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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.

The purpose of this paper is to analytically perform gaseous slip flow and heat transfer analysis within a parallel-plate microchannel partially filled with a centered porous medium under local thermal non-equilibrium (LTNE) condition. Heat transfer of gaseous flow in a porous microchannel is analytically studied. Energy communication at the porous-fluid interface is considered by two approaches: the gas rarefaction negatively impacts the heat transfer performance, and the optimum ratio of porous thickness is found to be around 0.8.

Both Models A and B are utilized to consider the heat flux splitting for the fluid and solid phases at the porous-fluid interface.

Analytical solutions for the fluid and solid phase temperature distributions and the Nusselt number are derived. In the no-slip flow limit, the present analytical solutions are validated by the partially and fully filled cases available in the literature.

The continuum flow (no-slip flow) is only a special case of the slip flow. Meanwhile, the effects of pertinent parameters on the heat transfer are also discussed.

A survey of available literature mentioned above indicates a shortage of information for slip flow and heat transfer in partially filled porous systems. The main objective of the present study is to investigate the slip flow and heat transfer characteristics for forced convection through a microchannel partially filled with a porous medium under LTNE condition. The porous substrate is placed at the center of the microchannel. Analytical solutions for the temperature distributions of the fluid and solid phases and the Nusselt number at the microchannel wall are obtained.

Heat transfer of gaseous flow in a porous microchannel is analytically studied. Energy communication at the porous-fluid interface is considered by two approaches: the gas rarefaction negatively impacts the heat transfer performance, and the optimum ratio of porous thickness is found to be around 0.8. Gaseous slip flow and heat transfer analysis is analytically performed within a parallel-plate microchannel partially filled with a centered porous medium under LTNE condition. Analytical solutions for the fluid and solid phase temperature distributions and the Nusselt number are derived for the first time. The effects of pertinent parameters on the heat transfer are also discussed. Compared with the results obtained for the continuum flow regime, the gas rarefaction negatively impacts the heat transfer efficiency and has little influence on the optimal porous thickness.

The purpose of this paper is to numerically investigate the heat transfer enhancement in a tube filled partially with porous media under non-uniform porosity distribution and thermal dispersion effects. The optimum porous thickness ratio [R_(r,Nu)] for the heat transfer enhancement under these conditions with and without considering required pumping power is evaluated.

The local thermal non-equilibrium and Darcy–Brinkman–Forchheimer models are used to simulated thermal and flow fields in porous region. The tube wall and flow regime are assumed to be isothermal and laminar, respectively. The impacts of Darcy number (Da = 10^-6 - 10^-1) and inertia parameter (F = 0 − 2) on the Nusselt number and friction factor are studied for non-uniform porosity distribution.

First, the effect of Nusselt number indicates that there are two different behaviors with respect to uniform and non-uniform porosity for partially and fully filled porous pipe. Second, variable porosity in porous region has significant influence on the optimum thickness ratio with considering required pumping power. For negligible inertia term, it depends on the Darcy number, whereas it is 0.9 at F > 1. Third, the plug flow assumption cannot be valid even at lower Darcy number under non-uniform porosity, while this assumption is applicable at Da < 10^-3 for constant porosity distribution in porous region.

According to the best knowledge of authors, the optimum porous thickness ratio for the heat transfer enhancement considering the pressure loss effects under variable porosity has not reported up to now. Also the plug flow assumption in such physics is not discussed.

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.

The purpose of this paper is to analyze two different approaches (Models A and B) for an adiabatic boundary condition at the wall of a channel filled with a porous medium. The analytical solutions for the velocity distribution, the fluid and solid phase temperature distributions are derived and compared with numerical solutions. The phenomenon of heat flux bifurcation for Model A is demonstrated. The effects of pertinent parameter C on the applicability of the Models A and B are discussed. Analytical solutions for the overall Nusselt number and the heat flux distribution at the channel wall are derived and the influence of pertinent parameters Da and k on the overall Nusselt number and the heat flux distribution is discussed.

Two approaches (Models A and B) for an adiabatic boundary condition in porous media under local thermal non-equilibrium (LTNE) conditions are analyzed in this work. The analysis is applied to a microchannel which is modeled as a porous medium.

