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• Thermal modeling of porous fiber composite with compressible fluid is proposed. • Compressive effect of the fluid phase on porous fiber composite is demonstrated. • Effect of heating sources on the thermal behavior of the materials is uncovered. The study of heat transfer behavior in porous fiber composite cylinders is vital for optimizing efficient thermal management, insulation materials, and heating equipment design, with applications spanning fields like materials drying, atomization equipment, and aerospace. However, the existing research in this area faces challenges including inadequate experimental data and a lack of clarity regarding fluid-porous material interactions, particularly under the influence of compressible fluids, which demand a more nuanced investigation. This study has developed a model to depict the unsteady heat transfer behavior of porous fiber composite cylinders containing compressible fluid. Consequently, a momentum equation describing the gradual diffusion of compressible fluid within the porous medium is established based on the Darcy-Brinkman-Forchheimer equation. For the purposes of this investigation, the air is treated as a compressible fluid. Concurrently, the corresponding energy equation is formulated, assuming Local Thermal Equilibrium. Ultimately, the devised model is solved by employing the finite volume method. Additionally, a temperature measurement experiment is designed to furnish boundary conditions and verify the model's reliability. The findings indicate that omitting the influence of compressible fluid yields a maximum predicted temperature deviation of approximately 5.6 K at a heating temperature of 420 K. The temperature deviation gradually expands as the heating temperature rises. Furthermore, the parametric analysis is conducted to investigate the impact of porosity, thermal conductivity, geometric size, and the type of heat source on the non-steady heat transfer behavior of composite cylinders. This novel model contributes to a more accurate prediction of the unsteady temperature distribution within porous fiber composite structure cylinders. [ABSTRACT FROM AUTHOR]

Various geoscientific processes in the shallow subsurface experience a temperature difference between the solid and the liquid or gaseous phase. Prominent examples include the injection of cold water into a hot host rock, the fast intrusion of supercritical CO2 from the mantle into shallower regions, or the rainwater infiltration into partially frozen soil. In such an absence of local thermal equilibrium between phases, heat transfer needs to be described explicitly by Newton's law of cooling and depends on the heat transfer coefficient and the specific heat transfer area between the involved phases. Despite various works, the quantification and the dissolution of dependencies of the heat transfer coefficient remain ambiguous. The study of heat transfer is separated between porous and fractured materials due to the different geometry, the applied flow rules, and common fields of applications. Identifying scenarios in which heat transfer effects in a local thermal non-equilibrium (LTNE) situation are relevant is already a challenging task but in past years more and more scenarios with persistent differences in phase temperatures were found. In this contribution, the mathematical governing equations for heat transfer between solid rock and moving fluid are given and various approaches of parameterization are discussed. This discussion of heat transfer includes various types of heat transfer mechanisms that can occur in the subsurface. Subsequently, the state of the art for heat transfer in porous and fractured media is presented with a special emphasis on resolving dependencies on geometry (grain size, fracture aperture) and flow velocity. Possible solution strategies addressing heat transfer in heterogeneous fractured porous media are presented, and possible applications with relevant LTNE effects are discussed with an outlook on future challenges in the field of geothermal energy exploitation and storage, shallow multi-phase infiltration scenarios, CO2 sequestration, and underground H2 storage. [ABSTRACT FROM AUTHOR]

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 h v is found to be greater than or equal to 108 W/(m3 K) 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 h v may now be used in combination with a local thermal non-equilibrium model. [ABSTRACT FROM AUTHOR]

In Stirling engine, the regenerator operates with oscillating flow, a detailed description of fluid flow and heat transfer become crucial. The oscillating flow is driven by a piston to assure an expansion-compression cycle. The scope of this work involves the development of a computational model of flow and heat transfer in a two-dimensional horizontal cylinder partially filled with an open cell metal foam block attached strip heat source at the lateral wall. The governing equations in two-dimensional laminar regime are written in local thermal equilibrium (LTE). The presence of the open-cell metal foam is modeled as a porous media by means of the Darcy-Brinkman-Forchheimer law. The numerical study is conducted by MVCEF Method, which is an efficiently way compared to that of the traditional continuum Navier-Stokes method, for a non-structured moved grid. The SIMPLER algorithm has been implemented. The effect of the foam on hydrodynamic and heat transfer behavior is showed. Simulations were performed for a fixed piston speed (Re =100) and for various metal foam radius (0.2R≤Rp≤R), porosity (0.5≤ε≤0.9), Darcy number (10−5≤Da≤10−3) and Womersley number (5≤Mo≤15). [ABSTRACT FROM AUTHOR]

