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This study aims to numerically study the buoyant convective flow of two different nanofluids in a porous annular domain. A uniformly heated inner cylinder, cooled outer cylindrical boundary and adiabatic horizontal surfaces are considered because of many industrial applications of this geometry. The analysis also addresses the comparative study of different porous media models governing fluid flow and heat transport.

The finite difference method has been used in the current simulation work to obtain the numerical solution of coupled partial differential equations. In particular, the alternating direction implicit method is used for solving transient equations, and the successive line over relaxation iterative method is used to solve time-independent equation by choosing an optimum value for relaxation parameter. Simpson’s rule is adopted to estimate average Nusselt number involving numerical integration. Various grid sensitivity checks have been performed to assess the sufficiency of grid size to obtain accurate results. In this analysis, a general porous media model has been considered, and a comparative study between three different models has been investigated.

Numerical simulations are performed for different combinations of the control parameters and interesting results are obtained. It has been found that the an increase in Darcy and Rayleigh numbers enhances the thermal transport rate and strengthens the nanofluid movement in porous annulus. Also, higher flow circulation rate and thermal transport has been detected for Darcy model as compared to non-Darcy models. Thermal mixing could be enhanced by considering a non-Darcy model.

The present results could be effectively used in many practical applications under the limiting conditions of two-dimensionality and axi-symmetry conditions. The only drawback of the current study is it does not include the three-dimensional effects.

The results could be used as a first-hand information for the design of any thermal systems. This will help the design engineer to have fewer trial-and-run cases for the new design.

A pioneering numerical investigation on the buoyant convective flow of two different nanofluids in an annular porous domain has been carried out by using a general Darcy–Brinkman–Forchheimer model to govern fluid flow in porous matrix. The results obtained from current investigation are novel and original, with numerous practical applications of nanofluid saturated porous annular enclosure in the modern industry.

This study aims to investigate a critical review on the applications of fluid-structure interaction (FSI) in porous media.

Transport phenomena in porous media are of continuing interest by many researchers in the literature because of its significant applications in engineering and biomedical sectors. Such applications include thermal management of high heat flux electronic devices, heat exchangers, thermal insulation in buildings, oil recovery, transport in biological tissues and tissue engineering. FSI is becoming an important tool in the design process to fully understand the interaction between fluids and structures.

This study is structured in three sections: the first part summarizes some important studies on the applications of porous medium and FSI in various engineering and biomedical applications. The second part focuses on the applications of FSI in porous media as related to hyperthermia. The third part of this review is allocated to the applications of FSI of convection flow and heat transfer in engineering systems filled with porous medium.

To the best knowledge of the present authors, FSI analysis of turbulent flow in porous medium never been studied, and therefore, more attention should be given to this area in any future studies. Moreover, more studies should also be conducted on mixed convective flow and heat transfer in systems using porous medium and FSI.

The wall of the blood vessel is considered as a flexible multilayer porous medium, and therefore, rigid wall analysis is not accurate, and therefore, FSI should be implemented for accurate predictions of flow and hemodynamic stresses.

The use of porous media theory in biomedical applications received a great attention by many investigators in the literature (Khanafer and Vafai, 2006a; Al-Amiri et al., 2014; Lasiello et al., 2016a, Lasiello et al., 2016b; Lasiello et al., 2015; Chung and Vafai, 2013; Mahjoob and Vafai, 2009; Yang and Vafai, 2008; Yang and Vafai, 2006; Ai and Vafai, 2006). A comprehensive review was conducted by Khanafer and Vafai (2006b) summarizing various studies associated with magnetic field imaging and drug delivery. The authors illustrated that the tortuosity and porosity had a profound effect on the diffusion process within the brain. AlAmiri et al. (2014) conducted a numerical study to investigate the effect of turbulent pulsatile flow and heating technique on the thermal distribution within the arterial wall. The results of that investigation illustrated that local heat flux variation along the bottom layer of the tumor was greater for the low-velocity condition. Yang and Vafai (2006) presented a comprehensive four-layer model to study low-density lipoprotein transport in the arterial wall coupled with a lumen (Figure 1). All the four layers (endothelium, intima, internal elastic lamina and media) were modeled as a homogenous porous medium.

