Local Thermal Equilibrium Assumption Research Articles

Heat transfer analysis of rectangular porous fins in local thermal non-equilibrium model

• Analytical solutions on convective-radiative porous fin in LTNE is accomplished. • Darcy model and Boussinesq approximation are used to simulate the porous medium. • The two energy equations are solved using the Adomian Decomposition Method. • Results are given as temperature profiles and total Nusselt numbers. • Criteria to compare LTNE and LTE hypothesis are given for both scale analysis and ADM. In this study, an analytical solution of a porous fin with natural convection and radiation heat transfer is carried out. For the first time, the analysis is accomplished in Local Thermal Non-Equilibrium (LTNE) model. The investigation is carried out on a porous fin with finite length and adiabatic tip. The Darcy model and Boussinesq approximation for buoyancy effects are used to evaluate the infiltration velocity in the porous medium. Two energy equations are solved using the Adomian Decomposition Method (ADM). The solution is validated with the numerical solution of the finite difference method, and with the asymptotic solution for the Local Thermal Equilibrium (LTE) model. The results are presented in terms of temperature profiles and total average Nusselt numbers. They pointed out the effects of internal and external radiation and convection heat transfer, as well as thermal conductivity ratio and dimensionless thickness. It was found that solid phase temperature profiles decrease as the Biot, Bi , and Rayleigh, Ra *, numbers decrease, whereas the difference between the solid phase and fluid phase temperatures, for assigned Bi , decreases for lower Ra . Thermal conductivity ratio and dimensionless thickness increase engender higher solid phase temperature for assigned Bi and Ra *. The total Nusselt number increases as Ra *, Bi and external radiation increase, whereas it decreases with the thermal conductivity ratio. Criteria to compare LTNE and LTE assumptions are proposed, and they highlight the fact that the minimum Biot number to accept the LTE assumption becomes lower as the Rayleigh number decreases.

Heat transfer enhancement with pressure drop optimisation in a horizontal porous channel locally heated from below

In this work, transient mixed convection heat transfer and fluid flow in a horizontal porous layer bounded by two impermeable plates with a localised heating from below is numerically studied. The study is conducted using the Brinkman–Forchheimer-extended Darcy model and the one-equation energy model based on the assumption of local thermal equilibrium. The effects of porosity (ɛ = 0.7−0.95) and permeability represented by Darcy number (Da = 0.1−100) are investigated for the following ranges of Richardson (Ri = 1−100) and Reynolds (Re = 0.1−50) numbers. The results show that the existence of the porous material increases Nusselt number, but does not change its trend with Reynolds number for all Richardson numbers. Interestingly, it is shown that unstable, oscillatory flow and temperature fields are generated in both empty and porous channels at higher Richardson number and/or higher Reynolds number. Also, both the heat transfer and the pressure drop are found to decrease as the porosity increases; however, the effect of Darcy number depends strongly on the range of Reynolds number.

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

Rayleigh-Bénard-Taylor convection in a Newtonian, nanoliquid-saturated high porous medium using the local thermal non-equilibrium model (LTNE) is studied analytically using the single term Galerkin technique. The Bousinessq approximation is considered to be valid and the exerted centrifugal force due to rotation is taken. A high porosity porous material glass reinforced fiber with porosity 0.88% is considered and hence the Brinkman model is adopted. The rate of rotation is quantified by the Taylor number and the stability of the system is controlled by thermal Rayleigh number. The expression for the critical eigenvalue (Rayleigh number) is obtained for both idealistic and realistic boundary conditions, that is, stress-free, isothermal and rigid-rigid, isothermal boundary conditions. The presumption of LTNE advances the inception of convection and increases the transport of heat in comparison with that of the local thermal equilibrium (LTE) assumption whereas the opposite phenomenon is seen with the effect of rotation. The effect of various non-dimensional parameters on the convection onset and on transport of heat is also investigated. The results of Rayleigh-Bénard-Taylor convection using the LTE assumption are obtained as limiting cases of the present study for infinite values of the ratio of thermal conductivities and the interphase heat transfer coefficient.

