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Here within the article, the consequences of Hall as well as slip taking place on the peristaltic stream of a Jeffrey solution all the way through a permeable middling within an inclined 2D strait below the extensive wavelength estimation are explored, nearby outline explanations are attained meant for the axial swiftness as well as the axial heaviness gradient’s. The possessions of a variety of up-and-coming constraints lying on the propelling distinctiveness are conversed by way of the charts.

Turbulence transportation across permeable interfaces is investigated using direct numerical simulation, and the connection between the turbulent surface flow and the pore flow is explored. The porous media domain is constructed with an in-line arranged circular cylinder array. The effects of Reynolds number and porosity are also investigated by comparing cases with two Reynolds numbers (Re≈3000,6000) and two porosities (φ=0.5,0.8). It was found that the change of porosity leads to the variation of flow motions near the interface region, which further affect turbulence transportation below the interface. The turbulent kinetic energy (TKE) budget shows that turbulent diffusion and pressure transportation work as energy sink and source alternatively, which suggests a possible route for turbulence transferring into porous region. Further analysis on the spectral TKE budget reveals the role of modes of different wavelengths. A major finding is that mean convection not only affects the distribution of TKE in spatial space, but also in scale space. The permeability of the wall also have an major impact on the occurrence ratio between blow and suction events as well as their corresponding flow structures, which can be related to the change of the Kármán constant of the mean velocity profile., Deutsche Forschungsgemeinschaft, Projekt DEAL, Cluster of Excellence SimTech

The lunar surface is a typical vacuum environment, and its harsh heat rejection conditions bring great challenges to the thermal control technology of the exploration mission. In addition to the radiator, the sublimator is recommended as one of the promising options for heat rejection. The sublimator makes use of water to freeze and sublimate in a porous medium, rejecting heat to the vacuum environment. The complex heat and mass transfer process involves many physical phenomena such as the freezing and sublimation phase change of water in the porous medium and the movement of the phase-change interface. In this paper, the visualized ground-based experimental approaches of space sublimation cooling were presented to reveal the moving law of three-phase point and the growth phenomenon of ice-peak and icicle in microchannels under vacuum conditions. The visualized experiments and results prove that the freezing ice is divided into the porous ice-peak and the transparent icicle. As the sublimation progresses, the phase-change interface moves downward steadily, the length of the ice-peak increases, but the icicle decreases. The visualized experiments of space sublimation cooling in the capillary have guiding significance to reveal the sublimation cooling mechanism of water in the sublimator for lunar exploration missions.

In this paper, by means of the finite element method, the MHD free convection flow of non-Newtonian nanoliquid inside a halved annulus enclosure considering a constant heat flux is being applied to the straight walls has been analyzed. The enclosure is loaded with water and nanoparticles of alumina (Al2O3) the combination of these tows produces a liquid that shows shear-thinning behavior. The governing parameters of this study are the Rayleigh number (103 ≤ Ra ≤ 106), inclination angle (0 ≤ α ≤ 90), power-law index (0.6 ≤ n ≤ 1) and Hartmann number (0 ≤ Ha ≤ 100). The outcomes indicate that the inclination angle of the cavity and the Hartmann number can be considered as effective control parameters at different Rayleigh numbers. While the magnetic field is applied the velocity field retarded and hence convection heat transfer and the Nusselt number diminished, and the increment of power-law index prompts the heat transfer to drop. It is shown that the power-law index and Hartmann reduces the local Nusselt number. Also, the average Bejan numbers corresponding of active parameters are discussed in this study.

The principal goal of the present investigation is to inspect the flow characteristics of an electrically conducting hybrid nanofluid containing copper and graphene nanoparticles past a linearly stretched sheet with velocity slip condition at the interface. Since, the non-Newtonian fluid models result in a better understanding of the flow and heat transfer attributes of the nanofluids, therefore, non-Newtonian Maxwell nanofluid has been chosen as the base fluid in our study with an unsteady magnetic field applied at a certain angle to the direction of the flow. Consideration of thermal radiation along with heat absorption under the mutual influence of viscous and Joule dissipations is one of the key features of this research investigation. With the help of similarity transformations, the governing flow equations have been converted into a system of coupled non-dimensional differential equations. After that, Shooting method along with Runge–Kutta–Fehlberg numerical technique is employed to find the solutions for velocity and temperature of the hybrid nanofluid. The obtained numerical results are well demonstrated with a number of graphs and tables. Apart from this numerical technique, a statistical method is implemented of multiple quadratic regression estimation analysis on the various graphs of skin friction coefficient and wall temperature gradient to establish the connection among physical entities and heat transfer rate. The applications of this investigation in solar energy, ventilation, heating as well as refrigeration , medical science, defence sector etc. Some noteworthy findings include that Maxwell parameter, velocity slip and porosity have a tendency to reduce the hybrid nanofluid velocity whereas graphene Maxwell hybrid nanofluid’s temperature is getting enhanced for rising the values of magnetic field’s inclination angle, radiation, unsteadiness parameters, Biot number and viscous dissipation whereas a reverse trend is visible for heat absorption parameter. Furthermore, the permeability of the porous medium has a more significant impact on changing the nanofluid velocity than that of magnetic parameter whereas the rate of heat transfer is high sensitive for thermal radiation than that of viscous dissipation. As per authors’ knowledge there is no such attempt where the mutual effects of hybrid Maxwell nanofluid (graphene and copper), porous media and viscous dissipation have been considered.