• Instead of Nusselt number, Sparrow number appears in the dimensionless governing equations by using equilibrium thermal diffusivity. • The Sparrow number is interpreted as the equilibrium conduction thermal resistance to the convection thermal resistance in the pores. • A good agreement between the pore scale and volume averaged results for the working fluid of water and air is observed. • A chart is presented in terms of Sparrow number, solid thermal diffusivity and thermal capacitance to estimate the local thermal equilibrium condition. The local thermal non-equilibrium condition for a porous medium with closed cells under unsteady state heat transfer is analyzed. Although the fluid circulates in the closed pores due to the buoyancy effect, the volume averaged velocity for a closed pore is zero causing excluding of the continuity and momentum equations from the volume averaged governing equations. The volume averaged governing equations are non-dimensionalized by using the equilibrium thermal diffusivity and Sparrow number appears in the dimensionless governing equations automatically. The Sparrow number is interpreted as the equilibrium conduction thermal resistance to the convection thermal resistance for the entire domain. For the high values of Sparrow number (such as 1000), the convection heat transfer resistance is considerably smaller than the heat conduction resistance resulting in high possibility of the local thermal equilibrium. Dimensionless governing equations show that four dimensionless parameters as porosity, Sparrow number, solid (or fluid) dimensionless thermal capacitance and thermal conductivity play important roles on the prediction of the local thermal non-equilibrium state in a closed cell porous medium. A chart for the prediction of local thermal non-equilibrium is presented for Sparrow number of 1, 50, 100 and 500. Furthermore, a pore scale study for a closed cell porous medium with working fluids as water and air is performed. A good agreement between the pore scale and volume averaged results is observed. The obtained pore scale results support the results of the volume averaged parametric study and also the suggested chart for the prediction of local thermal non-equilibrium state. [ABSTRACT FROM AUTHOR]

Ablative material response codes currently in use consider local thermal equilibrium between the solid phases and the pyrolysis gases. For typical entry conditions, this hypothesis may be justified by the fact that the thermal Peclet number within the pores is small, which is a necessary condition for thermal equilibrium in non-reactive materials. However, the validity of this analysis may fall under some circumstances. The thermal Peclet number may become large due to high pyrolysis gas velocities. Additional physical phenomena not accounted for in the Peclet analysis may become non-negligible, such as the change of enthalpy due to chemical reactions. The objective of this study is two-fold. First, a detailed two temperature material response model for porous reactive materials is presented. This model has been implemented and made available in the Porous material Analysis Toolbox based on OpenFOAM (PATO). Second, the model is applied to the Theoretical Ablative Composite for Open Testing (TACOT) in a wide range of conditions to assess the true range of validity of the thermal equilibrium hypothesis. Simulations are carried out on the Stardust and Mars Science Laboratory (MSL) atmospheric entries. The main design variables have been monitored and compared between the two models: temperature evolution and species concentration within the material, pyrolysis gas blowing rate, extension of the pyrolysis zone, and wall recession due to ablation. Results show that under chemical equilibrium conditions, no significant deviation in the monitored quantities are observed, while under chemical non-equilibrium conditions there is a large impact on the species concentration. [ABSTRACT FROM AUTHOR]

The present study numerically models the process of heat removal from a heat-generating porous bed with cold fluid injection from the bottom of the bed. This type of situation is encountered during post-accident situations in nuclear reactors and involves augmentation of heat removal capacity with forced coolant injection from the bottom. A steady-state analysis is carried out with the assumption of laminar flow regime and without accounting for phase change. Darcy-Brinkmann-Forchheimer approximation and local thermal equilibrium assumption are adopted for modelling the momentum and energy equations in porous media, respectively. It is observed that the fluid flow is determined based on the dominancy of the two co-existing flow mechanisms viz. inertial flow due to forced fluid injection and buoyancy-driven flow due to heat generation within the porous bed. In addition, permeability of the porous media significantly affects the flow mechanism, especially near the fluid inlet. Heat transfer characteristics closely follow the flow mechanism established within the enclosure. [ABSTRACT FROM AUTHOR]

Many engineering applications involve reacting porous materials submitted to high temperatures. This work presents a detailed but pragmatic heat and mass transfer model for porous materials containing several solid phases and a single gas phase. The detailed chemical interactions occurring between the solid phases and the gas phase are modeled at the pore scale assuming local thermal equilibrium. Homogenized models are obtained for solid pyrolysis, pyrolysis species injection in the gas phase, heterogeneous reactions between the solid phases and the gas phase, and homogeneous reactions in the gas phase. The chemistry models are integrated in a macroscopic model making use of volume-averaged governing equations for the conservation of solid mass, gas mass, species (finite-rate chemistry) or elements (equilibrium chemistry), momentum, and energy. The model has been implemented in the Porous Material Analysis Toolbox based on OpenFoam (PATO), distributed Open Source by NASA. Applications to two high-temperature engineering problems are presented. The first application concerns the design of heat-shields of space vehicles. The second one aims at improving the understanding of biomass pyrolysis for the production of biohydrocarbons. [ABSTRACT FROM AUTHOR]

The Complete liquid-vapour phase change process inside an asymmetrically heated porous channel has been numerically investigated in this article, based on the Two-Phase Mixture Model (TPMM), while employing both Local Thermal Equilibrium (LTE) and Non-Equilibrium (LTNE) conditions. For the latter condition, four different models have been considered for the partitioning of imposed wall heat flux. All simulations have been carried out by applying the recently proposed smoothing algorithm for the effective diffusion coefficient, without which, the occurrence of non-physical “jump” in the predicated properties, across the interface between the single and the two-phase regions could not be always avoided. The governing equations have been discretised using the finite volume method on a fixed staggered grid layout and solved iteratively in a SIMPLE-like manner. Only the imposed wall heat flux has been varied, while all other parameters and properties have been kept fixed during the present investigation. It has been observed that LTE model fails to produce realistic predictions, particularly when the superheated vapour phase is formed inside the evaporator. On the other hand, the conduction heat transfer through the solid phase and the internal heat exchange between the solid and the fluid phases across the interface separating the superheated vapour and the two-phase mixture regions provide two additionally required mechanisms for LTNE model for the realistic predictions. As far as different models for the partitioning of wall of heat flux is concerned, Model-2 appears to be the most realistic, while Model-1 has been found to be the most stable. [ABSTRACT FROM AUTHOR]

