Thermal Conductivity Of Porous Media Research Articles

Research on Effective Thermal Conductivity in Porous Media Embedded with Randomly Distributed Damaged Tree-like Bifurcation Networks

Due to the complexity of the microstructure of porous media, it is of great significance to explore the heat transport mechanism in porous media in many engineering applications. In this study, an expression for effective thermal conductivity (ETC) of porous media embedded with randomly distributed damaged tree-like bifurcation networks is derived based on the theory of thermodynamics and fractal features of tree-like bifurcation networks. We investigate the effect of heat conduction and heat convection in porous media embedded with randomly distributed damaged tree-like bifurcation networks on the ETC of the porous media. It is found that our fractal model has good consistency with the existing available experimental data. In addition, the influence of the microstructural parameters of the model on heat transfer in the porous media is analyzed in detail. The research results can provide significant theoretical guidance for the development and design of heat transfer systems.

A diffuse interface–lattice Boltzmann model for conjugate heat transfer with imperfect interface

A diffuse interface-lattice Boltzmann model is proposed for modeling conjugate heat transfer problems with imperfect interfaces. According to the continuity condition of heat flux and jump condition of temperature across the imperfect interface, a unified sharp interface equation of the temperature field with a singular source term in the composite media domain is established. Then a diffuse interface equation is obtained by making a smoothed approximation of the unified sharp interface equation. The novel diffuse interface equation is restructured into a second-order heat diffusion equation with an anisotropic diffusion coefficient tensor. To numerically solve the second-order anisotropic diffusion equation, a multiple-relaxation-time (MRT) lattice Boltzmann (LB) scheme is employed. Several numerical simulations of benchmark test examples with analytical solutions are carried out to demonstrate the accuracy of the present model, including the steady-state heat diffusion in a two-layer medium with a flat interface, steady heat diffusion in a square domain with a curved interface and unsteady-state temperature diffusion with two-layer media. The numerical results show that the phenomenon of temperature jump across the imperfect interface can be successfully and correctly captured. Moreover, as an example of practical application, the new proposed diffuse interface model is utilized to predict the effective thermal conductivity of porous media with thermal contact resistance at pore scale. The variation law of the effective thermal conductivity is obtained for each parameter by studying the effects of thermal conductivity ratios of the dual-component material, the shape and volume fraction of blocks in the material, the interfacial thermal conductance coefficient, and the number of blocks on the effective thermal conductivity. Both uniform and random pore structures are considered. The previous theoretical equations strongly support the validity of the present model.

Physics-informed neural networks for studying heat transfer in porous media

Numerous efforts have been devoted to studying heat transfer problems in porous media. Physics-based models, numerical methods and experiments are commonly adopted to obtain the temperature and heat flux fields, along with effective thermophysical properties like effective thermal conductivity for heat conduction, which exert significant impact on analyzing the heat transfer efficiency in porous systems. Recently, using data-driven machine learning methods to predict temperature/heat flux fields and effective thermal conductivity of porous media has gained attention, demonstrating the potential to achieve higher accuracy than physics-based models while requiring less computational time than numerical methods. However, machine learning approaches are commonly restricted by the requirement for sufficient labeled training data, which can be difficult and time-consuming to acquire. In this work, we apply physics-informed neural networks to investigate heat conduction in porous media. We show that, without any labeled training data, accurate predictions for temperature/heat flux fields in porous media can be achieved. The obtained effective thermal conductivity values for an ensemble of porous media samples have an average relative error of only 2.49%. Compared with numerical calculations, a computation acceleration of 5 orders of magnitude has been achieved. Compared with data-driven machine learning methods, this method offers enhanced flexibility since no labeled data is required. Furthermore, we also illustrate that physics-informed neural networks can be easily extended to predict nonlinear heat conduction in porous media. Our work demonstrates that physics-informed neural networks are promising tools for studying heat conduction problems and can also be possibly extended to study other complex heat transfer problems in porous media.