The intrinsic permeability is a crucial parameter to characterise and quantify fluid flow through porous media. However, this parameter is typically uncertain, even if the geometry of the pore structure is available. In this paper, we perform a comparative study of experimental, semi-analytical and numerical methods to calculate the permeability of a regular porous structure. In particular, we use the Kozeny-Carman relation, different homogenisation approaches (3D, 2D, very thin porous media and pseudo 2D/3D), pore-scale simulations (lattice Boltzmann method, Smoothed Particle Hydrodynamics and finite-element method) and pore-scale experiments (microfluidics). A conceptual design of a periodic porous structure with regularly positioned solid cylinders is set up as a benchmark problem and treated with all considered methods. The results are discussed with regard to the individual strengths and limitations of the used methods. The applicable homogenisation approaches as well as all considered pore-scale models prove their ability to predict the permeability of the benchmark problem. The underestimation obtained by the microfluidic experiments is analysed in detail using the lattice Boltzmann method, which makes it possible to quantify the influence of experimental setup restrictions., Deutsche Forschungsgemeinschaft, Projekt DEAL

Nature of carbon nanotubes (CNT’s) mechanical characteristics can only be disclosed through advanced studies. Carbon nanotubes show diverse features in radial and axial directions when studied geometrically. Since CNT’s have two dimensional symmetrical behavior and they are in cylindrical shape, they show strong electrical and thermal conductivity in base fluid. In order to develop energy equation, such characteristics must be kept in view, we nominate the heat flux model of Catteneo-Christov. Carbon nanotubes of singlewall and multiwall are analyzed and compared in base fluid of water. Cylindrical coordinates are used in mathematical formulation and modeling for the flow equations to be converted to partial differential equations. For solution and study of fluid equations shooting method and Keller box scheme are used. Our computations resulted in an increase in fluid temperature due to thermal relaxation time, while fluid temperature decreases with an increases in Prandtl number. Further more, porosity also has fluid velocity as its decreasing function. The results are displayed through tables and graphs.

The paper considers the process of imbibition in a porous medium under the action of capillary forces in microgravity. A description of experiments on the repeated imbibition of an artificial porous medium during parabolic flights is given. In some experiments, the porous medium is homogeneous; in others, the experimental cell contains regions with different permeability. The analysis of non-stationary and convective terms in the equation of momentum conservation and their influence on the imbibition process is carried out. The results of numerical modeling of the process of repeated imbibition under the action of capillary forces under microgravity in an inhomogeneous porous medium are presented. The results of numerical modeling are compared with experimental data.

Partial filling of a porous medium in a channel of a certain configuration attracts attention, as it tends to enhance convective heat transfer while reducing pressure drop remarkably, as compared t...

To simulate the three-dimensional interaction of waves and porous structures using the lattice Boltzmann method, a novel multi-relaxation-time lattice Boltzmann scheme corresponding to the volume-averaged Navier-Stokes equations incorporating porous flow is developed. The porosity is introduced into the equilibrium distribution function, and the frictional forces produced by the porous media are added by the discrete force model. Through the Maxwell iteration, the relation between the mesoscopic lattice Boltzmann scheme and the macroscopic governing equations is established. Large eddy simulation and the single-phase volume-of-fluid techniques are modified to take porous media into account. The friction parameters in this model are calibrated using the experimental data of two-dimensional dam-break waves interacting with porous media composed of crushed rocks. Validations are carried out by comparing the simulation result of the proposed model with the laboratory data of three-dimensional dam-break waves impacting a prism and three-dimensional surface gravity waves (solitary waves and cnoidal waves) interacting with a vertical permeable breakwater. Furthermore, the interaction of regular waves and a rubble mound breakwater is used to test the capability of the model to handle spatially varying porous media. The different simulation results strongly agree with the experimental data, which prove that the lattice Boltzmann model has the ability to simulate complex wave motions near porous structures.

In this investigation, a comprehensive and accurate numerical analysis of the local thermal non-equilibrium effects on the natural convection characteristics in a horizontal elliptical porous annulus saturated with nanofluid has been carried out using finite volume technique. The internal surface is isothermally heated while the external one is fixed at uniform lower temperature. The nanofluid phase and the solid phase of the porous structure are hors local thermal equilibrium situation. The heat and the hydrodynamics equations in their dimensionless form under Darcy-Brinkman Forchheimer model were solved computationally by the finite volume technique using the standard SIMPLER algorithm. The results have been examined for various porous medium properties under the LTNE condition. The standard 0.05 significance level was used to identify the local thermal equilibrium within the system. According to the obtained results, the higher the Darcy number and the smaller the non-dimensional heat transfer coefficient for the solid/nanofluid interface, the modified thermal conductivity ratio and the media’s porosity, the higher are the LTNE effects. In addition, the spatial distribution contours of the LTNE sources within the porous annulus were schematized.