In this paper, detailed numerical calculations of the spectral collocation method (SCM) to simulate natural convection in a square porous cavity using two different local thermal models, i.e., the local thermal equilibrium model and the local thermal non-equilibrium model, are presented and formulated. In this approach, stream function and temperature are approximated by the Chebyshev polynomials and the dimensionless governing equations are discretized by the Chebyshev–Gauss–Lobatto collocation points. The two step method, i.e., the matrix diagonalization method, is used to solve the discretized equations. The present results are compared with those reported in literature. It is found that these results are in excellent agreement. Furthermore, the exact solutions for local thermal equilibrium model have been constructed to test the accuracy of the method, and it can be observed from the test that the Chebyshev spectral collocation method can produce high accuracy. Meanwhile, the isotherms and the streamlines are analyzed to reveal the fluid flow and heat transfer for various parameters, i.e., the Rayleigh number, the inter-phase heat transfer coefficient, and the thermal conductivity ratio. [ABSTRACT FROM AUTHOR]

Changes in the porosity and permeability of a porous medium due to melting are modeled. A frozen phase, which initially fills a part of the porous medium, melts and gets dissolved in the injected hot solvent. The amount of melted material, the rate of melting as well as the profiles of temperature, porosity, and concentration are analyzed to understand the nature of this naturally and industrially important phenomenon. Four reference scenarios corresponding to instantaneous thermal equilibrium, no heat transfer to the frozen phase, no-melting, and instantaneous melting conditions are solved analytically and the effects of different parameters are discussed. Numerical simulation results show that the profiles of the fluid temperature, porosity of the medium, and solvent concentration, form three fronts moving at different rates. It is found that for heat transfer coefficients above a certain value, the rate of melting is independent of this parameter and the system can be considered to have reached instantaneous thermal equilibrium. Moreover, slow heat transfer in the medium is shown to increase the rate of melting at long time periods by involving larger areas in the melting process. Heterogeneous scenarios are also analyzed by introducing frozen blocks of different geometries. The ability of the flow to bypass the frozen region involves a new heat transfer mechanism identified as outer-boundary convection. The effects of the geometry of the block along with the other parameters on the melting process are examined. Furthermore a generalizing scheme is proposed to predict the melt production for different block geometries and values of the saturation of the frozen phase. [ABSTRACT FROM AUTHOR]

The additively manufactured multi-scaled periodic structure is considered as a thermal enhancer to accelerate melting rate of a PCM in a storage tank. Simulating this multi-phase problem can be carried out through different techniques each of which offering a unique interplay between accuracy and computational time. Full transient 3D simulations are offered as the most accurate and computationally involved benchmark case. In parallel, porous media models of the periodic structure is offered to save the computational time albeit at the expense of accuracy. Two cases of local thermal equilibrium (LTE) and local thermal non-equilibrium (LTNE) are investigated over a range of porosity for different solid matrix materials being copper, aluminium, nickel and stainless steel. To enable the use of LTE, a theoretical model for the effective thermal conductivity is developed and validated against detailed 3D results. The LTNE model, on the other hand, has to rely on an interfacial heat transfer coefficient which is developed in this study to minimize the error between simplified porous media models and the benchmark case. The LTNE model demonstrated excellent accuracy for higher thermal conductivity ratio and/or lower porosity, on the contrary, the LTE model for lower thermal conductivity ratio (stainless-steel cases) outperforms the LTNE model. • Different volume-averaging models are conducted, compared to pore-scale prediction. • Effective thermal conductivity of the periodic structure has been developed. • The accuracy of LTE and LTNE models has been reported for different conditions. [ABSTRACT FROM AUTHOR]

• We conduct transport experiment to test local thermal equilibrium (LTE) assumption. • The LTE assumption can be violated under natural groundwater flow conditions. • Violation of LTE significantly impacts mechanical thermal dispersion. • Effects of thermal disequilibrium on velocity estimates were negligible. • Modelling heat transport requires consideration of LTE condition. 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. [ABSTRACT FROM AUTHOR]

In this article, the fully boiling process inside pipe filled with porous media has been numerically investigated using Cu/water nanofluid. Two-Phase Mixture Model (TPMM) has been modified to include the impacts of adding nano-fluid instead of pure water under Local Thermal Equilibrium (LTE) model. The mathematical formulation have been solved utilising finite volume method on fixed grid mesh. Impacts of geometric parameters, operating parameters and properties of porous media on the profiles of temperature and liquid saturation have been presented. The obtained solutions using Cu/water have been compared with those obtained using pure water and hence, results clearly demonstrate that the using Cu/water strongly enhance the diffusive heat inside the pipe. The results of Cu/water indicate that the mixture region is further prolonged in the upstream and downstream parts in comparison with the results that obtained using pure water due to add further heat to the domain occurring from rising the axial diffusion. The using of Cu/water leads to move the boiling front considerably towards the pipe outlet and the exit temperature is substantially reduced as compared to the pure water case. Results of Cu/water also display that the solid volume fraction, heating and flow conditions, porous structure properties and geometric parameters have high influences on the starting and ending of mixture region. Based on this, the nanofluid can be used while modelling the fully boiling process since it supplies an extra technique for heat transfer and considers as a safety factor, particularly in the applications that required very high temperature. [ABSTRACT FROM AUTHOR]