Constraining the heat transfer coefficient of rock fractures

Estimating the heat transfer in deep underground geothermal systems is a challenging task. The concept of explicitly describing the heat transfer between phases has been shown superior to the conventional approach but the heat transfer coefficient of fractures is still ambiguous. In this work, a definition of the lower and upper bound of the heat transfer coefficient between rock and flowing fluid in a single rock fracture is derived and validated with almost 250 experiments from other studies. The resulting values range between 8 and 260 W/m2 °C, with upper bounds roughly a factor 10 larger. Further, as shown in this work, the assumption of local thermal equilibrium can result in lower production temperatures than the assumption of heat transfer between phases depending on reservoir conditions. A dimensionless number is derived to distinct those cases and to determine the lower limit of the outflow temperature in any scenario. The results of this work enable a quantification of the value range of the heat transfer coefficient from laboratory experiments and allow a tabulation of the heat transfer coefficient for all kind of scenarios. The presented results can be used in discrete fracture models for an improved prognosis of production temperatures.

Transient ionization potential depression in nonthermal dense plasmas at high x-ray intensity.

The advent of x-ray free-electron lasers (XFELs), which provide intense ultrashort x-ray pulses, has brought a new way of creating and analyzing hot and warm dense plasmas in the laboratory. Because of the ultrashort pulse duration, the XFEL-produced plasma will be out of equilibrium at the beginning, and even the electronic subsystem may not reach thermal equilibrium while interacting with a femtosecond timescale pulse. In the dense plasma, the ionization potential depression (IPD) induced by the plasma environment plays a crucial role for understanding and modeling microscopic dynamical processes. However, all theoretical approaches for IPD have been based on local thermal equilibrium (LTE), and it has been controversial to use LTE IPD models for the nonthermal situation. In this work, we propose a non-LTE (NLTE) approach to calculate the IPD effect by combining a quantum-mechanical electronic-structure calculation and a classical molecular dynamics simulation. This hybrid approach enables us to investigate the time evolution of ionization potentials and IPDs during and after the interaction with XFEL pulses, without the limitation of the LTE assumption. In our NLTE approach, the transient IPD values are presented as distributions evolving with time, which cannot be captured by conventional LTE-based models. The time-integrated ionization potential values are in good agreement with benchmark experimental data on solid-density aluminum plasma and other theoretical predictions based on LTE. The present work is promising to provide critical insights into nonequilibrium dynamics of dense plasma formation and thermalization induced by XFEL pulses.

Thermal behavior of Composite Material (nanoPCM/aluminum foam) used for thermal energy storage (TES) applications

Thermal energy storage systems (TESS) using phase change materials (PCM) have attracted interest in various fields of science and technology. However, the interest of these systems is limited by the relatively low thermal conductivity of PCMs and their leakage in the melted state. To overcome these drawbacks, the present paper suggests a new alternative for the enhancement of the PCMs by incorporating highly conductive materials, such as metal foam and/or nanoparticles. A Direct Numerical Simulation (DNS) was carried out to investigate the melting process of paraffin wax as PCM enhanced with alumina nanoparticles (i.e. nanoPCM) embedded in aluminum foam under constant temperature. A three-dimensional (3D) foam regular structure was designed. The effects of aluminum foam porosity and nanoparticles’ volume fraction on the thermal behavior of composite PCMs were investigated. The two-temperature model based on the assumption of local thermal non equilibrium was applied due to the great difference of thermal conductivity between nanoPCM and aluminum foam.

Approximate analytical characterization and multi-parametric optimization design of single-tank thermocline heat storage system

Compared with two tank thermal energy storage (TES) system, the single-tank thermocline (STTC) TES system provides a more cost-effective option for TES systems with low-cost solid filler, and it is progressively becoming an important research topic. In this study, analytical approach solutions derived from the one-dimensional two-phase (1D-2P) without heat loss model and one-dimensional one-phase (1D-1P) with heat loss model in the STTC system are compared with experimental data, it is found that local thermal equilibrium assumption is inappropriate in the thermocline tank because the internal heat transfer in fluid and solid is dominant. Besides, the analytical approach results of 1D-2P model are more exact than numerical results compared with experimental data. The algebraic equations of non-dimensional discharging time and discharging efficiency are derived from analytical modeling results. Based on these important correlations, a multi-parametric optimization design procedure of the thermocline tank considering of stress safety requirement is proposed. Then different design cases are studied and the effects of some critical non-dimensional parameters are investigated. The results show that optimal Pe number exists for designing a thermocline TES system, with which convection heat transfer is dominant and final discharging time is not that short. For the PROMES experimental case, not only the output power increases 145.9% but also the final discharging efficiency improves 0.75% compared with the experimental boundary condition with the optimum Pe = 960.63. Larger value of fluid volumtric heat capacity ratio and higher Bi number increases efficient discharging time and discharging efficiency while decreases thermocline thickness, the improvement is highly significant especially for Bi < 1 × 106.