Establishing a transient model of double-layer porous media interfacial evaporation system to reveal the relationship between porous media parameters and evaporation performance

The solar interfacial evaporation system can generate steam efficiently by localizing solar thermal energy to heat air–water interface, which has great application potential in seawater desalination, sewage treatment, and other fields. At present, the solar absorption layer and substrate of the interfacial evaporation system are mainly made of carbon materials, sponges, foams, and other porous media materials. However, the transient interfacial evaporation heat and mass transfer model and the influence of the physical parameters of porous media on evaporation performance have rarely been investigated. Based on heat and mass transfer theory of porous media, a transient theoretical model of porous media interfacial evaporation system is established in this paper. Moreover, the effects of physical parameters such as the porosity and thermal conductivity of porous media on evaporation performance are analyzed, and the accuracy of the model is verified through outdoor experiments. Based on the model calculation, as the porosity of the substrate increases, the evaporation rate and efficiency of the evaporator first increase and then decrease. The lower the thermal conductivity of the substrate and the higher the porosity and thermal conductivity of the solar absorption layer are, the better the evaporation performance is, but the growth rate gradually decreases. Therefore, the relationship between the improvement of evaporation performance and the increased cost caused by the improvement of material properties needs to be considered. The model and related theoretical analysis results can provide a theoretical basis for system structure optimization, material selection and other aspects of future research on double-layer porous media interfacial evaporation system.

A three-cell effective thermal conductivity model of two-phase porous media

Effective thermal conductivity of porous media is of interest in many heat transfer applications. In this study, a new three-cell two-phase model is developed to calculate porous medium thermal conductivity. In the proposed three-cell model, each solid particle is enveloped by two concentric cells with one being fluid and the other solid. The outermost solid cell is proposed to conceptualize the interactions among the solid particles and fluid. The temperature distributions in the three cells are separately solved and the effective thermal conductivity is then determined. Quantitatively, a contact factor (z factor), which is equal to the solid volume faction that is in the outermost cell, is introduced to reflect the extent of phase contact among the two phases. Under special cases with z = 0 and z = 1 when the three-cell model collapses to two-cell models, the model can bridge the Hashin-Shtrikman (H.S.) lower and upper bounds (or the two forms of Maxwell-Eucken model). In more general cases, the model always predicts thermal conductivity between the H.S. bounds when the z factor is between 0 and 1. The proposed model can well capture the trend of published models and experimental data as well as the results from detailed pore-scale numerical simulations when the z factor decreases non-linearly as the porosity increases.

Experimental study on burning characteristic of liquid fuel immersed in porous media bed: Effect of particle gradation

A series of burning test was conducted to investigate the effect mechanism of particle gradation on burning characteristic of liquid fuel immersed in porous media. High-purity quartz equipped with two-component discontinuous gradation and ethanol liquid were employed as porous bed and liquid fuel. The characteristic parameters, e.g., burning rate, temperature distribution, flame feature and burning duration, etc., were recorded and identified. Results show that the burning characteristic of liquid fuel immersed in porous media with gradation configuration is conjunctively influenced by capillary effect and thermal conductivity of porous media. For the porous media bed with fine particles, capillary effect plays a dominant role in the variation trend of burning rate. While for the porous media bed with good gradation, under the effect of better contact condition and more coordination numbers, thermal conduction enhanced by particle gradation dominates the burning characteristic. Meanwhile, the burning rate of porous bed immersed by liquid fuel demonstrates stage-variation feature: a rapid growth stage dominated by direct flame thermal feedback and an attenuation-stable stage dominated by thermal conduction. Due to the “back effect”, the burning rate has a quasi-stable phase in middle-and-late stage, which is positively correlated with the one-half power of media porosity. Moreover, due to the enhancement of thermal conductivity, the downward heat transfer rate of porous media with good gradation is relatively faster. In addition, there is still a positive tendency between flame height and burning rate. This work is expected to provide some references for understanding the burning characteristics of liquid fuel immersed in porous media and burning-decontamination operation.