The validity of the local thermal equilibrium assumption in the free convective steady flow over a circular cylinder heated at constant temperature and embedded in a packed bed of spheres is investigated numerically. For this purpose, the Forchheimer – Brinkman - extended Darcy momentum model and the local thermal non-equilibrium energy model are solved numerically using a spectral element method. Numerical solutions obtained over broad ranges of representative dimensionless parameters, i.e. Rayleigh number (10 3 ≤ Ra ≤ 5 × 10 7 ), solid-to-fluid thermal conductivity ratio (0.1 ≤ kr ≤ 10 4 ), cylinder-to-particle diameter ratio (20 ≤ D / d ≤ 100), porosity (0.3 ≤ ε ≤ 0.7), are used to present conditions at which the local thermal equilibrium assumption can or cannot be employed. This study yields that the local thermal equilibrium LTE assumption is true at lower Rayleigh number, higher solid-to-fluid thermal conductivity ratio, higher cylinder-to-particle diameter ratio and lower porosity. In addition, it is found that the solid conductivity has the significant influence on satisfying the LTE , where it is completely satisfied in the system for all values of flow and structural parameters, i.e. Ra , D / d and ε , at higher kr , and vice versa, it cannot be satisfied at lower kr , for the whole ranges of other parameters. [ABSTRACT FROM AUTHOR]

The unsteady, conjugate, forced convection heat transfer from a porous sphere embedded in another porous medium has been analysed. Both porous media are fluid saturated. Local thermal equilibrium between the two phases is assumed. The fluid flow inside and outside the sphere was considered axisymmetric, steady and incompressible (Darcy and Brinkman flows). The heat balance equations were solved numerically in spherical coordinates system by an implicit alternating direction finite difference method. The influence of the porous media permeability and sphere Peclet numbers on the heat transfer mechanism and rate was analysed for different values of the physical properties ratios (thermal conductivity ratio and heat capacity ratio). [ABSTRACT FROM AUTHOR]

This article aims to analyze the combined effects of Hall and ion slip currents, Darcy-Forchheimer porous medium, and non-uniform magnetic field under the suspension of hybrid nanoparticles. The flow situation is transformed into mathematical problems using conservation laws and correlations among thermophysical properties of base fluid nano and hybrid nanoparticles. These mathematical models are approximated under boundary layer (BL) approximations. The similarity analysis is performed and the finite element method (FEM) is deployed for the simulations and further investigations regarding non-Fourier behavior of heat and mass transfer. The present results have good agreement with the published benchmark which is a special case of present work. The numerical simulations for the motion of fluid particles under the variation of Weissenberg number are observed and it is noticed that fluid motion decelerates for higher values of Weissenberg number. Significant retardation to the motion of the fluid is seen because of an increase in the Darcy porous medium parameter as an increase in it implies a decrease in the permeability of the porous. Thermal relaxation is the property of the fluid due to which it avoids thermal changes to maintain thermal equilibrium. Therefore, a remarkable decrease in the temperature of fluid exhibiting thermal relaxation characteristics is noticed. It is also noted from numerical experiments that Hall and ion slip currents are responsible to slow down the Ohmic dissipation phenomenon. Thus the property of ionized fluid helps in controlling the thickness of thermal BL. Numerical experiments have shown that the solutal relaxation time for hybrid nanofluid is greater than that for mono nanofluid. Mass diffusivity of the fluid with hybrid nanofluid is less than that of mono nanofluid. [ABSTRACT FROM AUTHOR]

This paper investigates the linear and weakly nonlinear stability of thermosolutal rotating porous convection subject to a lack of thermal equilibrium. Being an example of a triply diffusive fluid system in porous media with multiparameters, some novel results on the linear instability are delineated for a few isolated cases. The otherwise stabilizing factors such as stabilizing solute concentration and rotation are shown to destabilize the system under certain parameters space. Besides, the existence of a completely detached closed convex oscillatory neutral curve from that of the stationary neutral curve is uncovered indicating the requirement of three critical thermal Darcy-Rayleigh numbers to identify the linear instability criteria instead of the usual single critical value. The multivalued nature of the stability boundaries for the case of completely detached oscillatory neutral curves is displayed. The co-dimension-2 points are found through a stability map with the demarcation of stationary and oscillatory convective regions in a plane of Darcy-Taylor and scaled Vadasz numbers. Weakly nonlinear stability theory is carried out for a stationary case by using a modified multi-scale method and thereby the complex Ginzburg-Landau amplitude equation is derived identifying the pitchfork bifurcation. Moreover, heat and mass transport are quantified in terms of average thermal and solute Nusselt numbers, respectively. [ABSTRACT FROM AUTHOR]