CO-to-H2 conversion and spectral column density in molecular clouds: the variability of the XCO factor

ABSTRACT Analysing the Galactic plane CO survey with the Nobeyama 45-m telescope, we compared the spectral column density (SCD) of $N_{\rm H_2}$ calculated for the 12CO (J = 1–0) line using the current conversion factor $X_{\rm ^{12}CO}$ to that for the 13CO (J = 1–0) line under the LTE (local thermal equilibrium) assumption in the M16 and W43 regions. Here, SCD is defined by $\mathrm{d}N_{\rm H_2}/\mathrm{d}v$ with $N_{\rm H_2}$ and v being the column density and radial velocity, respectively. It is found that the $X_{\rm ^{12}CO}$ method significantly underestimates the H2 density in a cloud or region, where SCD exceeds a critical value (∼3 × 1021 [H2 cm−2 (km s−1)−1]), but overestimates in lower SCD regions. We point out that the actual CO-to-H2 conversion factor varies with the H2 column density or with the CO line intensity: it increases in the inner and opaque parts of molecular clouds, whereas it decreases in the low-density envelopes. However, in so far as the current $X_{^{12}{\rm CO}}$ is used combined with the integrated 12CO intensity averaged over an entire cloud, it yields a consistent value with that calculated using the 13CO intensity by LTE. Based on the analysis, we propose a new CO-to-H2 conversion relation, $N_{\rm H_2}^* = \int X^*_{\rm CO} (T_{\rm B}) T_{\rm B}\ \mathrm{d}v$, where $X^*_{\rm CO} (T_{\rm B})=(T_{\rm B}/T_{\rm B}^*)^\beta X_{\rm ^{12}CO}$ is the modified spectral conversion factor as a function of the brightness temperature, TB, of the 12CO (J = 1–0) line, and β ∼ 1–2 and $T_{\rm B}^*=12\!-\!16$ K are empirical constants obtained by fitting to the observed data. The formula corrects for the over/underestimation of the column density at low/high CO line intensities, and is applicable to molecular clouds with TB ≥ 1 K (12CO (J = 1–0) line rms noise in the data) from envelope to cores at sub-parsec scales (spatial resolution).

Similarity Solutions for Local Thermal Non-equilibrium Boundary-Layer Flows in a Fluid-Saturated Porous Medium

A general boundary-layer coordinate transformation was proposed in order to find the necessary conditions under which similarity solutions exist for free, forced and mixed convective Darcian flows subject to local thermal non-equilibrium. The aim of this study is to present the effects of local thermal non-equilibrium on the boundary-layer heat transfer in porous media, identifying each of the parameters controlling the thermal boundary-layer development. The findings of this systematic study are quite beneficial to those dealing with thermal applications using porous media. Similarity solutions are found to exist for such local thermal non-equilibrium cases as forced convection around the stagnation regions of horizontal cylinder and sphere heated according to a power function of the distance from the stagnation point, free convection over a vertical plate with its temperature increasing linearly, and free and mixed convection around the stagnation regions of isothermally heated horizontal cylinder and sphere. The study clearly indicates that the local thermal equilibrium assumption results in substantial overestimation of heat transfer rates. The local non-equilibrium effects must be considered when the modified interstitial Stanton number is less than its criterion value around 10.

