Heat Transfer In Porous Media Research Articles

Effect of contact thermal resistance and skeleton thermodynamic properties on solid-liquid phase change heat transfer in porous media: A simulation study

Phase change materials (PCMs) have the potential for heat storage and release, but low thermal conductivity limits their wide application in thermal systems. This work proposes a mathematical model to simulate the freezing process of water in porous media. Unlike traditional methods that solve for two temperatures in different materials, the hybrid finite element method computes a single temperature satisfying the jump on the interface. The effect of contact thermal resistance and skeleton parameters on solid-liquid phase change heat transfer was investigated. This model was validated by experiments in reference. Results show that increased contact thermal resistance decreases temperature gradient, phase interface deflection and freezing rate. Specifically, with contact thermal resistance of 0.0001 K/W, 0.0005 K/W, and 0.001 K/W, freezing rates decrease by 36.4 %, 52.35 %, and 54.14 %, respectively, compared to the case without resistance. Although the contact thermal resistance reduced the temperature gradient, it stabilized the phase change process. Moreover, higher thermal conductivity of the skeleton enhances the freezing rate. However, after a certain value is reached, the rate increases only marginally. Skeletons with lower density and specific heat capacity are favorable to enhancing phase change heat transfer.

Research on the effect of water-cooling steel pipe on preventing spontaneous combustion of coal pile and its thermal migration behavior

During the storage and transportation process after mining, coal piles are placed in open environments, making them prone to self-heating and spontaneous combustion due to the nature of coal and factors like natural wind flow. In recent years, there have been frequent spontaneous combustion incidents involving coal piles, posing significant safety risks. To effectively prevent and control spontaneous combustion disasters in open-air coal storage piles, we propose a method involving the arrangement of water-cooling steel pipes within the coal piles. This method applies theories of coal spontaneous combustion mechanisms, porous media heat transfer, and non-isothermal pipeline heat transfer. The multi-physics coupling model of COMSOL numerical simulation software is used to analyze the spontaneous ignition process and prevention effect of open pit coal pile. In the model, the thin material transfer of porous media is taken as the oxygen concentration field, the heat transfer of porous media is taken as the temperature field, and the free and porous media flow is taken as the air seepage velocity field. The simulation results of the spontaneous combustion process in the coal pile indicate that the high-temperature zone of spontaneous combustion is situated within the range of 0.5 ~ 1.5 m inside the wind-facing surface and extends 0.5 m above the ground level. These findings serve as a basis for determining the optimal placement of water-cooling steel pipes within the coal pile. The simulation results of a single water-cooling steel pipe demonstrate a positive correlation between the cooling effect on the coal pile and the water cool flow, and a negative correlation with the water cool temperature. Additionally, the cooling radius of the water-cooling steel pipe is determined by the circumference of the pipe and remains unaffected by the water cool flow. Finally, simulations were conducted to evaluate the cooling effect of multiple rows of steel pipes, and optimal arrangement parameters were determined: a center distance between steel pipes of 1 m and a water cool flow rate of 1500 L/min. As a result, the onset of the self-heating period in the coal pile was delayed by 11 days, and the spontaneous combustion period was extended by 56 days. The arrangement of water-cooling steel pipes in the coal pile has demonstrated significant efficacy in preventing and controlling spontaneous combustion.

Expression of Concern: Lattice Boltzmann Method Pore-scale simulation of fluid flow and heat transfer in porous media: effect of size and arrangement of obstacles into a channel

Expression of Concern: Lattice Boltzmann Method Pore-scale simulation of fluid flow and heat transfer in porous media: effect of size and arrangement of obstacles into a channel

Multieffect bioconvective transport of oxytactic microorganisms with thermal radiation, Lorentz force, heat source, and chemical reaction over a flexible cylinder

AbstractThe multieffect bioconvective heat transfer in porous media is essential for many technological applications. However, the literature governing practical applications is very scarce. The bioconvective transport of magnetohydrodynamic cross nanofluid carrying oxytactic microorganisms across a flexible cylinder with velocity slip, viscous dissipation, thermal radiation, and chemical reaction with a heat source in Darcy–Forchheimer porous medium is predicted in this piece of work. The random movement and thermophoresis processes are revealed by the Buongiorno model. Using a suitable similarity transformation and boundary layer approximation, the simplified model equations are converted into coupled highly nonlinear ordinary differential equations (ODEs). The resulting ODEs are dealt with numerically utilizing the BVP4C and the shooting method with predetermined thermal radiation, heat source, chemical reaction, and so forth parameters. The velocity field is inversely influenced by the Forchheimer number and porosity parameter. The Sherwood number is significantly influenced by chemical reactions. For heat source parameter (S) and increasing radiation parameter (Rd), the Nusselt number increases and convection is shown for the value of Rd near about 3. Overall, this study will help researchers in science and engineering to understand the intricate and multieffective dynamic system and industrial applications like microbiology, and biodynamical systems, biological tissues, biofilms, soil, or filter media.