Future studies on the applications of FSI in porous media are recommended in this review.

A combination of highly conductive porous media and nanofluids is an efficient way for improving thermal performance of relevant applications. For precisely predicting the flow and thermal transport of nanofluids in porous media, the purpose of this paper is to explore the inter-phase coupling numerical methods.

Based on the lattice Boltzmann (LB) method, this study combines the convective flow, non-equilibrium thermal transport and phase interactions of nanofluids in porous matrix and proposes a new multi-phase LB model. The micro-scale momentum and heat interactions are especially analyzed for nanoparticles, base fluid and solid matrix. A set of three-phase LB equations for the flow/thermal coupling of base fluid, nanoparticles and solid matrix is established.

Distributions of nanoparticles, velocities for nanoparticles and the base fluid, temperatures for three phases and interaction forces are analyzed in detail. Influences of parameters on the nanofluid convection in the porous matrix are examined. Thermal resistance of nanofluid convective transport in porous structures are comprehensively discussed with the models of multi-phases. Results show that the Rayleigh number and the Darcy number have significant influences on the convective characteristics. The result with the three-phase model is mildly larger than that with the local thermal non-equilibrium model.

This paper first creates the multi-phase theoretical model for the complex coupling process of nanofluids in porous structures, which is useful for researchers and technicians in fields of thermal science and computational fluid dynamics.

Fluid flow and heat transfer in a dual scale porous media is investigated to determine the interfacial convective heat transfer coefficient, numerically. The studied porous media is a periodic dual scale porous media. It consists of the square rods which are permeable in an aligned arrangement. It is aimed to observe the enhancement of heat transfer through the porous media, which is important for thermal designers, by inserting intra-pores into the square rods. A special attention is given to the roles of size and number of intra-pores on the heat transfer enhancement through the dual scale porous media. The role of intra-pores on the pressure drop of air flow through porous media is also investigated by calculation and comparison of the friction coefficient.

To calculate the interfacial convective heat transfer coefficient, the governing equations which are continuity, momentum and energy equations are solved to determine velocity, pressure and temperature fields. As the dual scale porous structure is periodic, a representative elementary volume is generated, and the governing equations are numerically solved for the selected representative volume. By using the obtained velocity, pressure and temperature fields and using volume average definition, the volume average of aforementioned parameters is calculated and upscaled. Then, the interfacial convective heat transfer coefficient and the friction coefficient is numerically determined. The interparticle porosity is changed between 0.4 and 0.75, while the intraparticle varies between 0.2 and 0.75 to explore the effect of intra-pore on heat transfer enhancement.

The obtained Nusselt number values are compared with corresponding mono-scale porous media, and it is found that heat transfer through a porous medium can be enhanced threefold (without the increase of pressure drop) by inserting intraparticle pores in flow direction. For the porous media with low values of interparticle porosity (i.e. = 0.4), an optimum intraparticle porosity exists for which the highest heat transfer enhancement can be achieved. This value was found around 0.3 when the interparticle porosity was 0.4.

The results of the study are interesting, especially from heat transfer enhancement point of view. However, further studies are required. For instance, studies should be performed to analyze the rate of the heat transfer enhancement for different shapes and arrangements of particles and a wider range of porosity. The other important parameter influencing heat transfer enhancement is the direction of pores. In the present study, the intraparticle pores are in flow direction; hence, the enhancement rate of heat transfer for different directions of pores must also be investigated.

The application of dual scale porous media is widely faced in daily life, nature and industry. The flowing of a fluid through a fiber mat, woven fiber bundles, multifilament textile fibers, oil filters and fractured porous media are some examples for the application of the heat and fluid flow through a dual scale porous media. Heat transfer enhancement.

