Heat Transfer In Porous Media Research Articles

Investigating the Influence of Square Size Vanes on Heat Transfer in porous media: An In-depth Nusselt distribution

Abstract This research provides an extensive analysis with various γ on natural convection, thermal entropy generation, fluid flow, and temperature distribution in the porous cavity. On the thermal performance, the studying impact effective factors entailing geometrical parameters, Ha, Da, Pr, γ, and ε are analyzed meticulously. The finite element method (FEM) is carried out to analyze fluid flow and heat distribution in the present porous media. The innovation of this research is considered key parameters constitute Ha, Da, Pr, γ, and ε for substantial assesses average Nusselt number in porous media with different square size vanes at the corners and effect variable cooled size at the corners of the square porous cavity for an in-depth analysis of the thermal performance. In validation, the calculation of the results was adapted accurately to the finite element method's fluid flow, temperature distribution, and average Nusselt number. Numerical results revealed that various γ affected widely in the generation of entropy. Also, square-size vanes at the corners of the porous cavity markedly influenced fluid flow trend hot and cold temperature distribution. The Hartman number is the most important influence on the average Nusselt number, which observed a sharp increase in the average Nusselt number. Moreover, as the Darcy number grew, the average Nusselt number rose apart from in γ = 1 in porous media with size vanes 0.2.

Application of fuzzy PID control algorithm in hypersonic vehicle transpiration cooling control

As an efficient active cooling method, transpiration cooling is employed for thermal protection of blunt nose cones. However, most current systems utilize open-loop control for coolant supply. This study establishes a dynamic model of a one-dimensional blunt nose cone transpiration cooling system that concurrently considers aerodynamic heating, internal heat transfer in porous media, and the thermal insulation process of the air film layer formed by injected coolant. The findings indicate that the coolant film's thermal insulation effect significantly impacts the nose cone cooling system, with flow in the porous media causing a time-delay in the dynamic insulation effect. After implementing a closed-loop feedback controller, the fuzzy PID control algorithm demonstrates superiority over the conventional PID control algorithm in mitigating positive and negative feedback misalignment issues caused by time-delay, resulting in reduced temperature oscillation time and amplitude. Additionally, the fuzzy PID control algorithm achieves faster response and shorter stabilization time when external interference from varying Mach numbers occurs.

Multiple shape factor effects of nanofluids on marangoni mixed convection flow through porous medium

This study explores the effects of multiple shape factors on nanofluids within Marangoni mixed convection flows through porous media. Nanofluids, containing nanoparticles in a base fluid, show unique thermal properties, making them valuable in cooling systems, energy storage, and medical devices. Marangoni mixed convection, driven by surface tension gradients, adds complexity to fluid dynamics and heat transfer in porous media. Analytical and numerical analyses examine how various particle geometries, nanoparticle volume fractions, and porous medium configurations influence transport phenomena. Entropy analysis calculates thermodynamic irreversibilities. Findings reveal relationships between shape factors, heat transfer rates, velocity profiles, temperature distribution, and entropy generation rates, offering insights for optimizing nanofluid-based systems. The study also investigates magnetic forces, heat source/sink effects, and viscous dissipation on thermal energy transfer in Graphene oxide/water and Molybdenum disulfide/water nanofluids. Using similarity transformations, Partial Differential Equations are converted into Ordinary Differential Equations, solved with HAM and NDSolver by using the Wolfram tools. Results graphically depict velocity, temperature, entropy, and skin friction values, providing practical insights for engineering applications.

New Criteria to Estimate Local Thermal Nonequilibrium Conditions for Heat Transport in Porous Aquifers