In the current study, a mathematical model is developed to visualize the mixed convection boundary layer flow of a nanofluid containing gyrotactic microorganisms past a permeable vertical surface saturated in a porous medium with variable viscosity and velocity slip effects. Suction/injection impact is taken into detail through the flow with heat and mass transfer analysis. Appropriate transformations are applied to transform the governing partial differential equations into non-linear ordinary differential equations, before being solved numerically using Runge-Kutta procedure is used with shooting technique. A parametric study focusing the influence of involved parameters on various fields such as the local skin friction coefficient, local Nusselt number are graphed via plots along with the local Sherwood number and motile microorganisms density number. The present results indicate that the motile microorganism number is enhanced for increasing Peclet number estimations. Moreover, the growing in the thermophoresis parameter leads to sufficient enhancement in the skin friction coefficient, Sherwood number and the density of the motile microorganism number for injection case, while the opposite behavior occurred with suction case.

Hypothesis Imbibition of a fluid into a porous material involves the invasion of a wetting fluid in the pore space through piston-like displacement, film and corner flow, snap-off and pore bypassing. These processes have been studied extensively in two-dimensional (2D) porous systems; however, their relevance to three-dimensional (3D) natural porous media is poorly understood. Here, we investigate these pore-scale processes in a natural rock sample using time-resolved 3D (i.e., four-dimensional or 4D) X-ray imaging. Experiments We performed a capillary-controlled drainage-imbibition experiment on an initially brine-saturated carbonate rock sample. The sample was imaged continuously during imbibition using 4D X-ray imaging to visualize and analyze fluid displacement and snap-off processes at the pore-scale. Findings We discover a new type of snap-off that occurs in pores, resulting in the entrapment of a small portion of the non-wetting phase in pore corners. This contrasts with previously-observed snap-off in throats which traps the non-wetting phase in pore centers. We relate the new type of pore-snap-off to the pinning of fluid-fluid interfaces at rough surfaces, creating contact angles close to 90°. Subsequently, we provide correlations for displacement events as a function of pore-throat geometry. Our findings indicate that having a small throat does not necessarily favor snap-off: the key criterion is the throat radius in relation to the pore radius involved in a displacement event, captured by the aspect ratio.

In this study, the effects of swirling flow and porous media of triple coaxial ports inverse diffusion flame (TCP-IDF) on the flame shape, temperature and gas emissions are studied. In addition, a comparison between swirling and non-swirling TCP-IDF burner conducted using 5° air swirler. On the other hand, the effect of using a porous screen with 2 mm and 1 mm mesh size including 65°, 45° and 15° flow divergence diffuser on the flame radial and centerline temperatures, and emissions investigated. During all experiments, the air to fuel ratio was constant at 27. The results showed that using swirl reduce CO and UHC emissions and increase the peak temperature and NOx emissions of TCP-IDF. Also increasing the flow divergence angle, all of the CO, UHC, peak temperature and NOx emission decreasing. Concerning the increase in mesh size, it has been noticed that as the mesh size increased, NOx emissions increased while the CO, UHC and peak temperature decreased. Moreover, the combination between the swirl and 65° flow divergence diffuser recorded the lowest value of the CO and UHC emissions. While the combination between the swirl burner with 65° flow divergence diffuser and 1 mm porous screen produced the lowest peak temperature and NOx emissions.

The viscoelastic fluid flow over a non linear stretching porous sheet is considered in this analysis. The case of suction and injection is also discuused. The effects of thermophoresis and brownain motion with viscous dissipation is taken into account. Under the flow assumptions, boundary layer approximation applied on the mathematical model and developed the partial differential equations. The similarity variable is applied on the partial differential equations which converted into ordinary differential equations. The dimensionless system further solved through numerical technique bvp4c method. The results of the current problem achieved after solving the problem which presented through graphs and table. Influence of numerous physical parameters on velocity function, concentration function and temperature function are manipulated through graphs. The tabular results are schemed to display skin friction and local Nusselt number. The higher values of N b which enhanced the velocity profile but declines velocity profile due to higher values of Ec . The thermal thickness enhances due larger values of γ and Pr but thermal thickness declines due to higher values of Ec and N t . The concentration profile enhances due to enhancing the values of Ec and Pr but concentration profile declines due to increasing the values of N t . Nusselt number enhaced due to higher values of Ec , S c and N t but declines of higher values of Pr .

Biot’s theory of poroelasticity describes seismic waves propagating through fluid-saturated porous media, so-called two-phase media. The classic Biot’s theory of poroelasticity considers the wave dissipation mechanism as being the friction of relative motion between the fluid in the pores and the solid rock skeleton. However, within the seismic frequency band, the friction has a major influence only on the slow P-wave and an insignificant influence on the fast P-wave. To represent the intrinsic viscoelasticity of the solid skeleton, we incorporate a generalized viscoelastic wave equation into Biot’s theory for the fluid-saturated porous media. The generalized equation that unifies the pure elastic and viscoelastic cases is constituted by a single viscoelastic parameter, presented as the fractional order of the wavefield derivative in the compact form of the wave equation. The generalized equation that includes the viscoelasticity appropriately describes the dissipation characteristics of the fast P-wave. Plane-wave analysis and numerical solutions of our wave equation reveal that (1) the viscoelasticity in the solid skeleton causes the energy attenuation on the fast P-wave and the slow P-wave at the same order of magnitude and (2) the generalized viscoelastic wave equation effectively describes the dissipation effect of the waves propagating through the fluid-saturated porous media.

