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Lattice Boltzmann method (LBM) is employed to explore friction factor of single-phase fluid flow through porous media and the effects of local porous structure including geometry of grains in porous media and specific surface of porous media on two-phase flow dynamic behavior, phase distribution and relative permeability. The paper aims to discuss this issue.

The 3D single-phase LBM model and the 2D multi-component multi-phase Shan-Chen LBM model (S-C model) are developed for fluid flow through porous media. For the solid site, the bounce back scheme is used with non-slip boundary condition.

The predicted friction factor for single-phase fluid flow agrees well with experimental data and the well-known correlation. Compared with porous media with square grains, the two-phase fluids in porous media with circle grains are more connected and continuous, and consequently the relative permeability is higher. As for the factor of specific porous media surface, the relative permeability of wetting fluids varies a little in two systems with different specific surface areas. In addition, the relative permeability of non-wetting fluid decreases with the increasing of specific surface of porous media due to the large flow resistance.

Fluid-fluid interaction and fluid-solid interaction in the SC LBM model are presented, and schemes to obtain immiscible two-phase flow and different contact angles are discussed. Two-off mechanisms acting on the wetting fluids is proposed to illustrate the relative permeability of wetting fluids varies a little in two systems with different specific surface.

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.

The objective of this paper is to establish a solution strategy for obtaining dual solutions, namely trivial (conventional) and nontrivial (unconventional) solutions, of coupled pore-fluid flow and chemical dissolution problems in heterogeneous porous media.

Through applying a perturbation to the pore-fluid velocity, original governing partial differential equations of a coupled pore-fluid flow and chemical dissolution problem in heterogeneous porous media are transformed into perturbed ones, which are then solved by using the semi-analytical finite element method. Through switching off and on the applied perturbation terms in the resulting perturbed governing partial differential equations, both the trivial and nontrivial solutions can be obtained for the original governing partial differential equations of the coupled pore-fluid flow and chemical dissolution problem in fluid-saturated heterogeneous porous media.

When a coupled pore-fluid flow and chemical dissolution system is in a stable state, the trivial and nontrivial solutions of the system are identical. However, if a coupled pore-fluid flow and chemical dissolution system is in an unstable state, then the trivial and nontrivial solutions of the system are totally different. This recognition can be equally used to judge whether a coupled pore-fluid flow and chemical dissolution system involving heterogeneous porous media is in a stable state or in an unstable state. The proposed solution strategy can produce dual solutions for simulating coupled pore-fluid flow and chemical dissolution problems in fluid-saturated heterogeneous porous media.

A solution strategy is proposed to obtain the nontrivial solution, which is often overlooked in the computational simulation of coupled pore-fluid flow and chemical dissolution problems in fluid-saturated heterogeneous porous media. The proposed solution strategy provides a useful way for understanding the underlying dynamic mechanisms of the chemical damage effect associated with the stability of structures that are built on soil foundations.

This paper aims to provide a comprehensive literature review on modelling electro-osmotic flow in porous media.

Modelling electro-osmosis in fluid systems without solid particles has been first introduced. Then, after a brief description of the existing approaches for porous media modelling, electro-osmotic flow in porous media has been considered by analysing the main contributions to the development of this topic.

The analysis of literature has highlighted the absence of a universal model to analyse electro-osmosis in porous media, whereas many different methods and assumptions are used.

For the first time, the existing approaches for modelling electro-osmotic flow in porous have been collected and analysed to provide detailed indications for future works concerning this topic.

This study aims at developing a comprehensive model for the analysis of electro-osmotic flow (EOF) through a fluid-saturated porous medium. To fully understand and exploit a number of applications, such a model for EOF through porous media is essential.

The proposed model is based on a generalised set of governing equations used for modelling flow through fluid saturated porous media. These equations are modified to incorporate appropriate modifications to represent electro-osmosis (EO). The model is solved through the finite element method (FEM). The validity of the proposed numerical model is demonstrated by comparing the numerical results of internal potential and velocity distribution with corresponding analytical expressions. The model introduced is also used to carry out a sensitivity analysis of the main parameters that control EOF.

The analysis carried out confirms that EO in free channels without porous obstruction is effective only at small scales, as largely discussed in the available literature. Using porous media makes EO independent of the channel scale. Indeed, as the channel size increases, the presence of the charged porous medium is essential to induce fluid flow. Moreover, results demonstrate that flow is significantly affected by the characteristics of the porous medium, such as particle size, and by the zeta potential acting on the charged surfaces.