Experimental investigation on the effective thermal conductivities of different hydrate-bearing sediments

The natural gas hydrate has been regarded as an important future green energy. Significant progress on the hydrate exploitation has been made, but some challenges are still remaining. In order to enhance the hydrate exploitation efficiency, a significant understanding of the effective thermal conductivity (ETC) of the hydrate-bearing sediment has become essential, since it directly controls the heat and mass transfer behaviors, and thereby determines the stability of hydrate reservoir and production rate. In this study, the effective thermal conductivities of various hydrate-bearing sediments were in-situ measured and studied. The impacts of temperature, particle size and type of sediment were investigated. The effective thermal conductivities of the quartz sand sediments before and after hydrate formation were in-situ measured. The results show the weak negative correlation of effective thermal conductivity of the quartz sand sediment on the temperature before and after the hydrate formation. The effective thermal conductivity of the hydrate-bearing sediment decreases with the increase of particle size of the sediment. The dominant effect of the type of porous medium on the characteristics of the effective thermal conductivity of hydrate-bearing sediment was highlighted. The results indicate that both the effective thermal conductivities of hydrate-bearing quartz sand sediment and hydrate-bearing silicon carbide sediment are weakly negatively correlated with temperature, but the effective thermal conductivity of hydrate-bearing clay sediment is weakly positively dependent on the temperature. In addition, the values of the effective thermal conductivities of various hydrate-bearing sediments are in the order of hydrate-bearing silicon carbide sediment > hydrate-bearing quartz sand sediment > hydrate-bearing clay sediment. These findings could suggest that the intrinsic thermal conductivity of porous medium could control the characteristics of effective thermal conductivity of hydrate-bearing sediment.

NATURAL CONVECTION FLOW AND HEAT TRANSFER IN AN L-SHAPED CAVITY PARTIALLY FILLED WITH POROUS MEDIUM: NUMERICAL ANALYSIS

In an L-shaped cavity partially filled with a porous material, natural convection flow and heat transfer are quantitatively investigated. The effect of numerous significant parameters on isotherms, streamlines, and heat transport characteristics is investigated within the enclosure. The Rayleigh number, Darcy number, effective heat conductivity of the porous medium, aspect ratio, and thickness of the porous layer are all investigated. The governing equations are solved using the Galerkin technique with weighted residuals. The findings of this study demonstrate that an L-shaped cavity exhibits fascinating properties. As a result, as the aspect ratio of the L-shaped cavity increases, the average Nusselt number decreases. Furthermore, raising the Rayleigh number, as well as the effective thermal conductivity of porous media, improved the average Nusselt number. In the case of natural convection, the thickness of the porous layer is shown to be inconsequential.

A novel fractal model for effective thermal conductivity in granular porous media

Quantitative prediction of effective thermal conductivity in porous media is very important in various industrial applications and scientific researches. As the topology and geometry characteristics of pore-solid space is extremely complicated, an accurately theoretical calculation in porous media is still a great challenge. In this study, a novel theoretical model of effective thermal conductivity is derived in granular porous media originated from the Laplace's Equation with a new boundary condition. The proposed model considers the size of solid particles following the fractal distribution characteristics, which is expressed as a function of porosity, fractal dimension of solid particle, maximum particle radius, representative length, and thermal conductivity of both solid particle and pore phase. The predictions of proposed model show a good agreement with the existing models and various published experimental data, which validates its accuracy and reliability. The effect of different geometrical parameters for proposed model is analyzed and discussed. This novel proposed model of effective thermal conductivity may reveal a better insight for thermophysical mechanisms in granular porous media than conventional models.

Thermal Conductivity Model Analysis of Unsaturated Ice-Containing Soil

In cold locales, the thermal conductivity of soil porous media varies according to their composition and the phase state of the substance contained within the pore space. During the winter, water and other media in the soil pore space freeze-thaw, resulting in their phase state, composition, distribution, and significant thermal conductivity changes. There are some shortcomings in the current research regarding the thermal conductivity change pattern of unsaturated ice-containing soils. In this paper, the representative elementary volume (REV) selection method is given for unsaturated ice-containing soil with porosity as a representative state variable. Under the condition of freeze-thaw, two thermal conductivity REV analysis models for unsaturated ice-containing soil are established: a simplified volume-weighted average REV model and a fine volume-weighted average REV model; accordingly, a macroscopic thermal conductivity analysis model is given. The computational analysis is carried out with an actual unsaturated ice-containing soil example. The influence of the application of frozen soil in China is examined for its effect on the variation law of the thermal conductivity of porous medium. The variation characteristics of thermal conductivity of permafrost soil with related parameters (porosity, water ratio, moisture percentage, ice content, and tortuosity) are discussed. The model built in this paper provides novel concepts and methods for analyzing the thermal conductivity characteristics of unsaturated soil, as well as enhancing and advancing the analysis.