The present investigation analyzes the influence of Cattaneo–Christov heat and mass fluxes on peristaltic transport of an incompressible flow. The fluid is obeying Bingham alumina nanofluid. The fluid flows between two co-axial vertical tubes. The system is expressed by a varying radially magnetic field with respect to the space. Soret effect and non-Darcy porous medium are taken into account. The governing system of equations is tackled by utilizing the approximations of long wave length with low Reynolds number and with the help of homotopy perturbation method (HPM). It is noticed that the axial velocity magnifies with an increase in the value of Bingham parameter. Meanwhile, the value of the axial velocity reduces with the elevation in the value of the magnetic field parameter. On the other hand, the elevation in the value of thermal relaxation time leads to a reduction in the value of fluid temperature. Furthermore, increasing in the value of mass relaxation time parameter makes an enhancement in the value of nanoparticles concentration. It is noticed also that the size of the trapped bolus enhances with the increment in the value of Bingham parameter. The current study has many accomplishments in several scientific areas like medical industry, medicine, and others. Therefore, it represents the depiction of the gastric juice motion in the small intestine when an endoscope is inserted through it.

In this study, a free energy model of the Lattice Boltzmann Method (LBM) is performed to simulate the motion, deformation, and decomposition of a droplet in the presence of electrohydrodynamic flow in porous media. To simulate the multi-phase flow in the presence of dielectric current by using the LBM, three distribution functions are used. To implement the free energy mode of HCZ, two equilibrium distribution functions are considered, one for solving the Navier-Stokes equation and the other for solving the Cahn-Hillard equation. Initially, the ability of the code to apply surface tension is tested by using the Laplace law and the droplet release test. Results show that there is a linear relation is between surface tension and κ which is a parameter in the HCZ model. The results show that the present numerical program is capable of modeling the regulated surface tension force as well. Then, the Rayleigh–Taylor instability simulation is used to evaluate the code's ability to apply volume forces. Also, the obtained results of the written numerical program are in good agreement with the numerical results of other valid references. Obtained results show that the difference between droplet deformation measured by numerical method and Taylor function is less than 2%. After modeling the droplet motions to investigate the droplet deformation, two electric fields are inserted into the droplet with reverse directions of each other. Then, by various tests, it is shown that at a given potential difference the droplet breaks down after much deformation and is divided into smaller droplets. The decomposition of droplets in a pre-mixed emulsion is a common technique to produce the monodisperse droplets. The presence of monodisperse droplets in an emulsion improves the physical properties of polymer from the science expert's perspective. The results of this study are used to improve the quality of polymer components.

The evaporation demands upon a rock or soil surface can exceed the ability of the profile to bring sufficient amount of liquid water. A dry surface layer arises in the porous medium that enables just water vapor flow to the surface. The interface between the dry and wet parts of the profile is known as the evaporation front. The paper gives the exact definition of the evaporation front and studies its motion. A set of differential equations governing the front motion in space is formulated. Making use of a set of measured and chosen values, a problem is formulated that illustrates the obtained theory. The problem is solved numerically and the results are presented and discussed.

This investigation aims to present the unsteady motion of second grade fluid in an oscillating duct induced by rectified sine pulses. Some of the most dominant means for solving problems in engineering, mathematics and physics are transform methods. The objective is to modify the domain of the present problem to a new domain which is easier for evaluation. Such modifications can be done by different ways, one such way is by using transforms. In present work Fourier sine transform and Laplace transform techniques are used. The solution thus obtained is in form of steady state, with combination of transient solution which fulfills all required initial and boundary conditions. The influence of various parameters of interest for both developing and retarding flows on the flow characteristics will also be sketched and discussed. Also, the problem is reduced to the flow model where side walls are absent by bringing the aspect ratio parameter (ratio of length to width) to zero.

The power transmitters, guyed masts and other lattice structures are exposed to wind action. The aerodynamic forces acting on tall tower constructions have crucial importance on the stability of the structure. The lattice structure drag coefficient determination is the subject of the international standards ESDU 81027 and 81028 and Eurocode 3 Part 3.1, but it can also be determined by numerical methods. For that purpose modelling using CFD proved to be both accurate and reliable. In this study the fluid-flow around the segment of a power transmitter was simulated by a 3-D model, where the geometry of the segment is approximated with a porous structure having the appropriate factor of porosity, in order to simplify the geometry. We have used three representative models of turbulence, standard k-? model, RNG k-? model, and Reynolds stress model. Drag coefficient values are extracted from the flow field and compared for all studied cases and with available experimental results from the wind tunnel. Simulations were performed for four wind velocities between 10 m/s and 30 m/s. The results are supplemented by the ones obtained by artificial neural network. The aim of this study is to show how the simple turbulence model coupled with approximated geometry can be used in the analysis of the aerodynamic forces acting on the lattice structure.