The enhancement of heat transfer is a significant topic that gained the attention of researchers in recent years. The importance of topic increases day-by-day because of further demands for downsizing of thermal equipment and heat recovery devices. The aim of thermal designers is to enhance heat transfer rate in thermal devices and to reduce their volume (and/or weight in some applications) by using lower mechanical power for cooling.

The present study might be the first study on determination of thermal transport properties of dual scale porous media yielded interesting results such as considerable enhancement of heat transfer by using proper intraparticle channels in a porous medium.

In this work, a new two-phase version of the finite element-based Artificial Compressibility (AC) Characteristic-Based Split (CBS) algorithm is developed and applied for the first time to heat and mass transfer phenomena in porous media with associated phase change. The purpose of this study is to provide an alternative for the theoretical analysis and numerical simulation of multiphase transport phenomena in porous media. Traditionally, the more complex Separate Flow Model was used in which the vapour and liquid phases were considered as distinct fluids and mathematically described by the conservation laws for each phase separately, resulting in a large number of governing equations.

Even though the adopted mathematical model presents analogies with the conventional multicomponent mixture flow model, it is characterized by a considerable reduction in the number of the differential equations for the primary variables. The fixed-grid numerical formulation can be applied to the resolution of general problems that may simultaneously include a superheated vapour region, a two-phase zone and a sub-cooled liquid region in a single physical domain with irregular and moving phase interfaces in between. The local thermal non-equilibrium model is introduced to consider the heat exchange between fluid and solid within the porous matrix.

The numerical model is verified considering the transport phenomena in a homogenous and isotropic porous medium in which water is injected from one side and heated from the other side, where it leaves the computational domain in a superheated vapour state. Dominant forces are represented by capillary interactions and two-phase heat conduction. The obtained results have been compared with the numerical data available in the scientific literature.

The present algorithm provides a powerful routine tool for the numerical modelling of complex two-phase transport processes in porous media.

For the first time, the stabilized AC-CBS scheme is applied to the resolution of compressible viscous flow transport in porous materials with associated phase change. A properly stabilized matrix inversion-free procedure employs an adaptive local time step that allows acceleration of the solution process even in the presence of large source terms and low diffusion coefficients values (near the phase change point).

The classical advection-dispersion equation (ADE) model cannot accurately depict the gas transport process in natural geological formations. This paper aims to study the behavior of CO₂ transport in fractal porous media by using an effective Hausdorff fractal derivative advection-dispersion equation (HFDADE) model.

Anomalous dispersion behaviors of CO₂ transport are effectively characterized by the investigation of time and space Hausdorff derivatives on non-Euclidean fractal metrics. The numerical simulation has been performed with different Hausdorff fractal dimensions to reveal characteristics of the developed fractal ADE in fractal porous media. Numerical experiments focus on the influence of the time and space fractal dimensions on flow velocity and dispersion coefficient.

The physical mechanisms of parameters in the Hausdorff fractal derivative model are analyzed clearly. Numerical results demonstrate that the proposed model can well fit the history of gas production data and it can be a powerful technique for depicting the early arrival and long-tailed phenomenon by incorporating a fractal dimension.

To the best of the authors’ knowledge, first time these results are presented.

Accurately evaluating fluid flow behaviors and determining permeability for deforming porous media is time-consuming and remains challenging. This paper aims to propose a novel machine-learning method for the rapid estimation of permeability of porous media at different deformation stages constrained by hydro-mechanical coupling analysis.

A convolutional neural network (CNN) is proposed in this paper, which is guided by the results of finite element coupling analysis of equilibrium equation for mechanical deformation and Boltzmann equation for fluid dynamics during the hydro-mechanical coupling process [denoted as Finite element lattice Boltzmann model (FELBM) in this paper]. The FELBM ensures the Lattice Boltzmann analysis of coupled fluid flow with an unstructured mesh, which varies with the corresponding nodal displacement resulting from mechanical deformation. It provides reliable label data for permeability estimation at different stages using CNN.