Numerical investigation of porous stack for a solar-powered thermoacoustic refrigerator

This article proposes a numerical analysis for performance improvement of the stack, which represents a crucial element on the solar-powered thermoacoustic refrigerator. The stack is considered as a saturated parallelepiped homogeneous porous media. Numerical simulation of the flow and the heat transfer in the thermoacoustic refrigerator is carried out. The physical flow is governed by the modified Darcy–Brinkmann–Forchheimer model. The governing equations are solved numerically using the lattice Boltzmann method. Furthermore, the local thermal equilibrium assumption is applied to examine heat transfer. Particular attention is paid a new form of the lattice Boltzmann equation system describing the flow and the heat transfer in porous media and fluid regions. The effects of several parameters characterizing the thermal behaviour in the porous medium are studied. The parametric results lead to the optimization of the porous media form. The presence of the viscous dissipation term in the heat transfer formulation within the thermoacoustic system is particularly highlighted, due to its significant effects introduced by the Eckert number.

Effect of heat source on forced convection in a partially-filled porous channel under LTNE condition

An analysis of forced convection is presented within a channel partially filled by porous medium inserted in the core, with the inclusion of internal heat source in fluid and solid phases. By employing Brinkman extended Darcy model and local thermal non-equilibrium (LTNE) model in porous region, exact solutions are obtained including fluid velocity, solid and fluid temperatures and Nusselt number, and pertinent parameters' effects on heat transfer enhancement are performed. In addition, the solutions are also compared to that by applying the local thermal equilibrium (LTE) assumption and the LTE validity is discussed. The results find that for a partially-filled porous channel, existed heat source terms can intensify the occurrence of the singularity in Nusselt number, especially with the variation of porous filling ratio more than one singularity points can be observed under both LTE and LTNE conditions. In addition, even if the singularity exists the Nusselt number can reach to LTE condition at a high Biot number (Bi) or at a very high solid to fluid thermal conductivity ratio (K), and at a small K the LTE also holds with the fluid heat source only. Overall, partially-filled porous systems with internal heat source have more rich thermal characteristics.

Prediction of flow and heat transfer through a microtube filled with bidisperse porous medium under local thermal nonequilibrium condition

AbstractIn this paper, the thermal and hydrodynamic solutions of a microtube filled with bidisperse porous medium (BDPM) under the local thermal nonequilibrium (LTNE) condition are presented. Considering the LTNE condition, the energy equations have been numerically solved. The rarefaction effects are considered for Knudsen numbers ranging from 0 to 0.1; therefore, first‐order boundary condition is applied on the wall. The temperature distribution of each phase is examined with respect to the involved parameters in the BDPM system. For the first time, the Nusselt number ratio (NRDP) is introduced to study the influence of Darcy number on the Nusselt number more precisely. Also, the effect of different thermophysical parameters on the Nusselt number is studied. The advantage of BDPM system over monodisperse porous medium (MDPM) structure is examined through the heat transfer performance parameter. The findings exhibit a good agreement with the literature. Also, the LTNE condition produces more realistic results in comparison to local thermal equilibrium assumption. On the whole, although implementing the BDPM enhances the heat transfer rate compared with the MDPM, it does not improve the thermal hydrodynamic performance significantly.

Testing of a new non-equilibrium heat and moisture transfer model in porous building materials

In this paper the new non-equilibrium model of heat and moisture transfer in heterogenous building materials is presented and tested. The new hygro-thermal model differs from the other approaches which are based on the classical assumption of instantaneous local mechanical, thermal and hygric equilibrium between vapour and water in the pores in building materials. Instead of this assumption the model uses the finite rate of transition of moisture from the liquid to the vapour state and vice versa while still keeping mechanical and thermal equilibrium between components of the medium. The linear kinetics of this transition is applied. The assessment of the model correctness is also performed in the paper. In the first step of the testing the model predictions were successfully verified with the reference data obtained numerically. Then the model was validated using reference data obtained experimentally. Finally, the influence of volumetric mass transfer coefficient between vapour and water as well as water and vapour in pores is investigated, i.e., kinetics of the vapour-water/water-vapour transition is analysed. During the model testing traditional building material were considered (i.e., ceramic brick). However, the model may be used for investigation of hygro-thermal behaviour of bio-based materials.