Fracture has significant effect on the production of hydrogen–carbon compound reservoirs. Underground fluid always flows through different spaces which involves different flow patterns. In this study, the embedded discrete fracture method (EDFM) to couple the flow in matrix and fracture is introduced. The Darcy flow is considered in fracture while the Pre-Darcy flow is employed in matrix. The model of two phase flow problem is established. The governing equations are coupled through multiple spatial scales. The structured mesh is applied to discrete the whole matrix domain. The fracture grids are embedded to the matrix meshes. The verification shows good accuracy of the fully implicit method for solving the model. Based on the numerical simulation, the results of 1D, 2D flow problems considering Pre-Darcy flow are presented. The characteristic of pressure and saturation is analyzed. Some numerical experiment examples are conducted to demonstrate the capability of the method including multiple wells system, complex fracture problem, and hydraulic fractured horizontal well system. Furthermore, we extend the model to 3D transport problem. The newly developed numerical simulation method improves the limitations of EDFM in Pre-Darcy flow. The newly developed simulation method can be taken as an effective tool for hydrocarbon production analysis when Pre-Darcy flow happens in fractured porous media.

Subsurface hydrogen (H2) storage in geological formations is of growing interest for decarbonization. However, there is a knowledge gap in understanding the multiphase flow involved in this process, which can have a significant impact on the recovery performance of H2. Therefore, a full-compositional modeling study was conducted to analyze potential issues and to understand the fundamental hydrodynamic mechanisms of H2 storage. We performed a range of 2D vertical simulations at the decametre scale with a very fine cell size (0.1 m) to observe the detailed flow behaviour of H2 with carbon dioxide (CO2) as cushion gas in various flow regimes. Issues such as viscous instability, capillary bypassing, gas trapping and gravity segregation are analysed here. To generalize our calculations, we have validated and applied the scaling theory in the context of subsurface H2 storage. Since this study is focused on the hydrodynamic behaviour, three dimensionless groups, including aspect factor, capillary/viscous ratio and gravity/viscous ratio were identified to correlate recovery performance between various scales in a fixed heterogeneous system. It was found that H2 could infiltrate the cushion gas in the proximity of the injectors, meaning that CO2 is not displaced away from the injectors in a piston-like fashion. As a result, the purity of the back produced H2 is much degraded, particularly in a viscous-dominated scenario. On the other hand, the injected H2 mostly accumulates at the top forming a highly restricted mixing zone with CO2 in the gravity-dominated case. The recovery performance is therefore much improved in this case. Although the gas distribution can be significantly altered by capillary forces leading to bypassed zones, the recovery performance of H2 is hardly influenced. This is because the back-produced H2 recovery is not dependent on the sweep efficiency of the gas. H2 can be back produced following the same paths which were formed during injection.

This paper reports a numerical study of double-diffusive natural convection through an annular space delimited by a square cylinder on the outside and a cylindrical cylinder on the inside covered by a porous layer. The Darcy-Brinkmann-Forchheimer is used for modeling flow in both fluid and porous areas. The annular space is partially or completely filled with an isotropic porous medium. A finite volume method, using the Patankar-Spalding technique is used for solving the discretization of the dimensionless equations governing the problem. The effects of simultaneously applied thermal and solutal buoyancy forces on heat and mass transfer are shown in the results for a large range of buoyancy ratios N, Rayleigh number, and thermal conductivity. Streamlines, isotherms, and iso-concentrations are presented to analyze the flow structure transition from mass species dominated to thermal dominated flow. Results show that the buoyancy ratio can change the flow pattern and the increased thermal conductivity ratio can improve heat and mass transfer. A good agreement was obtained between the present results and those published were found.

To more accurately predict the migration behavior of pollutants in porous media, we conduct laboratory scale experiments and model simulation. Aniline (An) is used in one-dimensional soil column experiments designed under various media and hydrodynamic conditions. The advection-dispersion equation (ADE) and the continuous-time random walk (CTRW) were used to simulate the breakthrough curves (BTCs) of the solute transport. The results show that the media and hydrodynamic conditions are two important factors affecting solute transport and are related to the degree of non-Fickian transport. The simulation results show that CTRW can more effectively describe the non-Fickian phenomenon in the solute transport process than ADE. The sensitive parameter in the CTRW simulation process is β, which can reflect the degree of non-Fickian diffusion in the solute transport. Understanding the relationship of β with velocity and media particle size is conducive to improving the reactive solute transport model. The results of this study provide a theoretical basis for better prediction of pollutant transport in groundwater. This article is protected by copyright. All rights reserved.

Diffusion-thermo effect (Dufour effect) and thermal-diffusion effect (Soret effect) on an MHD flow through porous medium taking nanoparticles may be considered to be useful in many engineering problems when there is a species concentration along with the solid nanoparticles. To study such an attracting problem, it is necessary to consider the flow to be single-phase. In the present investigation, the hydromagnetic flow of H2O-based nanofluids due to an exponentially expanding sheet saturated in non-Darcian porous material is examined with Dufour and Soret effects. In addition, temperature and species concentration along the surface in flow distribution are considered to be variable exponentially. Two sorts of nanofluids are considered, to be specific, Cu–H2O and Ag–H2O. Use of proper similarity transformations transfers the governing PDEs to coupled ODEs. Then the solutions of the coupled equations are computed by very efficient shooting method. Non-dimensionless velocity species concentration and temperature are introduced in graphical mode for several values of involved parameters. Out of several obtained outcomes, it is noticeable that similar to the magnetic parameter and permeability parameter, due to increase in non-Darcy Forchheimer parameter velocity diminishes and while temperature and species concentration increments are witnessed. Due to presence of Dufour effect, temperature enhances and similarly, the concentration increases for Soret effect. While due to Dufour effect, the concentration initially decreases, but away from surface it increases and similar behaviour is found for temperature in the case of Soret effect. Also, it is obtained that skin-friction coefficient for Cu–H2O nanofluid is larger than it value for Ag–H2O nanofluid. Dufour effect turns into the reason for the reduction of Nusselt number and increment of Sherwood number for both nanofluids, but Soret effect affects the two nanofluids reversely. The analysis and its findings provide some tools which may be applied in engineering and industrial problems.