AbstractA fundamental assumption in numerous studies of heat transfer in porous media is local thermal equilibrium (LTE), which assumes that the temperature of the porous media at the fluid and solid interface is in instantaneous equilibrium. Although significant efforts have been made to quantify the occurrence and consequences of local thermal nonequilibrium (LTNE), where the temperatures of the fluid and adjacent solid phases differ, there is no simple expression for quantifying the occurrence and effects of local thermal disequilibrium. Using a numerical model combining LTE and LTNE models, we develop here two simple general criteria based on Darcian velocities (q) and particle sizes (dp) of porous media for determining when LTNE effects occur (denoted as g(dp, q)) and when they become significant (denoted as f(dp, q)). Results show that using an LTE model can result in an underestimation of effective thermal diffusivity and the unaffected Darcian velocities when g(dp, q) > 0. It is possible that using the LTE model can result in an underestimation of the effective thermal diffusivity by more than 200 times within Darcian velocities ranging from 0 to 60 m/d. In the case of g(dp, q) < 0, the use of the LTE model can result in an overestimation of effective thermal diffusivity and Darcian velocities. The performances of the newly developed general criteria are demonstrated using three typical data sets and corresponding numerical models. These data sets include new heat tracer tests conducted in the laboratory and the field, as well as temperature‐time series collected in streambed sediments from a previous study by Shanafield et al. (2012, https://doi.org/10.5194/hessd‐9‐4305‐2012). The potential LTNE effects should be considered when using heat as a tracer to characterize flow and heat transport in porous media in the presence of Darcian velocities less than 2 m/d and particle sizes larger than 10 mm.

Thermo‐hydraulic analysis of wavy microchannel heat sinks with porous fins based on field synergy principle

AbstractIn order to enlarge the area and intensity of convective heat transfer among the coolant and heated surface, the vertical fins of microchannel heat sinks (MCHSs) with microencapsulated phase change material slurry (MPCMS) as coolant are arranged into wavy porous channels to realize more heat being dissipated to the outside. The phase transition of microencapsulated particles in laminar flow state is described, and the Brinkman–Forchheimer–Darcy model based on volume average approach and the energy equation for local heat equilibrium are adopted to portray flow and heat transfer in porous medium. The impacts of geometrical parameters on flow and heat transfer behaviour of wavy porous MCHS are numerically analyzed, and performance evaluation factor (PEF) is defined to estimate the thermo‐hydraulic capability of heat exchanger. The numeric outcomes match well with the experiments. Results indicate that MPCMS has a significant heat transfer improvement in the newly designed channel configuration compared with the coolant fluid flowing in the straight microchannel. Based on field synergy principle, the comprehensive capability enhancement mechanism of MPCMS in new MCHS is explored, and its superior thermal performance can be attributed to the improvement of the synergistic degree among flow and temperature fields, and its reasonable structural design can effectively improve the heat rejection capacity in the limited space.

Evaporation Mechanisms and Heat Transfer in Porous Media of Mixed Wettabilities with a Simulated Solar Flux and Forced Convection Through the Media

Abstract An experimental apparatus was designed to study the impacts of wettability on evaporation of water for: 1) a 5.7-cm-thick layer of hydrophilic Ottawa sand; 2) a 5.7-cm-thick layer with 12% hydrophobic content, consisting of a 0.7-cm-layer of n-Octyltriethoxysilane-coated hydrophobic sand buried 1.8 cm below the surface of hydrophilic sand; and 3) a 5.7-cm-thick layer with mixed wettabilities, consisting of 12% n-Octyltriethoxysilane-coated hydrophobic sand mixed into hydrophilic sand. The sand-water mixtures experienced forced convection above and through the sand layer, while a simulated solar flux (i.e., 112 ± 20 W/m2) was applied. Evaporation from homogeneous porous media is classified into the constant-rate, falling-rate, and slow-rate periods. Wettability affected the observed evaporation mechanisms, including the transition from constant-rate to falling-rate periods. Evaporation entered the falling-rate period at 12%, 20%, and 24% saturations for the all hydrophilic sand, hydrophobic layer, and hydrophobic mixture, respectively. Wettability affected the duration of the experiments, as the all hydrophilic sand, hydrophobic layer, and hydrophobic mixture lasted 17, 20, and 26 trials, respectively. Both experiments with hydrophobic particles lasted longer than the all hydrophilic experiment and had shorter constant-rate evaporation periods, suggesting hydrophobic material interrupts capillary action of water to the soil surface and reduces evaporation. Evaporation fluxes were up to 12× higher than the vapor diffusion flux due to enhanced vapor diffusion and forced convection.

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.

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

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.

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.