Design and Performance Investigation of a Compact Catalytic Reactor Integrated with Heat Recuperator

The catalytic combustion has the advantage of lower auto-ignition temperature and helps to expand the combustible limit of lean premixed gas. However, the intake needs to be preheated to certain temperature commonly through an independent heat exchanger. Similar to the principles of non-catalytic RTO combustion, this paper presents a similar approach whereby the combustion chamber is replaced by a catalytic combustion bed. A new catalytic reactor integrated with a heat recuperator is designed to enhance the heat recirculation effect. Using a two-dimensional computational fluid dynamics model, the performance of the reactor is studied. The reaction performances of the traditional and compact reactors are compared and analyzed. Under the same conditions, the compact reactor has better reaction performance and heat recirculation effect, which can effectively decrease the ignition temperature of feed gas. The influences of the inlet velocity, the inlet temperature, the methane concentration, and the thermal conductivity of porous media on the reaction performance of integrated catalytic reactor are studied. The results show that the inlet velocity, inlet temperature, methane concentration, and thermal conductivity of porous media materials have important effects on the reactor performance and heat recirculation effect, and the thermal conductivity of porous media materials has the most obvious influence. Moreover, the reaction performance of multiunit integrated catalytic reactor is studied. The results show that the regenerative effect of multiunit integrated catalytic reactor is further enhanced. This paper is of great significance to the recycling of low calorific value gas energy and relieving energy stress in the future.

AN ANALYTICAL MODEL FOR EFFECTIVE THERMAL CONDUCTIVITY OF THE MEDIA EMBEDDED WITH FRACTURE NETWORKS OF POWER LAW LENGTH DISTRIBUTIONS

The effective thermal conductivity of porous media is of steady interest in the design of new materials. In this study, an analytical model for dimensionless effective thermal conductivity of media embedded with fracture networks of the power law length distributions is proposed. It is found that the proposed dimensionless effective thermal conductivity is a function of micro-structural parameters of media, such as the porosity [Formula: see text] and fracture orientation (dip [Formula: see text] and azimuth [Formula: see text]). The present results show that the dimensionless effective thermal conductivity of the media increases with the increase in the ratio [Formula: see text] and the power law exponent [Formula: see text] at [Formula: see text]. Inversely, when [Formula: see text], it decreases with the increase in the power law exponent [Formula: see text]. In addition, the dimensionless effective thermal conductivity is gradually independent of the orientation as the ratio [Formula: see text]. The present model may provide a significant insight into the mechanism of heat transfer in the media embedded with fracture networks of power law length distributions.

A comparative study of different heat transfer enhancement mechanisms in a partially porous pipe

The effect of porous material position on the heat transfer inside a pipe working in a turbulent regime is studied here to obtain a detailed understanding of the heat transfer enchantment mechanisms in different porous substrate positions. To this end, an in-house Fortran code is developed to solve the governing equations using the finite volume method and SIMPLE algorithm. Turbulent flow in porous media is modeled using a modified version of k–ε model. The flow field and heat transfer inside the partially filled pipe are investigated for the two cases of central and boundary configurations. The porous and flow characteristics including Reynolds number, Darcy number, the conductivity ratios of solid to fluid and the thickness of inserted porous layer are varied and the heat transfer performance is studied in different cases. It is observed that two entirely different phenomena enhance the heat transfer in central and boundary configurations. While the channeling of fluid between the porous media and the pipe wall highly affects the heat transfer performance in the former, the thermal conductivity of porous media plays a highly critical role in the latter configuration. It is shown that, for the same filling ratio, inserting the porous layer at the core of the pipe is more effective than placing it at the wall. Investigating porous materials with different solid conductivities revealed that covering the pipe wall with a porous material is justified only for solid matrixes with high thermal conductivities.