Hypothesis Spreading of wetting liquids on rough surfaces can occur in a regime termed hemiwicking in which liquid advances ahead of the bulk liquid droplet front under the influence of capillary forces induced by the surface topography. When the surface topography is periodic as in the case for micropillar arrays, the wetting front is sharp and models describing the wetting dynamics can be derived directly from the periodic geometry. For materials with a highly irregular surface topography, the wetting front is diffuse and deriving analytical spreading model parameters directly from the surface topography is not generally possible. Experiments In this work, a previously published model for liquid spreading on thin porous materials is modified to incorporate unsaturated spreading ahead of the bulk liquid droplet using Richards equation. The permeability, K, and capillary pressure, pc, of the liquid in the surface roughness are the primary model parameters describing the spreading dynamics in Richards equation. These are determined by fitting to one-dimensional spreading experiments of silicone oil on a polyurethane-based paint coating with roughness on the scale of microns. Findings The resulting predictions of spreading dynamics for droplets with different initial sizes is good. It is also shown that reasonable model parameters can also be determined from the irregular surface topography by spatial filtering over 10 µm wavelength increments covering the range 10–500 µm. Approximate periodic micropillar arrays are defined from the filtered topography for each wavelength increment, enabling analytical estimates of the permeability and capillary pressure. Although using only the surface topography results in somewhat less accurate predictions, the savings in experimental and computational effort make it an attractive method for determining spreading model parameters.

Understanding drug release from pharmaceutical granules is vital to the development of targeted release profiles. A model describing diffusion and solubility-limited drug dissolution and release from a porous spherical granule of drug and excipient is considered. Radially varying porosity and initial concentration profiles which can arise in pharmaceutical granules are incorporated. A range of boundary-value and moving-boundary-value problems arise, depending on the relationship between the drug saturation concentration in the solvent medium and the initial drug concentration and porosity profiles. The model is derived in detail for the case where the initial drug concentration is greater than the drug saturation concentration in all parts of the granule. In this case, a moving boundary forms at the granule surface and propagates inwards, separating an unextracted inner core from a shell region which undergoes extraction via diffusion. The full model is non-dimensionalised and analysed using asymptotic methods and numerical solution. A leading-order model is derived by exploiting a small parameter corresponding to the ratio of the drug saturation concentration to the maximum initial concentration in the granule, allowing estimation of the time taken for the moving boundary to reach the granule centre. The behaviour of the full model is considered by solving it using a boundary immobilisation method and the finite element method for a range of parameters and comparing to the leading-order model. Finally, the model outputs for the moving boundary position and normalised drug release are compared with experimental data from the literature.

Hypothesis Geometrical analyses of pore-scale fluid-fluid-rock interfaces have recently been used for in-situ characterization of capillary pressure and wettability in natural porous media. Nevertheless, more robust techniques and multi-scale, well-characterized experimental data are needed to rigorously validate these techniques and enhance their efficacy when applied to saturated porous media. Experiments and Image analysis We present two new techniques for automated measurements of in-situ capillary pressure and contact angle, which offer several advancements over previous methodologies. These approaches are methodically validated using synthetic data and X-ray images of capillary rise experiments, and subsequently, applied on pore-scale fluid occupancy maps of a miniature Berea sandstone sample obtained during steady-state drainage and imbibition flow experiments. Findings The results show encouraging agreement between the image-based capillary pressure-saturation function and its macroscopic counterpart obtained from a porous membrane experiment. However, unlike the macroscopic behavior, the micro-scale measurements demonstrate a nonmonotonic increase with saturation due to the intermittency of the pore-scale displacement events controlling the overall flow behavior. This is further explained using the pertinent micro-scale mechanisms such as Haines jumps. The new methods also enable one to generate in-situ contact angle distributions and distinguish between the advancing and receding values while automatically excluding invalid measurements.

In this article, the fluid flow and heat transfer on MHD Casson nanofluid influenced by the non-coaxial rotation of moving disk passing through a porous medium is analyzed. A mixture of single-wall and multi-wall carbon nanotubes in the human Casson blood is used as the nanoparticles. Make use of the Laplace transform technique, the analytical solutions of the temperature and velocity profiles are obtained. The results show that the temperature and velocity profiles increase with the incorporation of CNTs. The nanofluid velocity reduces with a higher magnetic strength, but it is improved with the porosity. The imposition of CNTs has descended both primary and secondary skin friction and amplified the Nusselt number. SWCNTs have provided a greater heat transfer rate and skin friction as compared to MWCNTs. The obtained solution is verified when the present results show an excellent agreement with the published results and numerical values by Gaver-Stehfest algorithm.