Study of Rayleigh–Bénard Convection of a Newtonian Nanoliquid in a High Porosity Medium Using Local Thermal Non-equilibrium Model

In the paper we make linear and non-linear stability analyses of Rayleigh–Benard convection in a Newtonian, nanoliquid-saturated porous medium using local thermal non-equilibrium model (LTNE). The LTNE assumption results in advanced onset of convection and increase in heat transport when compared to that of local thermal equilibrium assumption. Free–free and rigid–rigid, isothermal boundaries are considered for investigation. The Galerkin method is used to obtain the critical eigen value. The influence of inter-phase heat transfer coefficient, ratio of thermal conductivities, Brinkman number, porous parameter on the onset of convection as well as on heat transport has been presented graphically and discussed in detail. The effect of increasing the value of porosity modified thermal conductivities advances the onset of convection and enhances the amount of heat transport whereas the remaining parameters have an opposing influence on both onset of convection as well as heat transport.

NUMERICAL ANALYSIS OF SOLAR TOWER SYSTEM UTILIZED WITH FLAT PLATE AND POROUS ABSORBER

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°.

Transient thermoporoelastic model under local thermal non-equilibrium

Wellbore stability is a key challenge for oil and gas industry since it adds a great deal of additional cost to the industry. Traditional wellbore stability models such as elastic and poroelastic models may not produce reliable stress field around a wellbore since they consider isothermal wellbore condition. During the drilling phase, the drilling fluid temperature is different from the formation temperature due to geothermal gradient and circulation of the fluid inside the wellbore. Therefore, the assumption of isothermal condition will not predict the correct wellbore stability condition, especially for high pressure and high temperature wells. Hence, consideration of a thermoporoelastic model in stress estimation is more appropriate. Although there are several thermoporoelastic models in the literature, they employ the assumption of local thermal equilibrium (LTE) in their modeling. However, thermal properties of phases in a porous medium are rarely similar. This dissimilarity evokes the validation of LTE assumption. The local thermal non-equilibrium assumption ignores additional pore and thermal stresses in the porous medium caused by temperature variations of the fluid and solid phases. Under pure heat conduction, LTE is valid if thermal boundary conditions in a medium is constant or thermal conductivities of phases are similar according to Vadasz (2005) 1. Hence, using a local thermal non-equilibrium (LTNE) approach is required to establish each phase temperature, and update thermoporoelastic model accordingly. In this paper, the effects of induced thermal stresses on wellbore stress resolution and LTNE on thermoporoelastic model around a wellbore during drilling phase are investigated in low and high permeable formations. The LTNE thermoporoelastic model developed herein is a transient model considering conductive and convective heat transfers.

Intensity contrast of solar network and faculae

Aims. We aim to gain insight into the effect of network and faculae on solar irradiance from their apparent intensity. Methods. Taking full-disc observations from the Solar Dynamics Observatory, we examined the intensity contrast of network and faculae in the continuum and core of the Fe I 6173 Å line and 1700 Å, including the variation with magnetic flux density, distance from disc centre, nearby magnetic fields, and time. Results. The brightness of network and faculae is believed to be suppressed by nearby magnetic fields from its effect on convection. We note that the degree of magnetically crowding of an area also affects the magnetic flux tube sizes and the depth at which magnetic concentrations are embedded in intergranular lanes, such that intensity contrast can be enhanced in magnetically crowded areas at certain flux densities and distances from disc centre. The difference in intensity contrast between the quiet-Sun network and active region faculae, noted by various studies, arises because active regions are more magnetically crowded and is not due to any fundamental physical differences between network and faculae. These results highlight that solar irradiance models need to include the effect of nearby magnetic fields on network and faculae brightness. We found evidence that suggests that departures from local thermal equilibrium (LTE) might have limited effect on intensity contrast. This could explain why solar irradiance models that are based on the intensity contrast of solar surface magnetic features calculated assuming LTE reproduce the observed spectral variability even where the LTE assumption breaks down. Certain models of solar irradiance employ chromospheric indices as direct indications of the effect of network and faculae on solar irradiance. Based on past studies of the Ca II K line and on the intensity contrast measurements derived here, we show that the fluctuations in chromospheric emission from network and faculae are a reasonable estimate of the emission fluctuations in the middle photosphere, but not of those in the lower photosphere. This is due to the different physical mechanisms that underlie the magnetic intensity enhancement in the various atmospheric regimes, and represents a fundamental limitation of these solar irradiance models. Any time variation in the radiant properties of network and faculae is, of course, relevant to their effect on solar irradiance. The data set, which extends from 2010 to 2018, indicates that their intensity contrast was stable to about 3% in this period. Conclusions. This study offers new insights into the radiant behaviour of network and faculae, with practical implications for solar irradiance modelling.