Characteristics of the Temperature and Humidity Variations of Burial-Type Stone Relics and a Fitting Model

Burial stone relics remain in a humid, semi-enclosed environment for long periods, and temperature and humidity variations can cause deterioration acceleration. Yang Can’s tomb was selected as the research object, and field monitoring and simulations were performed to investigate the characteristics of temperature and humidity variations, after which the simulation results were evaluated. The monitoring results showed that solar radiation, rainfall, wind speed, and depth of entry are important factors affecting the variation in the temperature and humidity of burial stone relics. The temperature outside the chamber is greatly affected by seasonal variations, while the humidity inside the chamber is influenced by seasonal variations, so appropriate measures should be implemented inside and outside the chamber during different seasons to alleviate deterioration. On the basis of the above analysis, a temperature and humidity model for the interior chamber of burial stone relics was established in COMSOL software 5.6, combined with a porous medium heat transfer model and computational fluid dynamics (CFD) model. The temperature and humidity inside the chamber can be calculated by the temperature and humidity outside the chamber. This study provides data support for hydrothermal, condensation and other related studies of burial stone relics.

Enhancing unsteady heat transfer simulation in porous media through the application of convolutional neural networks

This research describes a novel technique for anticipating unstable heat transfer in porous media. Convolutional neural networks (CNNs) are used with finite volume method (FVM) and long short-term memory (LSTM) networks to accomplish this. Heat transport networks are difficult to characterise using traditional numerical methodologies owing to their nonlinearity and complexity. The proposed solution combines FVM’s precise physical modelling with CNN’s and LSTM’s superior pattern identification and temporal analysis. This collaboration supports the suggested strategy. Heat transport dynamics simulations in porous materials are more accurate, efficient, and adaptable when employing this hybrid framework. The experimental setup focused on porous material properties and gathered and processed a large amount of data. The building’s three-dimensional shape, heat transfer, and time were investigated. Temporal fluctuations were also used. Multiple indicators are used to evaluate the overall performance of the model. These criteria include convergence speed, F1 score, accuracy, precision, recall, and computational cost. In the most notable numerical results, the proposed strategy surpasses both the Finite Element and the Lattice Boltzmann methods. The presented method enabled fast convergence and reduced processing costs. These results were: accuracy (0.92), precision (0.93), recall (0.91), and F1 score (0.92). The proposed method is generalizable and adaptable, and it can address a variety of heat transport simulation problems in porous media. Unlike CNNs, which can identify significant spatial patterns, LSTM cells can only see temporal dynamics. These two components are required to show heat transfer, which is a continually changing phenomenon. Modern technology enables more complex simulations. Processing expenses are lowered, and estimations are more accurate. These two discoveries were obtained through the inquiry and methodologies. Finally, the CNN-FVM-LSTM technique simulates heat transport using complicated computer models. Predicting unusually high temperatures in porous materials may improve the model’s accuracy, computational efficiency, and flexibility.

Experimental investigation of pressure drop and heat transfer in porous media based on 3D printed triple periodic minimum surfaces

ABSTRACT Porous media are widely preferred for heat transfer applications because of complex structure and high porosity. It is relatively easy to produce complex structures with the additive manufacturing method. In this study, Gyroid-based triple periodic minimal surface is produced ABS (Acrylonitrile butadiene styrene) and PLA (polylactic acid) materials using 3D printers. The pressure drops and heat transfer in the porous structure with the gyroid model are investigated experimentally. Permeability and Forchheimer coefficients are determined for each gyroid porous channel. While the permeability and Forchheimer coefficient of the porous medium of PLA were calculated as 2.97 × 10−8 m2 and 0.07, respectively, the permeability and Forchheimer coefficient of the porous medium of ABS were calculated as 5.52 × 10−8 m2 and 0.09. The correlation between the Reynolds number and pressure drop per length is given. The gyroid structure-filled channel is heated by an asymmetric heat flux on the bottom side. The convection heat transfer in polymer-based porous media was investigated. Also, the correlation between the Nusselt number and the Reynolds number based on permeability is presented. While the Nusselt correlation of the PLA porous medium was obtained as N u K = 0.08 R e K 0.57 , the Nusselt correlation of the ABS porous medium was found to be N u K = 0.09 R e K 0.61 . There are improvements in heat transfer due to the flow mixing effect of the porous medium. The study aims to broaden the current knowledge of heat transfer in polymer porous structures. Especially, this study investigates heat transfer and flow in polymer-based porous structures with a low thermal conductivity coefficient produced by 3D printers.