The proposed CNN can rapidly and accurately estimate the permeability of deformable porous media, significantly reducing processing time. The application studies demonstrate high accuracy in predicting the permeability of deformable porous media for both the test and validation sets. The corresponding correlation coefficients (R²) is 0.93 for the validation set, and the R² for the test set A and test set B are 0.93 and 0.94, respectively.

This study proposes an innovative approach with the CNN to rapidly estimate permeability in porous media under dynamic deformations, guided by FELBM coupling analysis. The fast and accurate performance of CNN underscores its promising potential for future applications.

Natural gas leak from underground pipelines could lead to serious damage and global warming, whose spreading in soil should be systematically investigated. This paper aims to propose a three-dimensional numerical model to analyze the methane–air transportation in soil. The results could help understand the diffusion process of natural gas in soil, which is essential for locating leak source and reducing damage after leak accident.

A numerical model using finite element method is proposed to simulate the methane spreading process in porous media after leaking from an underground pipe. Physical models, including fluids transportation in porous media, water evaporation and heat transfer, are taken into account. The numerical results are compared with experimental data to validate the reliability of the simulation model. The effects of methane leaking direction, non-uniform soil porosity, leaking pressure and convective mass transfer coefficient on ground surface are analyzed.

The methane mole fraction distribution in soil is significantly affected by the leaking direction. Horizontally and vertically non-uniform soil porosity has a stronger effect. Increasing leaking pressure causes increasing methane mole flux and flow rate on the ground surface.

Most existing gas diffusion models in porous media are for one- or two-dimensional simulation, which is not enough for predicting three-dimensional diffusion process after natural gas leak in soil. The heat transfer between gas and soil was also neglected by most researchers, which is very important for predicting the gas-spreading process affected by the soil moisture variation because of water evaporation. In this paper, a three-dimensional numerical model is proposed to further analyze the methane–air transportation in soil using finite element method, with the presence of water evaporation and heat transfer in soil.

The paper aims to clarify the relationship between the micro-structures of porous media and the coefficient of permeability. Most materials involve different types of defects like caves, pores and cracks, which are important characters of porous media and have a great influence on the physical properties of materials. To study the seepage mechanical characteristics of damaged porous media, the constitutive model of porous media dealing with coupled modeling of pores damage and its impact on permeability property of a deforming media was studied in this paper.

The paper opted for an exploratory study using the approach of continuum damage mechanics (CDM).

The paper provides some new insights on the fluid dynamics of porous media. The dynamic evolution model of permeability coefficient established in this paper can be used to model the fluid flow problems in damaged porous media. Moreover, the modified Darcy's law developed in this paper is considered to be an extension of the Darcy's law for fluid flow and seepage in a porous medium.

Owing to the limitations of time, conditions, funds, etc., the research results should be subject to multifaceted experiments before their innovative significance can be fully verified.

The paper includes implications for the development of fluid dynamics of porous media.

This paper fulfils an identified need to study the relationship between the micro-structures of porous media and the coefficient of permeability.

The purpose of this paper is to develop an empiricism free, first principle‐based model to simulate fluid flow and heat transfer through porous media.

Conventional approaches to the problem are reviewed. A multi‐scale approach that makes use of the sample simulations at the individual pore levels is employed. The effect of porous structures on the global fluid flow is accounted for via local volume averaged governing equations, while the closure terms are accounted for via averaging flow characteristics around the pores.

The performance of the model has been tested for an isothermal flow case. Good agreement with experimental data were achieved. Both the permeability and Ergun coefficient are shown to be flow properties as opposed to the empirical approach which typically results in constant values of these parameters independent of the flow conditions. Hence, the present multi‐scale approach is more versatile and can account for the possible changes in flow characteristics.

Further validation including non‐isothermal cases is necessary. Current scope of the model is limited to incompressible flows. The methodology can accommodate extension to compressible flows.

This paper proposes a method that eliminates the dependence of the numerical porous media simulations on empirical data. Although the model increases the fidelity of the simulations, it is still computationally affordable due to the use of a multi‐scale methodology.