A dual-probe heat pulse-based sensor that simultaneously determines soil thermal properties, soil water content and soil water matric potential

A dual-probe heat pulse (DPHP) sensor is a robust tool that can measure soil thermal properties and associated soil physical properties and processes. A new DPHP based sensor was developed to simultaneously measure soil thermal properties, soil water content and soil water matric potential. A series of experiments were performed to evaluate the sensor performance. The new sensor was able to measure each soil property with acceptable accuracy. The accuracy of the matric potential determinations was approximately 10% in log scale. The effective range for ψ measurements was −1000 to −2.5 m of water, and the accuracy of the ψ determinations was best between −350 and −2.5 m of water, which included values of field capacity and wilting point for most soils and crops. The sensor design included a single heater wire to provide simultaneous heat inputs to two different materials, i.e., the soil and the sensor porous medium. The single heater wire did not influence sensor accuracy as long as the soil and the sensor porous medium thermal conductivity values were not significantly different. The new DPHP based sensor effectively measured various soil properties, including soil water matric potential, soil water content, and soil thermal property values.

Validation suite for numerical solvers calculating effective thermal conductivity in porous media

A validation suite for numerical solvers calculating effective thermal conductivity in porous media is presented. In a first step an appropriate numerical solver based on the finite volume method is developed. Subsequently validation is done with six benchmark cases. The benchmarks are grouped in one-dimensional and three-dimensional problems. Each group includes one case with homogeneous material, one case with function-graded material and one case with heterogeneous material. Building on that, five application cases will be examined. The cases can be grouped in two academic problems and three real world rock samples. During the validation process the focus is set on two main questions. Firstly, how to ensure the quality of numerical results? Secondly, how do different interpolation techniques for the determination of interfacial conductivity influence numerical results? In general extensive use of mesh refinement studies is made. With a maximum relative error of 25% between coarsest possible mesh and expected converged solution, it is shown that refinement studies are an important step towards numerical quality control. Further it is observed, that step-wise defined thermal conductivities, as it is the case in porous media, might lower the theoretical order of accuracy of a given numerical scheme.

A new pool boiling heat transfer correlation for wetting dielectric fluids on metal foams

Porous structures, as metal foams, can enhance the heat transfer performance. For a safe industrial application, a predictive model for both heat transfer coefficient and maximum heat flux is required. But, there is no correlation for dielectric fluids on metal foams available in the literature. This work aims to develop a correlation based on dimensional analysis for metal foam surfaces in pool boiling with different dielectric fluids. The model takes into account the porous heating surface characteristics (porosity, pore diameter, and thickness), the working fluid thermophysical properties, and its interaction. The model was developed based on the experimental database obtained by the authors and validated with the open literature database. Two metal foams with different characteristics were used for carrying out the pool boiling tests with two different working fluids: HFE-7100 and ethanol. The newly developed correlation predicted well the database with an average error equal to 10.8% where 93.8% within the error range of ± 30%. To the maximum heat flux, the average error was 13.6% where 100% within the error range of ± 30%. The pore diameter and thickness play an important role in both models. The porosity and solid-phase thermal conductivity from the metal foam change the porous medium thermal conductivity, which influences the heat transfer coefficient (HTC). Finally, the properties of the working fluid also influence the predictive model, mainly the latent heat of vaporization, liquid thermal conductivity, and saturation temperature.

Thermal conductivity of porous sintered metal powder and the Langmuir shape factor

The objective of this study is to re-examine the classical parallel and classical series models of the effective thermal conductivity of porous media and review the underlying assumptions used to develop these asymptotic models. The Langmuir shape factor concept is introduced to gain insight into these classical models and add extra degrees of freedom to formulate semi-empirical correlations for the effective thermal conductivity based on the parallel, series, and combination of parallel and series heat flow configurations. The analytical models reveal the average areas of the heat flow as potential targets for curve fitting equations with fitting parameters. Experimental data for sintered porous copper were used to calibrate the theoretical models. Correlations for the effective thermal conductivity, Langmuir shape factors, average heat conduction areas, and the average lengths of the heat transfer pathway of the two phases as functions of porosity were obtained and compared graphically.