Significance of the natural convection to the heat transfer of porous media: A pore-scale study

Heat conduction in porous media is generally accompanied by the natural convection of the fluid within the pores driven by the temperature gradient. However, the criterion to determine the critical pore size of porous media where the natural convection cannot be neglected remains elusive. In this study, a pore-scale model is established to investigate the contributions of natural convection on the effective thermal conductivity (ETC) of porous media, which takes the reconstructed microstructures as the geometry input. We thus examine the effects of the porosity, thermal conductivity of the fluid and solid phases, and heating direction on the critical pore size where the natural convection starts to work. The results show that the critical pore size decreases with increasing porosity and heating temperature, but increases with the rise in the thermal conductivity of solid phase. Moreover, the critical pore size is significantly lower for the lateral heating, compared with the bottom heating. Finally, we proposed a new formula as an indicator to determine the significance of natural convection to the heat transfer in porous media.

Numerical simulation on staggered grids of three-dimensional brinkman-forchheimer flow and heat transfer in porous media

Numerical simulation on staggered grids of three-dimensional brinkman-forchheimer flow and heat transfer in porous media

Influence of pore-crack environment on heat propagation of underground coalfield fire: A case study in Daquanhu, Xinjiang, China

The development of pores and cracks in coalfield fire area promote the abnormal temperature, the greenhouse effect, and the release of toxic gases. It is of great significance to study the dynamic distribution characteristics of temperature field and concentration field of typical gas products in a coalfield fire area under different pore-crack environments for revealing the spreading law of underground coalfield fire. In this paper, the combined effect of coal combustion chemical reaction, heat energy transmission, flue gas seepage and pore-crack environment were considered. Taking Daquanhu coalfield fire area as an example, an optimized multi-field coupling model, which included the chemical reaction of coal combustion, convection heat transfer in cracks, heat transfer in porous media, gas seepage and improved partial differential equation of pore-crack evolution was constructed. The coalfield fires area was divided into combustion zone, caving zone, sagging subsidence zone, crack zone. The evolution law of temperature field, CO2 concentration field in the coalfield fire area under different air leakage and geological crack conditions was analysed. The results showed that the temperature development of coalfield fire is divided into rapid heating stage and stable development stage. At the rapid heating stage, the greater the air leakage flow was, the faster the maximum temperature rise in the combustion zone. At the stable development stage, with the air leakage decreased, the thermal buoyancy increased. The greater the number of cracks was, the greater the area of the drying zone (673.15 K < T < 1073.15 K) closed to the crack zone. The influence of crack environment on heat flux in the sagging subsidence zone and crack zone was obvious. The total heat flow in the crack zone was about 25 times that in the caving zone. The relationship between the maximum temperature in the combustion zone and the CO2 concentration at the crack outlet showed an exponential model (ExpGro1 exponential model). The area spread by coalfield fire increased linearly with the rang of surface temperature abnormal. The research results provided a basis for judging the spread trend of coalfield fire and extracting coalfield fire of heat energy.

Transient Convective Heat Transfer in Porous Media

In this study, several methods to analyze convective heat transfer in a porous medium are presented and discussed. First, the method of Fourier was used to obtain solutions for reduced temperatures θs and θf. The results showed an exponentially decaying propagating temperature front. Then, we discuss the method of integration that was presented earlier by Schumann. This method makes use of a transformation of variables. Thirdly, the system of partial differential equations was directly solved with the Finite Difference method, of which the result showed good agreement with the Fourier solutions. For the chosen Δτ and Δξ, the maximum error for θf=3.7%. The maximum error for θs for the first ξ and first τ is large (36%) but decays rapidly. The problem was extended by adding a linear heat source term to the solid. Again, making use of the change in variables, analytical solutions were derived for the solid and fluid phases, and corrections to the previous literature were suggested. Finally, results obtained from a numerical model were compared to the analytical solutions, which again showed good agreement (maximum error of 6%).