Scientific community from the field of thermo-fluidics have focused extensive attention towards investigating techniques of enhancing the heat transfer in varied thermal systems. One of the most suitable techniques for augmenting the heat transfer is incorporating porous medium into thermal systems. The transport processes through porous media, which consists of a fluid phase and a solid matrix, can be modelled by either considering both to be in thermal equilibrium or in thermal non-equilibrium. Hence, two different modelling strategies viz. local thermal equilibrium (LTE) model and local thermal non-equilibrium (LTNE) model have been employed by different researchers. In this work, a comprehensive review of the published literatures in respect of the modelling approaches used for determining the implications of embedding porous media in different thermal systems from the perspective of heat transfer and entropy generation has been presented. The effects of various key determinants on the fluid flow, heat transfer characteristics and entropy generation in thermal systems are discussed. This discussion is then followed by a critical assessment of the applicability of LTE and LTNE approaches. At the end, conclusions and recommendations about the less explored systems and the areas that needs further investigations are summarized. • Critical review of forced convective heat transfer in porous media is presened. • The review article categorically discusses LTE and LTNE modelling strategies. • Effects of key determinants on heat transfer and entropy generation are discussed. • Recommendations are provided in areas having potentials for future research. [ABSTRACT FROM AUTHOR]

Highlights: [•] The performance of four methods used to implement fast gradient separations is compared. [•] The reproducibility of the peak areas, retention times, and peak widths are presented. [•] Conditions include constant flow rate, and two constant inlet pressures. [•] Columns of core-shell particles give more reproducible data than those of fully porous ones. [•] The influence of the length of the post-run times on the reproducibility is also discussed [ABSTRACT FROM AUTHOR]

Highlights: [•] The performance of four methods used to implement fast gradient separations are compared. [•] The reproducibility of the peak areas, retention times and peak widths are presented. [•] Conditions include constant flow rate and two inlet pressures. [•] An original programmed flow nearly constant pressure method is included. [•] The influence of the length of the post-run times on the reproducibility is also discussed. [ABSTRACT FROM AUTHOR]

Abstract: Taking the influences of chemical reaction mechanisms into account, a mathematical model has been developed to simulate the coupled heat and mass transfer as well as endothermic reactions in a non-thermal equilibrium packed bed with Soret and Dufour effects, which was numerically solved and validated by comparing with experimental data. It was found that the chemical reaction mechanisms have a great influence on the calculated solutions, and the cross-diffusion effects on the reactive characteristics of the packed beds are diverse under different chemical reaction mechanism. For the heat transfer controlled mechanism, the maximum reductions of the concentration of gas product and the solid fractional conversion induced by the Soret and Dufour effects are 25.1% and 14.4% respectively at superficial velocity 53.3cms−1 and the Nusselt number 4.1. However for the mass transfer controlled model, the calculated solid fractional conversions are higher than that obtained by neglecting the cross-diffusion effects and the increase being less than 16% at superficial velocity 11.9cms−1 and the Sherwood number 47.1. The differences induced by the Soret and Dufour effects are demonstrated numerically to increase gradually with the Nusselt number or the Sherwood number. [Copyright &y& Elsevier]

This paper presents the mathematical framework and the asynchronous finite element solver that captures the brittle fractures in multi-phase fluid-infiltrating porous media at the mesoscale where the constituents are not necessarily in a thermal equilibrium state. To achieve this goal, we introduce a dual-temperature effective medium theory in which the distinct constituent temperatures are homogenized independently whereas the heat exchange among the constituents is captured via phenomenological heat exchange laws in analog to the dual-permeability theory. To handle the different growth rates of the boundary layers in a stable and computationally efficient manner, an asynchronous time integrator is proposed and implemented in an operator-split algorithm that updates the displacement, pore pressure, phase field, and temperature of each constituent in an asynchronous manner. Numerical examples are introduced to verify the implementation and compare the path-dependent behaviors predicted by the dual-temperature and one-temperature models. [ABSTRACT FROM AUTHOR]

Local thermal non-equilibrium effects on heat natural convection features in a horizontal confocal elliptical annulus with the inner cylinder covered with a nanofluid-saturated porous sleeve is investigated in this study. The steady and laminar natural convective flow is incited by the thermal buoyancy resulting from the differential heating between the inner and outer annulus' surfaces. The nanofluid phase and the solid phase of the porous sleeve are hors local thermal equilibrium situation. The heat and the hydrodynamics equations in their dimensionless form under Darcy-Brinkman Forchheimer model for the porous region were computationally solved by the finite volume technique using the standard SIMPLER algorithm. The results were analyzed according to different porous materials characteristics under LTNE condition. The standard 0.05 significance level was employed to determine the local thermal equilibrium situation in the porous sleeve. For the first time, contours of the spatial distribution of the LTNE sources within the porous sleeve region were represented. [ABSTRACT FROM AUTHOR]

Abstract: In this paper an analytical model was developed to minimize the thermal resistance of an air cooled porous matrix made up of solid spheres with internal heat generation. This was done under the assumption of local thermal equilibrium. The analytical solution of the optimum sphere diameter was found to be independent of the heat generation rate of the solid spheres, but was dependent on the applied pressure drop and fluid properties. The analytical model compared very well to a numerical model found in a computational fluid dynamics code when air and liquid water properties were used for the fluid phase and wood and silica/sand properties were used for the solid phase. [Copyright &y& Elsevier]