The reflection and transmission problems of elastic waves through a partially saturated porous interlayer sandwiched between two elastic solid half-spaces are investigated. The partially saturated porous interlayer contains solid phase, gas phase and liquid phase. The solid frame is modeled by the fractional Zener model where the fractional order derivatives are used to describe the complex history-dependent viscoelastic behavior. Due to the coupled effects of the multiple fields, there exist three longitudinal waves and one transverse wave in the porous medium. The numerical results of reflection and transmission coefficients and the energy dissipation ratios are provided and shown graphically. The effects of the gas saturation, the interlayer thickness and the viscoelasticity of the solid frame are discussed based upon the numerical results. It is observed that the reflection and transmission coefficients and the energy dissipation ratios are affected noticeably by the gas saturation, the interlayer thickness and the viscoelasticity of the solid frame. In particular, there exists the characteristic gas saturation where the energy dissipation increases drastically.

We present regime maps for subsonic flow in dense gas-particle systems, which demarcate regions of compressible and (effectively) incompressible flow. These maps should aid researchers and industrialists in selecting the appropriate modeling approach, as well as in verifying numerical solvers. Demonstrating compressibility at Mach numbers lower than 0.3, we show that this commonly used criterion is insufficient for flows in porous media. For M

PurposeThe objective of this paper is to develop a semi-analytical finite element method for solving chemical dissolution-front instability problems in fluid-saturated porous media.Design/methodology/approachThe porosity, horizontal and vertical components of the pore-fluid velocity and solute concentration are selected as four fundamental unknown variables for describing chemical dissolution-front instability problems in fluid-saturated porous media. To avoid the use of numerical integration, analytical solutions for the property matrices of a rectangular element are precisely derived in a purely mathematical manner. This means that the proposed finite element method is a kind of semi-analytical method. The column pivot element solver is used to solve the resulting finite element equations of the chemical dissolution-front instability problem.FindingsThe direct use of horizontal and vertical components of the pore-fluid velocity as fundamental unknown variables can improve the accuracy of the related numerical solution. The column pivot element solver is useful for solving the finite element equations of a chemical dissolution-front instability problem. The proposed semi-analytical finite element method can produce highly accurate numerical solutions for simulating chemical dissolution-front instability problems in fluid-saturated porous media.Originality/valueAnalytical solutions for the property matrices of a rectangular element are precisely derived for solving chemical dissolution-front instability problems in fluid-saturated porous media. The proposed semi-analytical finite element method provides a useful way for understanding the underlying dynamic mechanisms of the washing land method involved in the contaminated land remediation.

Fluid heating and cooling is significant in a variety of industries, including power generation and transportation. Improvements in the thermal conductivity of the base fluid can also help in heat transmission. For this purpose, the effects of magneto hydrodynamics (MHD) and thermal radiation on mixed convection flow of Williamson nanofluid across a stretched sheet embedded in a porous medium in the presence of slip and convective boundary conditions is investigated. The Boungiorno model is adopted to analyze the impact of various dimensionless parameters on velocity, temperature, and nanoparticle concentration in the presence of slip and convective boundary conditions. The nonlinear governing equations are non-dimensionalized using similarity transformations, and the Keller box technique is utilized to solve them numerically. The current code is validated by generating numerical results for wall shear stress and compared them to previously published results. The comparison demonstrates that the outcomes are extremely similar. The results reveal that in the presence of a porous media, raising the magnetic and slip parameters reduced the nanofluid's velocity. It is also noticed that by increasing the radiation parameter, the heat and mass transfer rates on the surface of the stretching sheet are improved. In the presence of convective boundary conditions, the effect of Brownian motion and thermophoresis parameters on nanoparticle concentration was observed to be more profound.

We analyze analytically the effects of anisotropy in permeability and that of a transverse magnetic field on thermal convection in a porous medium saturated with a binary fluid and confined in a horizontal cavity. The porous medium, of great extension, is subjected to various conditions at the thermal and solutal boundaries. The axes of the permeability tensor are oriented obliquely with respect to the gravitational field. Based on a scale analysis, the velocity, temperature, and heat and mass transfer rate fields were determined. These results were validated by the study of borderline cases which are: pure porous media and pure fluid media discussed in the literature. It emerges from this study that the anisotropy parameters influence the convective flow. The application of a transverse magnetic field significantly reduces the speed of the flow and thereby affects the temperature field and the rate of heat and mass transfer.

This paper examines the unsteady hydro-magnetic boundary layer flow of a reacting and radiating electrically conducting fluid past a slippery permeable vertical plate embedded in a porous medium. T...

This study describes the linkage leakage in sewage pipes through a porous media using computational fluid dynamics with the presence of one leak through fluid simulations using the Ansys fluent 17.2 commercial software based on standard k-ε model under steady-state condition. The pipe section is three-dimensional with a pipe length of 40 mm, a pipe diameter of 20 mm, and leak orifice diameter of 2 mm with a porous media of length 25 mm and width 30 mm. The interest of this study was to reduce the rate of sewage leakage in pipes laid underground by use computational fluid dynamics. The simulation results obtained shows that when the flow is subjected to an outlet pressure between 100000 Pa to 275000 Pa the sewage leaks at pressures of 99499 Pa to 278799.8 Pa indicating that increase of outlet pressures increases the pressure at the leak point and also an increase in the inlet velocity resulted into an increase of velocity at the leak point and no significant change in sewage flow rate with increased inlet velocities. Therefore, monitoring of the pressure and velocity fields along the pipeline is an extremely important tool to identify leaks since these fields are affected by perturbations both before the leak point and after the leak point.