Geothermal gradients in a high-organic content landfill

Geothermal gradients in a high-organic content landfill

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.

Robust calibration and evaluation of a percolation-based effective‐medium approximation model for thermal conductivity of unsaturated soils

Thermal conductivity (λ) is a property characterizing heat transfer in porous media, such as soils and rocks, with broad applications to geothermal systems and aquifer characterizations. Numerous empirical and physically-based models have been developed for thermal conductivity in unsaturated soils. Recently, Ghanbarian and Daigle (G&D) proposed a theoretical model using the percolation-based effective-medium approximation. An explicit form of the G&D model relating λ to water content (θ) and equations to estimate the model parameters were also derived. In this study, we calibrated the G&D model and two widely applied empirical λ(θ) models using a robust calibration dataset of 41 soils. All three λ(θ) model performances were evaluated using a validation dataset of 58 soils. After calibration, the root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R2) of the G&D model were 0.092 W−1 m−1 K−1, 0.067 W−1 m−1 K−1 and 0.97, respectively. For the two empirical models, RMSEs ranged from 0.086 to 0.096 W−1 m−1 K−1, MAEs from 0.063 to 0.071 W−1 m−1 K−1, and R2 values were about 0.97. All three metrics indicated that calibration improved the performance of the G&D model, and it had an accuracy similar to that of the two empirical λ(θ) models. Such a robust performance confirmed that the theoretically-based G&D model can be applied to study soil heat transfer and potentially other related fields.

Effects of porous medium filling on thermally developing forced convection in a parallel plate channel

This study obtains the semi-analytical solutions and explores the thermal characteristics of a thermally developing flow in a parallel plate channel, partially filled with a porous medium at the core, while considering local thermal non-equilibrium conditions, and viscous dissipation for the first time. The developing temperature field, for a porous medium filling of volume fraction fixed at 0.9, indicates an increasing difference in temperature between the solid and fluid phases with the axial distance. Besides, heat flux bifurcation starts in the entrance region as more heat diffuses to the solid at the interface, more markedly with a decreasing Darcy number, Da. When the thermal transport is dominated by interstitial heat transfer between solid and fluid in the porous medium, the thermal entrant length is the shortest. An increasing amount of porous medium filling with such quality and an increasing Da tend to shorten the thermal entry length. Nonetheless, as a lower Da porous media convects more heat away from the interface, it expedites the thermal development in cases where interstitial heat transfer in porous medium is poor. With an increasing porous medium fraction, the impact of viscous dissipation on heat transfer magnifies at the entrance region, thereby reducing the effectiveness of porous medium insert.

Modeling enhanced geothermal systems using a hybrid XFEM–ECM technique

Heat extraction from Enhanced Geothermal Systems (EGS) involves several multi-physics coupling processes, including the seepage through the fractured porous media, the thermal exchange between the working fluid and the matrix, and the deformation of fractured porous media, which play essential roles in exploiting the geothermal energy contained in hot dry rocks. In this study, a fully coupled numerical model for Thermo-Hydro-Mechanical simulation of EGS is presented based on the local thermal non-equilibrium using the eXtended Finite Element Method (XFEM) and Equivalent Continuum Method (ECM). The ECM can provide the equivalent tensors of not only fluid permeability but also solid compliance, which is an essential feature for coupled Thermo-Hydro-Mechanical simulation of fracture networks. In the model, the XFEM is employed for large-scale fractures to capture the mass and heat transfer between the fracture and matrix more accurately, while the ECM is applied on the network of small-scale fractures since considering their details explicitly is not usually cost-effective. Hence, the proposed model benefits from the advantages of both methods, and it allows for managing between accuracy and cost. The model is validated against the analytical solutions of heat transfer in porous media as well as single fracture problems. Moreover, its flexibility and applicability are shown by assessing the effects of the connectivity of fractures, characteristics of fracture networks, coupling conditions, and local thermal non-equilibrium assumption on the EGS simulation results. It is observed that the network connectivity and fracture alignment are both influential in the early thermal breakthrough; however, each can take dominance under different conditions. The results show the proposed computational model is a promising tool for estimation of the heat mining performance of EGS.