To the best of the authors’ knowledge, a comprehensive FEM model, based on the generalised equations to simulate EOF in porous media, is proposed here for the first time.

The purpose of this study is to analyze a new idea for external flow over a cylinder to increase the heat transfer and reduce pressure drop. Using wedge-shaped porous media in the front and wake regions of the cylinder can improve its hydrodynamic, and the rotating flow in the wake region can enhance the heat transfer with increased porous–liquid contact. Permeability plays a vital role, as a high-permeable medium improves heat transfer, whereas a low-permeable region improves the hydrodynamic.

Therefore, in the current research, external forced convection of nanofluid laminar flow over a bundle of cylinders is simulated using a two-phase mixture model. Four cases with different porous blocks around the cylinder are assessed: rectangular porous; wedge shape in trailing edge (TEP); wedge shape in leading and trailing edges (LTEP); and no porous block case. Also, three different lengths of wedge-shaped regions are considered for TEP and LTEP cases.

Results are presented in terms of Nusselt (Nu), Euler (Eu) and the performance evaluation criterion (PEC) numbers for various Reynolds (Re) and Darcy (Da) numbers.

It was found that in most situations, LTEP case provides the highest Nu and PEC values. Also, optimal Re and porous medium length exist to maximize PEC, depending on the values of Da and nanofluid volume fraction.

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.

The purpose of this study is to determine interfacial convective heat transfer coefficient numerically, for a porous media consisting of square blocks in inline arrangement under mixed convection heat transfer.

The continuity, momentum and energy equations are solved in dimensionless form for a representative elementary volume of porous media, numerically. The velocity and temperature fields for different values of porosity, Ri and Re numbers are obtained. The study is performed for the range of Ri number from 0.01 to 10, Re number from 100 to 500 and porosity value from 0.51 to 0.96. Based on the obtained results, the value of the interfacial convective heat transfer coefficient is calculated by using volume average method.

It was found that at low porosities (such as 0.51), the interfacial Nusselt number does not considerably change with Ri and Re numbers. However, for porous media with high Ri number and porosity (such as 10 and 0.51, respectively), secondary flows occur in the middle of the channel between rods improving heat transfer between solid and fluid, considerably. It is shown that the available correlations of interfacial heat transfer coefficient suggested for forced convection can be used for mixed convection for the porous media with low porosity (such as 0.51) or for the flow with low Ri number (such as 0.01).

To the best of the authors’ knowledge, there is no study on determination of interfacial convective heat transfer coefficient for mixed convection in porous media in literature. The present study might be the first study providing an accurate idea on the range of this important parameter, which will be useful particularly for researchers who study on mixed convection heat transfer in porous media, macroscopically.

This paper aims to numerically investigate the thermal performance evaluation of a microchannel with different porous media insert configurations.

Heat transfer and pressure drop of fluid flow through a three-dimensional (3D) microchannel with different partially and filled porous media insert configurations are investigated numerically. The number of divisions and positions of porous material inside the microchannel for 12 different arrangements are considered. A control volume method is used for single-phase laminar flow with the Darcy–Forchheimer model used for the porous media. The geometry of the problem consists of a microchannel with a rectangular cross-section of 0.4 mm × 0.2 mm and length 20 mm, with a stainless steel porous material insert with a porosity coefficient of ε = 0.32 and a Darcy number of Da = 2.7 × 10⁻⁴.

Numerical results show that when the transverse arrangement is used, as the number of partitions increases, the thermal performance is improved and the heat transfer increases up to 300% compared to that of the plain microchannel. Comparing the obtained results from the microchannels with transverse and longitudinal configurations, at low Reynolds numbers, the transverse arrangement of porous blocks and at high Reynold numbers, the longitudinal arrangement present the best thermal performance which is virtually four times higher compared to the obtained Nu numbers from the plain microchannel. The results show that as the volume of porous material is constant in the cases with various transverse porous blocks, the pressure drop is not changed in these cases. Also, the highest thermal performance ratio is when the porous material is placed along the walls in a longitudinal direction.

To the best knowledge of the authors, in the previous research, the effect of the arrangement and location of the porous medium in the transverse and longitudinal direction in the microchannel and their effect in different states on the behavior of flow and heat transfer has not been numerically investigated. In this study, the porous media configuration and its placement in a 3D microchannel were numerically studied. The effect of porous material layout and configurations in different longitudinal and transverse directions on the pressure drop, heat transfer and thermal performance in the 3D microchannel is investigated numerically.

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.