free Convection Boundary Layer Flow Over a Horizontal Cylinder Embedded in an Infinite Saturated Porous Medium

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.

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

Abstract 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) 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.