Thermal Investigations of Double Pass Solar Air Heater with Two Types of Porous Media of Different Thermal Conductivity

This study describes an experimental investigation of the thermal efficiency of stainless steel mesh and steel wool as a porous medium in the lower channel of a double pass solar air heater. An experimental setup was planned and developed. Various types of porous media with high thermal conductivity and with different porosities have been tested. The effects of the porosity of wire mesh, the thermal conductivity of porous media, mass flow rate, and the intensity of radiation have been studied. Experimental results show that thermal efficiency with using porous media is greater than without using porous media. When used steel wool as a porous medium, the thermal efficiency reached 79.82 percent while it can be achieved 76. The percent by using stainless mesh as porous material. The reduction in porosity increasing thermal efficiency. The thermal efficiency of multi-pass solar air collector when used steel wool as porous media is 6, 12.6 and31.7percent higher than without porous media at porosity 98.75, 97.5, and 96.25percent. While it can increase 8.1 and 28.5 percent at porosity 97.875 and 95.75 percent when using stainless steel as porous media.

Applying dynamic mesh to examine evolution of effective thermal conductivity in porous medium undergoing macrostructure change

Heat transfer dynamics in packed bed appears to be vital, particularly with respect to thermochemical conversion of solid fuels. However, due to complex bed structure varying under high temperatures the prediction of its thermal behavior is very demanding. Heating of coke oven charge is one example, regarded as being considerably affected by radiation through fissures and cracks that cross cut coke zone as the carbonization proceeds. The investigation and quantification of such impact encounters difficulties due to irregularity of fissure network that depends on a parent coal type and the process temperature regimes. Unfortunately, the analyses of this issue are very limited, meanwhile an uncertainty in the assessment of radiation contribution might be a source of notable discrepancy in effective thermal conductivity of coal/coke bed reported to date in the literature. In this respect, the CFD simulations of heating of a coal/coke bed while taking into account the crack propagation were performed to estimate an influence of structure alteration on heat transfer process. The computations were carried out using Ansys Fluent package and the dynamic mesh was implemented to simulate the crack development. The numerically-derived temperature profile at the coke oven center plane is in good agreement with the experimental temperature history. The predicted thermal conductivity values in the near-wall zone are significantly higher than for the case excluding fissure presence, and achieved ∼6.2 W(m K)-1 at the end of process (for 1373 K), showing additionally a clear increase from 1.4 to 2.9 W(m K)-1 within 1070–1090 K. The computation results also revealed that slower developing cracks, contrary to faster propagating ones, lead to higher thermal conductivity.

Parameter analysis and fast prediction of the optimum eccentricity for a latent heat thermal energy storage unit with phase change material enhanced by porous medium

The melting performance of porous-medium-enhanced phase change material (PCM) in a horizontal shell-and-tube latent-heat thermal energy storage unit (LHTESU) with eccentric structure is studied through a fixed-grid numerical method. The effects of ratio of outer and inner diameter, thermal conductivity of porous medium, porosity and heating temperature on the recommended eccentricity of LHTESU are discussed. Correlations for fast prediction of the optimum eccentricity are built. Results show that the mixed use of porous medium and eccentric structure can save as much as 43.1% of the total melting time compared with the pure use of porous medium. There exists an optimum eccentricity to get the shortest total melting time. The optimum eccentricity increases with the increase of ratio of outer and inner diameter, porosity and heating temperature, and decreases with the increase of thermal conductivity. For fast prediction of the optimum eccentricity and saved melting time, a modified Rayleigh number is proposed to reflect the effect of porous medium on natural convection, especially the flow resistance caused by porous medium. The effects of the four parameters on the optimum eccentricity can be integrated by the relationship between the optimum eccentricity and the modified Rayleigh number. Correlations of The optimum eccentricity and saved melting time are obtained respectively for convenient calculation and evaluation of the feasibility of eccentricity.