The phenomenon of heat flux bifurcation at the wall for Model A is demonstrated. The effect of pertinent parameter C on the applicability of each model is discussed. Model A is applicable when C is relatively large and Model B is applicable when C is small. The heat flux distribution is obtained and the influence of Da and k is discussed. For Model A, ϕ_Afin increases and ϕ_Asub, ϕ_Acover decrease as Da decreases and k is held constant, ϕ_Asub increases and ϕ_Afin, ϕ_Acover decrease as k increases while Da is held constant; for Model B, ϕ_Bfin increases and ϕ_Bsub decreases either as Da decreases or k decreases. The overall Nusselt number is also obtained and the effect of Da and k is discussed: Nu increases as either Da or k decrease for both models. The overall Nusselt number for Model A is larger than that for Model B when Da is large, the overall Nusselt numbers for Models A and B are equivalent when Da is small.

Proper representation of the energy equation and the boundary conditions for heat transfer in porous media is very important. There are two different models for representing energy transfer in porous media: local thermal equilibrium (LTE) and LTNE. Although LTE model is more convenient to use, the LTE assumption is not valid when a substantial temperature difference exists between the solid and fluid phases.

Fluid flow and convective heat transfer in porous media have many important applications such as thermal energy storage, nuclear waste repository, electronic cooling, geothermal energy extraction, petroleum processing and heat transfer enhancement.

This work has important fundamental implications.

In this work the microchannel is modeled as an equivalent porous medium. The analytical solutions for the velocity distribution, the fluid and solid phase temperature distributions are obtained and compared with numerical solutions. The first type of heat flux bifurcation phenomenon, which indicates that the direction of the temperature gradient for the fluid and solid phases is different at the channel wall, occurs when Model A is utilized. The effect of pertinent parameter C on the applicability of the models is also discussed. The analytical solutions for the overall Nusselt number and the heat flux distribution at the channel wall are derived, and the effects of pertinent parameters Da and k on the overall Nusselt number and the heat flux distribution are discussed.

This study aims to investigate the effect of two-dimensional Darcy-Forchheimer flow over second-grade fluid with linear stretching. Heat transfer through convective boundary conditions is taken into account.

Nonlinear coupled governing equations are tackled with a homotopy algorithm, while for numerical computation the computer software package BVPh 2.0 is used. The convergence analysis is also presented for the validation of analytical and numerical results.

Valuation for the impact of key parameters such as variable thermal conductivity, Dufour and Soret effects and variable magnetic field in an electrically conducted fluid on the velocity, concentration and temperature profiles are graphically illustrated. It is observed from the results that temperature distribution rises by Dufour number whereas concentration distribution rises by Soret number. The Forchheimer number and porosity parameter raise the skin friction coefficient. The permeable medium has a vital impact and can help in reining the rate of heat transfer.

The permeable medium has a vital impact and can help in reining the rate of heat transfer.

To the best of the authors’ knowledge, this study is reported for the first time.

This paper aims to investigate the effect of Powell–Eyring fluid induced by a stretched sheet. Heat and mass transfer under the influence of magnetic dipole over a stretching sheet are taken into account.

Nonlinear coupled governing equations are solved using the optimal homotopy asymptotic technique, and a computer software package BVPh 2.0 is used for numerical computations.

Impact of significant quantities is graphically examined. It is seen that the heat transfer deceases for higher values of viscous dissipation parameter, radiation parameter, Dufour number, whereas it increases for bigger values of Prandtl number. The numerical results have been validated through comparison with existing literature as a special case of proposed model and perceived that the Soret number has reining role to increase the rate of heat transfer.

To the best of the authors’ knowledge, this study is reported for the first time.

Numerical simulations of a multistage multiphase pump at different operating conditions were performed to study the variational characteristics of flow parameters for each impeller. The simulation results were verified against the experimented results. Because of the compressibility of the gas, inlet volume flow rate qi and inlet flow angle ß_i for each impeller decrease gradually from the first to the last stage. The volume flow rate at the entrance of the pump q, rotational speed n and inlet gas volume fraction (IGVF) affect the characteristics of qi and ß_i.

The hydraulic design features of the impellers in the multistage multiphase pump are obtained based on the flow parameter characteristics of the pump. Using the hydraulic setup features, stage-by-stage design of the multistage multiphase pump for a nominal IGVF has been conducted.