A study on MHD flow of SWCNT-Al2O3 /water hybrid nanofluid past a vertical permeable cone under the influence of thermal radiation and chemical reactions

This study investigates the steady, incompressible MHD flow of a hybrid nanofluid over a vertical solid cone embedded in a porous medium under suction effect. The research explores the effects of various factors, such as thermal radiation, chemical reactions, heat generation, viscous dissipation, and Joule heating on heat and mass transfer phenomena. To investigate the effects of hybrid nanoparticles, we consider single-walled carbon nanotubes (SWCNT) and alumina (Al2O3 ) along with water (H2O) as the base fluid. After a suitable similarity transformation, the governing equations are reconstructed and solved using the Keller-box numerical scheme. We present graphical and tabular analyses of various parameter impacts on heat transfer profiles and coefficients. This study provides valuable insights into the control of fluid dynamics and heat transfer in porous media, which have significant implications for industrial and engineering applications. The findings of the current article are in excellent agreement with previously published works.

Lattice Boltzmann Method Pore-scale simulation of fluid flow and heat transfer in porous media: Effect of size and arrangement of obstacles into a channel

The flow characteristics at a pore-scale porous medium has a significant role to the development of cooling modules. Despite this fact, still there is no adequate knowledge about the effect of size, pattern and position of the obstacles, on fluid flow and heat transfer. In this work, fluid flow through the porous media and heat transfer have been modeled by means of the Single Relaxation Time SRT-LBM with BGK approximation and D2Q9 model. The effect of size and arrangement of cold square obstacles in a heated wall channel is investigated for incompressible flow in case of fixed porosity degree, ε=75%. Results are presented in terms of velocity and temperature fields, streamlines, and Nusselt number. The results show that, for the same porosity degree, by changing the number of the obstacles or their arrangement, the tortuosity changes and therefore velocity and temperature fields are modified, as well as local and average Nusselt number. The results show that, for the same porosity degree, by changing the number of the obstacles or their arrangements, the value of Nuavg of the channel walls and tortuosity increased up to 24.7% and 9%, respectively, in comparison with the Poiseuille flow.

Application of CFD-DSMC coupling method in H2 flow and heat transfer in microtube

In the research of porous media and the interior of microelectronic devices, fluids frequently shuttle among pores and wall cracks, therefore it is of great significance to explore the influence of media wall on fluid flow and heat transfer. In this paper, CFD-DSMC coupled iterative algorithm is first used in the research of the flow and heat transfer of gas near the wall in the porous media, which simplified into the flow and heat transfer in micron-scale tube with smooth and rough wall conditions. It is found that compared with the pure CFD method, the velocity field obtained by the coupled method is quite different in the region close to the wall, and this will affect the flow field in the mainstream region, that is, with the higher roughness of the wall, the velocity in the central region will be smaller. There is no significant difference in the temperature distribution in the microtube before and after coupling, but the temperature in the mainstream decreases with the increase of the roughness of the wall. In addition, the temperature jump was found from some of the coupling results close to the wall. The results will contribute to a deeper understanding of the influence of rough surfaces on gas flow and heat transfer near the wall, and provide guidance for the regulation of flow and heat transfer in porous media.

A Comprehensive Review of Nanofluid Heat Transfer in Porous Media

In the present paper, recent advances in the application of nanofluids in heat transfer in porous materials are reviewed. Efforts have been made to take a positive step in this field by scrutinizing the top papers published between 2018 and 2020. For that purpose, the various analytical methods used to describe the flow and heat transfer in different types of porous media are first thoroughly reviewed. In addition, the various models used to model nanofluids are described in detail. After reviewing these analysis methods, papers concerned with the natural convection heat transfer of nanofluids in porous media are evaluated first, followed by papers on the subject of forced convection heat transfer. Finally, we discuss articles related to mixed convection. Statistical results from the reviewed research regarding the representation of various parameters, such as the nanofluid type and the flow domain geometry, are analyzed, and directions for future research are finally suggested. The results reveal some precious facts. For instance, a change in the height of the solid and porous medium results in a change in the flow regime within the chamber; as a dimensionless permeability, the effect of Darcy's number on heat transfer is direct; and the effect of the porosity coefficient has a direct relationship with heat transfer: when the porosity coefficient is increased or decreased, the heat transfer will also increase or decrease. Additionally, a comprehensive review of nanofluid heat transfer in porous media and the relevant statical analysis are presented for the first time. The results show that Al2O3 nanoparticles in a base fluid of water with a proportion of 33.9% have the highest representation in the papers. Regarding the geometries studied, a square geometry accounted for 54% of the studies.