Abstract: A detail numerical analysis of the effect of particle diameter of a packed bed of spherical particles on forced convection about an embedded circular cylinder is presented. This parametric study focusses on the two-phase energy (LTNE—local thermal non-equilibrium) model, which does not assume local thermal equilibrium (LTE) between the solid medium and the fluid. The investigation is performed for a cylinder-to-particle diameter ratio D cy /d p =10–100, at a wide ranges of Reynolds number Re D =1–250 and solid-to-fluid thermal conductivity ratio k r =0.01–1000. A comparison of predictions from the LTNE and LTE energy models is also made. This paper quantifies the influence of the key non-dimensional parameters on the heat transfer rate. It is also shown that although the presence of the porous materials around the heated cylinder enhances the overall heat transfer and increases the pressure drop in the bed compared to an empty channel, using a porous medium with large particle diameters increases considerably this enhancement in heat transfer and decreases significantly the unfavorable pressure drop. [Copyright &y& Elsevier]

Abstract: A vertical porous layer subject to lack of local thermal equilibrium and differentially heated from its sidewalls experiences extremely different conditions when it is heated via a constant heat flux, rather than via a hot temperature imposed on the sidewall. For a start the steady state basic temperatures of the fluid and solid differ, as distinct from the corresponding case of imposed temperature on the sidewall when both fluid and solid temperatures are identical and linear at steady state and the lack of local thermal equilibrium (LaLotheq) can manifest itself at transients or when the basic temperature profiles stated above become unstable. In addition, in the case of heating via a constant heat flux the steady state basic temperatures of the fluid and solid are not only distinct but also nonlinear. The analytical derivation of these nonlinear solutions for the basic natural convection in a vertical porous layer differentially heated from its sidewalls, subject to lack of local thermal equilibrium and heating via a constant heat flux is presented and the results analyzed over a wide range of parameter space. In general it is shown that the lack of local thermal equilibrium destroys the symmetry of the problem via deviatoric terms in the solutions. [Copyright &y& Elsevier]

Abstract: Porous media combustion (PMC) has interesting advantages compared with free flame combustion due to higher burning rates, increased power dynamic range, extension of the lean flammability limits, and low emissions of pollutants. Extensive experimental and numerical works were carried out and are still underway, to explore the feasibility of this interesting technology for practical applications. For this purpose, numerical modeling plays a crucial role in the design and development of promising PMC systems. This article provides an exhaustive review of the fundamental aspects and emerging trends in numerical modeling of gas combustion in porous media. The modeling works published to date are reviewed, classified according to their objectives and presented with general conclusions. Numerical modeling of liquid fuel combustion in porous media is excluded. [ABSTRACT FROM AUTHOR]

Abstract: An apparent paradox that appears in problems of heat conduction in porous media subject to lack of local thermal equilibrium (LaLotheq) that was introduced by Vadasz [Transport in Porous Media 59 (2005) 341–355] is reformulated and resolved. This apparent paradox relates to a combination of Dirichlet and insulation boundary conditions and leads the solution towards local thermal equilibrium (Lotheq). [Copyright &y& Elsevier]

Abstract: An analytical characterization of the heat transfer in an oscillating flow through a porous medium is presented in this work. Based on a two-equation model, two important dimensionless parameters are identified as the ratio of the thermal capacities between the solid and fluid phases and the ratio of the interstitial heat conductance between the phases to the fluid thermal capacity. The analytic solutions are obtained for both the fluid and solid temperature variations, and the heat transfer characteristics between the phases are classified into four regimes. In addition, a criterion for the validity of the local thermal equilibrium is suggested in a simple form as the ratio of the two time scales intrinsically involved in any transient heat transfer in porous media, namely the time scale relevant to the thermal inertia of porous media and the time scale pertinent to the transient variation of the boundary condition. [Copyright &y& Elsevier]

Abstract: This work presents an algorithm model for estimating the heat transfer by forced convection of the porous heat sink in a channel by applying the fin theory and the concept of the thermal network. The proposed algorithm model is simpler and more convenient than numerical analysis. By comparison with numerical calculations and other experiments, the model was verified to predict accurately heat transfer in various porous channels, such as metal foam channels and sintered porous channels. The inlet thermal boundary condition is also examined. The finding reveals that the effect of the inlet thermal boundary condition on the numerical calculations becomes weaker as the interstitial heat transfer coefficient increases. Additionally, a parameter Ω in terms of h v , and H ∗ is postulated to determine the local thermal equilibrium (LTE) in porous channels. Analytical results reveal some criteria for LTE in various porous channels. For instance, the criterion for LTE in aluminum foam channels is: if ε =0.91 and H =45mm, Re ⩾4700; if ε =0.95/10PPI and H =45mm, Re ⩾1600; if ε =0.95/10PPI and H =25.4mm, then Re ⩾6600. Besides, the scope of LTE in sintered copper bead porous channels with ε =0.38/d =1.59mm and H =10mm is about Re ⩾6600. Accordingly, the one-equation model, which is simpler than the two-equation model, can be used to analyze heat transfer through porous media in the applicable regions. [Copyright &y& Elsevier]