The melting phenomenon in two-dimensional (2D) flow of fourth-grade material over a stretching surface is explored. The flow is created via a stretching surface. A Darcy-Forchheimer (D-F) porous medium is considered in the flow field. The heat transport is examined with the existence of the Cattaneo-Christov (C-C) heat flux. The fourth-grade material is electrically conducting subject to an applied magnetic field. The governing partial differential equations (PDEs) are reduced into ordinary differential equations (ODEs) by appropriate transformations. The solutions are constructed analytically through the optimal homotopy analysis method (OHAM). The fluid velocity, temperature, and skin friction are examined under the effects of various involved parameters. The fluid velocity increases with higher material parameters and velocity ratio parameter while decreases with higher magnetic parameter, porosity parameter, and Forchheimer number. The fluid temperature is reduced with higher melting parameter while boosts against higher Prandtl number, magnetic parameter, and thermal relaxation parameter. Furthermore, the skin friction coefficient decreases against higher melting and velocity ratio parameters while increases against higher material parameters, thermal relaxation parameter, and Forchheimer number.

This study investigates an approach of enhancing heat transfer in heat exchangers by increasing heat transfer area of the heat exchanger, and this is done by filling the rectangular test section with porous media to extend the heat transfer surface area and thus enhance the heat transfer. The permeability of the used nickel foam is determined by conducting pressure drop measurements through the nickel foam in the test section, and the heat transfer and pressure drop parameters are measured and compared with the empty test section. The results show that the values of the friction coefficient are 24.5 times the values of the empty test section, and the Nusselt number is observed to be three times higher when using nickel foam than that without foam in the test section. No transition regime is observed for the foam-filled test section on both heat transfer and pressure drop results; however, the transition from laminar to turbulent is found for the test section without foam. The results of thermal factor of the foam-filled test section show a thermal performance factor higher than unity through the entire Reynolds number range of 2000–6500, with better thermal performance factor at lower Reynolds number.

The present research work scrutinizes numerical heat transfer in convective boundary layer flow having characteristics of magnetic ( Fe 3 O 4 ) and nonmagnetic ( Al 2 O 3 ) nanoparticles synthesized into two different kinds of Newtonian (water) and non-Newtonian (sodium alginate) convectional base fluids of casson nanofluid which integrates the captivating effects of nonlinear thermal radiation and magnetic field embedded in a porous medium. The characterization of electrically transmitted viscous incompressible fluid is taken into account within the Casson fluid model. The mathematical formulation of governing partial differential equations (PDEs) with highly nonlinearity is renovated into ordinary differential equations (ODEs) by utilizing the suitable similarity transform that constitutes nondimensional pertinent parameters. The transformed ODEs are tackled numerically by implementing b v p 4 c in MATLAB. A graphical illustration for the purpose of better numerical computations of flow regime is deliberated for the specified parameters corresponding to different profiles (velocity and temperature). To elaborate the behavior of Nusselt and skin friction factor, a tabular demonstration against the distinct specific parameters is analyzed. It is perceived that the velocity gradient of Newtonian fluids is much higher comparatively to non-newtonian fluids. On the contrary, the thermal gradient of non-Newtonian fluid becomes more condensed than that of Newtonian fluids. Graphical demonstration disclosed that the heat transfer analysis in non-Newtonian (sodium alginate)-based fluid is tremendously influenced comparatively to Newtonian (water)-based fluid, and radiation interacts with the highly denser temperature profile of non-Newtonian fluid in contrast to that of Newtonian fluid. Through such comparative analysis of magnetic or nonmagnetic nanoparticles synthesized into distinct base fluids, a considerable enhancement in thermal and heat transfer analysis is quite significant in many expanding engineering and industrial phenomenons.

This article investigates the natural convection heat transfer and inclined magnetic-field effects of a nanofluid past a vertical stretching sheet embedded in a porous medium with a non-uniform hea...

Control strategy on Rayleigh-Benard convection in rotating nanofluids saturated in anisotropic porous layer heated from below is studied in the presence of uniformly internal heat source for rigid-rigid, free-free, and lower-rigid and upper-free boundaries. Feedback control strategy with an array of sensors situated at the top plate and actuators located at the bottom plate of the nanofluids layer are considered in this study. Linear stability analysis based on normal mode technique has been performed, the eigenvalue problem is obtained numerically by implementing the Galerkin method and computed by using Maple software. Model employed for the nanofluids includes the mechanisms of Brownian motion and thermophoresis. The problem of the onset of convective rolls instabilities in a horizontal porous layer with isothermal boundaries at unequal temperatures known as Horton-Roger-Lapwood model based on the Darcy model for the fluids flow is used. The influences of internal heat source’s strength, modified diffusivity ratio, nanoparticles concentration Darcy-Rayleigh number and nanofluids Lewis number are found to advance the onset of convection, meanwhile the mechanical anisotropy parameter, thermal anisotropy parameter, porosity, rotation, and controller effects are to slow down the process of convective instability. No visible observation on the modified particle density increment and rigid-rigid boundaries are the most stable system compared to free-free and rigid-free boundaries.