The numerical simulation results show that hydraulic loss in impellers of the optimized pump is substantially reduced. Furthermore, the hydraulic efficiency of the optimized pump increases by 3.29 per cent, which verifies the validation of the method of stage-by-stage design.

Under various operating conditions, q_i and ß_i decrease gradually from the first to the fifth stage because of the compressibility of the gas. For this characteristic, the fluid behavior varies at each stage of the pump. As such, it is necessary to design impellers stage by stage in a multistage rotodynamic multiphase pump.

These results will have substantial effect on various practical operations in the industry. For example, in the development of subsea oilfields, the conventional conveying equipment, which contains liquid-phase pumps, compressors and separators, is replaced by multiphase pumps. Multiphase pumps directly transport the mixture of oil, gas and water from subsea oilwells through a single pipeline, which can simplify equipment usage, decrease backpressure of the wellhead and save capital costs.

Characteristics of a multistage multiphase pump under different operating conditions were investigated along with features of the inlet flow parameters for every impeller at each compression stage. Our simulation results have established that the change in the inlet flow parameters of every impeller is mainly because of the compressibility of the gas. The operational parameters q, n and IGVF all affect the characteristics of qi and ß_i. However, the IGVF has the most prominent effect. Lower values of IGVF have an insignificant effect on the gas compressibility. Higher values of IGVF have a significant effect on the gas compressibility. All these characteristics affect the hydraulic design of the impellers for a multistage multiphase pump. In addition, the machining precision should also be considered. Considering all these factors, when IGVF is lower than 10 per cent, all the impellers in the pump can be designed uniformly. When IGVF varies from 10 to 30 per cent, the first two stages should be designed separately, and the latter stages are uniform starting with the second stage. When IGVF varies from 30 to 50 per cent, the first three stages should be designed separately, and the latter stages are going to be similar to the third stage. An additional increase in IGVF results in degeneration of the differential pressure of the pump, which will reduce the compressibility of the gas. As such, it can be deduced that only the first three stages should be designed separately, and the latter stages will be similar to the third stage. In addition, for the pump working under a lower volume flow rate than 25 m³/h, the first three stages should be designed individually while keeping the geometrical structure of the subsequent stages the same as the third stage.

This paper aims to establish a mathematical model for water-flooding considering the impact of fluid–solid coupling to describe the process of development for a low-permeability reservoir. The numerical simulation method was used to analyze the process of injected water channeling into the interlayer.

Some typical cores including the sandstone and the mudstone were selected to test the permeability and the stress sensitivity, and some curves of the permeability varying with the stress for the cores were obtained to demonstrate the sensitivity of the formation. Based on the experimental results and the software Eclipse and Abaqus, the main injection parameters to reduce the amount of the injected water in flowing into the interlayer were simulated.

The results indicate that the permeability of the mudstone is more sensitive to the stress than sandstone. The injection rate can be as high as possible on the condition that no crack is activated or a new fracture is created in the development. For the B82 block of Daqing oilfield, the suggested pressure of the production pressure should be around 1–3MPa, this pressure must be gradually reached to get a higher efficiency of water injection and avoid damaging the casing.

This work is beneficial to ensure stable production and provide technical support to the production of low permeability reservoirs containing an interlayer.

The purpose of this study is to examine the impact of activation energy with binary chemical reaction for unsteady flow on permeable stretching surface.

The simultaneous effects of multiple slip and magneto-hydrodynamic effects at the boundary are taken into account. The thermal buoyancy parameter and thermal radiation are included in both energy and momentum equations, while expression of activation energy is considered in concentration equation. Three-stage Lobatto IIIa finite difference collocation technique with bvp4c MATLAB package is used to obtained numerical results.

The influence of key elements (Schmidt number, buoyancy force ratio factor, factor of radiation, magnetic element, unsteadiness factor, suction/injection parameter, Prandtl number, activation energy, chemical reaction rate parameter, heat source and sink parameters, velocity, thermal and concentration slips, porosity parameter and temperature difference parameter) on velocity, temperature and concentration profiles are illustrated pictorially. A detailed discussion is presented to see how the graphical aspects justify the physical prospect.

In the best of author’s knowledge, this work is yet not available in existing literature.