Abstract: This study shows that the physical conditions necessary for thermal waves to materialize in Dual-Phase-Lagging porous media conduction are not attainable in a porous slab subject to a combination of constant heat flux and temperature (Neumann and Dirichlet) boundary conditions. It is demonstrated that the approximate equivalence between Dual-Phase-Lagging (DuPhlag) heat conduction model and the Fourier heat conduction in porous media subject to Lack of Local Thermal Equilibrium (La Lotheq) that suggested the possibility of thermal oscillations and resonance reveals a condition that cannot be fulfilled because of physical constraints. [Copyright &y& Elsevier]

The validity of the local thermal equilibrium assumption in natural convection over a vertical flat plate embedded in porous medium is investigated analytically. The study is based on the two-phase (Schumann) model, using the Brinkman term (no-slip condition) to cover the flow. It is found that there are four dimensionless parameters controlling the local thermal equilibrium assumption: the volumetric Biot number (Biv), the modified Rayleigh number (Ram), the modified Darcy number (Da) and the ratio of effective to dynamic viscosity (λ). The effects of these parameters are investigated and a correlation equation is developed in order to determine the region where the local thermal equilibrium assumption is valid. [Copyright &y& Elsevier]

In the paper, we make a linear stability analysis in a Newtonian, liquid-saturated high porous medium in the presence of a heat source under the assumption of local thermal non-equilibrium(LTNE). The heat source is represented by an internal Rayleigh number R I and is considered in two ways (i) internal heat source in a liquid phase (R I l) and (ii) internal heat source in a solid phase (R I s). The internal heat generation parameter's effect is to destabilize the onset of stationary convection due to an increase in the system's energy. The results of local thermal equilibrium are obtained as a limiting case of the problem. The effect of various parameters on the onset of convection is analyzed and depicted graphically. • The effect of internal heat source and local thermal non-equilibrium (LTNE) on onset of Brinkman–Bénard convection (BBC). • Internal heat source considered in liquid and solid phases individually. • Classical results of local thermal equilibrium (LTE) as a limiting case of the present study (LTNE). • Effect of various parameters of heat source/sink on onset of BBC. • Asymptotic analysis of critical Rayleigh number for small and large values of H. [ABSTRACT FROM AUTHOR]

The single-blow transient testing technique has been used for more than 50 years, and many correlations have been proposed from this technique. However, these correlations differ significantly from one another and the behind reasons are still unknown. In this study, we used numerical simulation to detect the detailed temperature evolution of an entire porous matrix during the single-blow experiment. The numerical simulation was performed on a three-dimensional geometry with idealized packed tetrakaidecahedron structures, and the numerical method was based on three-dimensional RANS equations. The initial and boundary conditions of the simulation were the same as those of the single-blow transient testing technique. The detailed temperature evolution of the sample and air stream was obtained. Computational results indicated a local thermal equilibrium region inside the porous matrix during the single-blow transient experiment. The local thermal equilibrium is affected by the sample thickness, superficial velocity, and thermal capacity. The "local thermal equilibrium" inside the porous matrix during the single-blow transient test contradicts the prerequisites of this measurement method. This finding is validated by experimental data and is crucial to heat transfer inside porous media, as well as to the design and optimization of heat exchangers, volumetric solar receivers, and thermal storage systems. [ABSTRACT FROM AUTHOR]

This paper presents new fully-coupled analytical thermo-poroelastic solutions, introducing four new components to the traditional Local Thermal Non-Equilibrium (LTNE) theory: thermo-osmosis; thermal-filtration; heat sinks due to thermal expansion of the pore fluid and the solid phase; and vertical confinement. Thermo-osmosis, thermal-filtration, and fluid dilation are found to have very different effects in case of LTNE versus local thermal equilibrium (LTE), resulting in a fundamentally different thermo-hydraulic-mechanical (THM) response. The aforementioned non-traditional thermal processes cause generation of notably higher pore pressures in the porous medium that cannot be otherwise predicted using current solutions. Fluid temperatures are more sensitive to these non-traditional thermal processes, compared to the solid phase temperatures. Thermo-osmosis is found to have more significant effects under LTNE compared to LTE, and to be the dominant mechanism affecting solid temperatures, pore pressures and stresses. Thermal-filtration and heat sink due to fluid thermal expansion are the dominant mechanisms affecting fluid temperatures. The vertical confinement and formation anisotropy is shown to notably impact the THM response of a porous layer to heat source or sink. The impact of the aforementioned four novel components are found to be enhanced under an impermeable hydraulic boundary compared to a permeable boundary condition. [ABSTRACT FROM AUTHOR]

• Complete evaporation process in a double-pipe porous evaporator has been considered. • One dimensional phase change problem is assumed as demonstrative example. • Modified enthalpy formulation has been utilized along with LTE model. • Radius ratio strongly influences beginning and ending of phase change process. • Power index of relative permeabilities have significant impact on phase change process. In this article, two-phase flow in a double-pipe porous heat exchanger and associated phase change processes has been numerically analysed to investigate the impacts of the relative permeabilities. The modified h -formulation along with the assumption of Local Thermal Equilibrium condition has been employed. Finite Volume Method (FVM) has been used to discretise the governing equations. The solutions of incomplete evaporation process have been validated with the experiments and they show an excellent agreement between them. The pertinent parameters have been systematically investigated to demonstrate the importance of the above mentioned influences on the complete evaporation process. It has been observed that the power index of the relative permeabilities for either liquid or vapour region has a significant effects on the beginning and ending of phase change operation, especially when the steam is formed inside the pipe. Comparison between results obtained with maximum and minimum values of the power index indicated that the latter value must be used while simulating the complete evaporation process, particularly for very low inlet Reynolds number and very high wall temperature. It is also evident that the operating conditions and geometric parameters of the heat exchanger have been substantially changed the location of the beginning and ending of the phase change process. On the other hand, the properties of porous media have only minor influence. [ABSTRACT FROM AUTHOR]