Heat and fluid flow analysis of metal foam embedded in a double-layered sinusoidal heat sink under local thermal non-equilibrium condition using nanofluid

The present study aims to enhance the hydrothermal performance of a porous sinusoidal double-layered heat sink using nanofluid. The optimum thickness of metal foam (nickel) for different Reynolds numbers ranging from 10 to 100 for the laminar regime and Darcy numbers ranging from 10−4 to 10−2 is obtained. At the optimum porous thicknesses, nanofluid (silver–water) with three volume fractions of nanoparticles equal to 2, 3, and 4% is employed to enhance the heat sink thermal performance. Darcy–Brinkman–Forchheimer model and the local thermal non-equilibrium model or two equations method are employed to model the momentum equation and energy equations in the porous region, respectively. It was found that in the cases of Darcy numbers 10−4, 10−3, and 10−2 the dimensionless optimum porous thicknesses are 0.8, 0.8, and 0.2, respectively. It was also obtained that the maximum PEC number is 2.12 and it corresponds to the case with Darcy number 10−2, Reynolds number 40, and volume fraction of nanoparticles 0.04. The validity of local thermal equilibrium (LTE) assumption was investigated, and it was found that increasing the Darcy number which results in an enhancement in porous particle diameter leads to some errors in results, under LTE condition.

Generalized Hydrodynamics on an Atom Chip.

The emergence of a special type of fluidlike behavior at large scales in one-dimensional (1D) quantum integrable systems, theoretically predicted in O. A. Castro-Alvaredo etal., Emergent Hydrodynamics in Integrable Quantum Systems Out of Equilibrium, Phys. Rev. X 6, 041065 (2016)10.1103/PhysRevX.6.041065 and B. Bertini etal., Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents, Phys. Rev. Lett. 117, 207201 (2016)10.1103/PhysRevLett.117.207201, is established experimentally, by monitoring the time evolution of the insitu density profile of a single 1D cloud of ^{87}Rb atoms trapped on an atom chip after a quench of the longitudinal trapping potential. The theory can be viewed as a dynamical extension of the thermodynamics of Yang and Yang, and applies to the whole range of repulsive interaction strength and temperature of the gas. The measurements, performed on weakly interacting atomic clouds that lie at the crossover between the quasicondensate and the ideal Bose gas regimes, are in very good agreement with the theory. This contrasts with the previously existing "conventional" hydrodynamic approach-that relies on the assumption of local thermal equilibrium-which is unable to reproduce the experimental data.

Critical review of the local thermal equilibrium assumption in heterogeneous porous media: Dependence on permeability and porosity contrasts

Increasing demand for green energy sparked a renewed interest in extracting geothermal energy resources. An accurate description of the temperature field and related heat extraction potential remains a challenge and is critical for successful geothermal energy exploitation. Typically, two main approaches are used when modeling heat exchange and transport in geothermal reservoirs. The standard approach assumes immediate local thermal equilibrium between solid and fluid phases (LTE), while another approach considers heat transport separately for fluid and solid (LTNE). Both are then coupled through a heat exchange term. In these simple and common models, the host system is described as a heterogeneous porous media in which regions of higher fracture density are represented implicitly by areas of higher permeability within the porous media.In this work, we investigate both, LTE and LTNE, approaches and how they are affected by fluid and host rock characteristic properties. We especially focus on the influence of hydraulic heterogeneity in the porous material on the temperature difference between both approaches. We compare LTE and LTNE heat transfer models in a simple, two dimensional model with a layer of different hydraulic parameters embedded in a host rock, and study in detail the role of heterogeneous distributions of permeability and porosity. This simple geometrical model allows us to gain insights into the complex interaction between the different heat transfer models and fluid flow. Porosity and permeability contrast determine separate regimes in which the LTE assumption is lower or upper bound of outflow temperature. Using these results, we compare LTE and LTNE models in a synthetic field case with a complex heterogeneous porous media with large permeability contrast. We show that both models can diverge up to 7% in local fluid temperature, while the LTNE model is the lower bound if high permeability regions are also assumed to have a higher porosity.