• Higher inlet velocities into volumetric heat absorbers cause quicker stabilization times and decreases equilibrium temperature, T eq. Increasing porosity lower T eq and shorten time for temperature stabilization. • Less permeable solid matrices result in slightly higher T eq due to better enhancement of energy exchange between phases. • Thermal efficiency η increases for lower inlet velocities and higher thermal conductivity ratios, whereas η is reduced for more permeable structures and higher porosities. Volumetric heat absorbers made of porous materials allow for a greater contact area between the porous matrix and the working fluid. In such devices, heat is collected in a volume rather than a surface. This work deals with transient behavior of Volumetric Heat Receivers using the thermal non equilibrium approach. Balances for energy amounts for the porous ceramic materials and air are solved numerically using the backward Euler discretization method and application of the SIMPLE method. After obtaining the algebraic equation system, relaxation by the SIP method is applied. We investigate here the effects of permeability, thermal conductivity ratio, inlet velocity and porosity on the temperature reached after thermal equilibrium. Higher inlet velocities attain quicker stabilization times and decreases equilibrium temperature, T eq. In addition, increasing porosity lower T eq and shorten time for temperature stabilization. Less permeable solid matrices, i.e. porous structures with lower Da , result in slightly higher T eq due to better enhancement of energy exchange between phases. Increasing k s k f / increases stabilization time as well as equilibrium temperatures. Thermal efficiency increases for lower inlet velocities and higher thermal conductivity ratios, whereas η is reduced for more permeable structures and higher porosities. [ABSTRACT FROM AUTHOR]

• Based on the suggested new formulation for nondimensionalization, Sparrow number appears in the dimensionless equations automatically. • The good agreement between the pore scale and volume average results shows that the time and space average of the interfacial heat transfer coefficient provides sufficiently accurate results for the volume average analysis. • A local thermal equilibrium chart is established based on thermal diffusivity ratio and Sparrow number to find out the equilibrium state of a solid/liquid phase change in a porous medium. • The possibility of local thermal equilibrium is high for the large values of Sparrow number (such as 500) and thermal diffusivity ratio around 1. The problem of solid/liquid phase change in a cavity assisted by a closed cell porous medium is analyzed by pore scale and volume average approaches. The volume average governing equations are non-dimensionalized by using the porous media stagnant thermal diffusivity and Sparrow number appears automatically. The study consists of four parts as the derivation of new formulation based on Sparrow number, proving the validation of volume average method based on the given formulation for the closed cell porous media, discussion on the change of interfacial heat transfer coefficient with time and finally presenting a thermal equilibrium chart in terms of Sparrow number and thermal diffusivity ratio for prediction of local thermal equilibrium state. A good agreement between the pore scale and volume average results is observed. Based on the established thermal equilibrium chart, it is found that the possibility of local thermal equilibrium is high for the large values of Sparrow number (such as 500) and for the thermal diffusivity ratio around 1. The established equilibrium chart is verified by prediction of local thermal equilibrium state for two different closed cell porous media and then the validation of predication is proved by using the results of pore scale study. [ABSTRACT FROM AUTHOR]

• A new solver based on OpenFOAM is developed to solve porous media heat transfer. • For porous media attached near to the walls, heat transfer can be enhanced up to 65%.% • Increase in heat transfer rate for core side configuration is about 938%.% • There is a critical thickness of porous media for each of the porosity value. • Increasing porosity at the wall side increases Nu but for the core side, it deceases. In the present work, forced convective heat transfer and pressure drop in the entrance and fully developed regions of a square duct, which is partly filled by porous medium, is numerically investigated. The porous medium is placed (i) adjacent to the wall or (ii) at the core of the square duct. This 3D analysis was essential because in the earlier studies the thermal hydraulic characteristics were predicted by considering the flow to be between two parallel plates or as axisymmetric, which is not applicable for square ducts. Apart from the thickness of the porous medium, changes in porosity is also considered in the analysis. The porous medium is taken to be wire mesh screens, as it is the most common case. The flow through porous medium is modelled using Darcy–Forchheimer model and the heat transfer is modelled using local thermal equilibrium model. For solving this problem, a new solver is developed using the open source CFD package OpenFOAM. From the results it is observed that, adding porous inserts at the core of the duct provides better heat transfer rate with lesser pressure drop. The effect of porosity on heat transfer and pressure drop is accentuated only if the porous medium thickness ratio is greater than 0.625. The maximum heat transfer that can be achieved for wall side case when thickness ratios in the range 0.8-1.0 is approximately 1.65 times than that of a duct without porous medium. If the porous medium is at the core side case, maximum heat transfer is 10.4 times when the thickness ratio is between 0.85-0.95. It is also found that, when the porous medium is at the wall side, the Nusselt number increases with increases in porosity. However, if the porous medium is in the core side, the Nusselt number increases with decreasing porosity. [ABSTRACT FROM AUTHOR]