Flow In Porous Channel Research Articles

Exploring the significance of nanoparticle shapes and the impact of thermal radiation on MHD viscoelastic nanofluid flow in porous channels

ABSTRACT This study investigates analytically the influence of nanoparticle shapes on an unsteady mixed convective viscoelastic MHD nanofluid flow in a horizontal channel with oscillating walls in a saturated porous medium. The effect of radiation is also considered in the energy equation. The considered NPs are Cu, Ag, Al2O3, TiO2, and Fe3O4, with base fluids H2O and C2H6O2. The considered different shapes of NPs are cylinder, platelet, blade, and brick. The study examines three flow situations based on physical boundary conditions. The perturbation method is employed to solve the flow governing equations for three different flow situations based on physical boundary conditions: Case (i) flow in a horizontal channel with both lower and upper walls stationary; Case (ii) the upper wall of the channel is in oscillation while the lower one is constant; Case (iii) both walls of the channel are in oscillatory motion. The velocity and temperature distributions, as well as the skin friction coefficient and heat transfer rate, are analyzed through graphs and tables to assess the impact of various governing parameters. From the results, it is found that brick-shaped NPs exhibit more strength to the velocity and temperature distributions, followed by cylinder, platelet, and blade for both water-based and EG-based NF.

Multiple solution of MHD Casson fluid flow in porous channel with chemical reactions and thermal radiation effects

This study focused on evaluating the synergistic effects of magnetohydrodynamics, Casson fluid properties, thermal radiation, chemical reactions, and heat transfer mechanisms within a porous channel. Through the application of similarity transformation, nonlinear governing equations are converted into nonlinear ordinary differential equations. These modified equations were then numerically solved in MATLAB using the Runge–Kutta method alongside the shooting technique to ensure precise results. The investigation yielded various numerical solutions for the dimensionless velocity, temperature, concentration, skin friction coefficient, heat transfer coefficient, and Sherwood number, all of which are presented in both tabular and graphical formats. Three distinct solutions emerged from the analysis, differentiated by variations in the Reynolds number, Casson number, expansion or contraction ratio, and magnetic parameters. These solutions demonstrate differences in the parameters under investigation. Solutions within the ranges of γ[5,∞] and R[31.07,∞] are influenced by the specific values of the magnetic number M[0,2.0]. For each M value, there exists a unique set of solutions for γ and R that satisfy the established parameters. As the magnetic number varies, so does the range of feasible solutions, highlighting the sensitivity of the system to magnetic influence. The values of γ and R are adjusted according to the chosen M value.

Modeling the Link Between Electric Fields and Three Films of Porous Channel Flow

Modeling the Link Between Electric Fields and Three Films of Porous Channel Flow

Improved perturbation solution for viscous flow in a dilating–contracting permeable channel with velocity slip

Recently, Mandal and Ghosh [“Lie-group method solutions for a viscous flow in a dilating-squeezing permeable channel with velocity slip,” Phys. Fluids 35, 047121 (2023)] constructed perturbation solutions for viscous flow in porous channels with a slip condition and moving walls restricted to slow wall dilation–contraction rates. Herein, we show that this “slowness” assumption may be completely removed. In doing so, we develop a more widely applicable and more accurate perturbation scheme for all dilation–contraction rates. Our strategy involves generating new and exact solutions to the linear, inviscid problem with slip condition, and then we draw on this precise form to construct more accurate perturbation expansions for solutions to the nonlinear flow model than are currently available.

Computational Irreversibility Analysis in Transient Flow of a Non-Newtonian Fluid through a Channel with Porous Walls

A second law analysis is explored to investigate the irreversibility properties in a transient, porous channel flow of a viscous, incompressible, and non-Newtonian fluid. The non-Newtonian fluid model is of a Generalized Newtonian Fluid type with no elastic properties but with shear-thinning viscosity. Additionally, given that the flow is non-isothermal, the viscosity is therefore expectedly also assumed to be temperature dependent. The porous channel is subjected to constant suction and injection of fluid through the walls. Computational solutions for the underlying fluid dynamical equations, based on robust finite difference numerical techniques, are developed and implemented in time and space. We demonstrate the effects of the embedded fluid flow and heat transfer parameters on the fluid velocity and temperature profiles. We also explore the competing effects of heat transfer irreversibility versus fluid friction irreversibility. The major observations are that, in the flow regions where the maximum velocity obtains, heat transfer irreversibility significantly dominates over the otherwise insignificant fluid friction irreversibility. It is also observed that, in those flow regions away from the region of maximum velocity, the opposite scenario obtains, and hence fluid friction irreversibility significantly dominates over heat transfer irreversibility. Along the channel walls, fluid friction irreversibility notably dominates over heat transfer irreversibility. The possibility that certain parameter choices may lead to reverse scenario is not discounted.

On the mechanism of turbulent heat transfer in composite porous-fluid systems with finite length porous blocks: Effect of porosity and Reynolds number

The majority of literature studies on composite porous-fluid systems involve fully-developed porous channel flows where the porous media covers the whole length of the channel. These studies utilized periodic boundary conditions at the inlet and outlet. In these systems, the stagnation at the frontal face of the porous block, turbulent separation bubble over the porous-fluid interface, and flow leakage from the porous to non-porous regions do not exist. The existence of these flow features in the case of a finite porous block immersed in a channel flow modifies turbulent interactions across the porous-fluid interface. In contrast to the previous studies, this paper investigates the flow and thermal characteristics of turbulent channel flow containing a porous block with a finite length. To this end, pore-scale large eddy simulations are performed in composite porous-fluid systems with two porosities (53% and 91%) at three Reynolds numbers of 3600, 7200 and 14400. Flow visualization shows that two distinct regions are formed over the interface in low-porosity cases: Region#1 near the leading edge with organised hairpin structures and high flow leakage; Region#2 away from the leading edge with unorganised hairpin structures and lower flow leakage. In region#1, maximum turbulent fluctuations occur far away from the interface while they approach the interface in region#2. The results showed that by increasing either the Reynolds number or porous length, the location of maximum turbulence statistics approaches the interface. This observation supports earlier findings for fully-developed porous channel flows which are only valid in region#2. Whereas, with a low Reynolds number or a short porous length, the turbulent statistics peak far from the interface, consistent with the observations in region#1. Besides, it was found that increasing the porosity and Reynolds number reduces the flow leakage (from the porous region to the non-porous region) up to 50% and 10%, respectively, which in turn disrupts the patterns of contour-rotating vortex pairs and hairpin structures over the interface. It is further found that for a fixed Reynolds number, the overall Nusselt number for the high-porosity case is 2.6 times higher than that of the low-porosity case. The pressure drop for the low-porosity cases is 1.8 times more than that for the high-porosity cases.

Study of MHD Mixed Convention Flow and Heat Transfer Through Porous Media

In this present paper, the effects of chemical reaction on two-dimensional mixed convection flow and heat transfer of an electrically conducting micropolar fluid in a porous medium between two parallel plates with Soret and Dufour have been considered. The reduced flow field equations are solved using the quasilinearization method. The effects of various parameters such as Hartmann number, inverse Darcy's parameter, Schmidt number, Prandtl number, chemical reaction rate, Soret and Dufour numbers on the velocity components, microrotation, temperature distribution, and concentration are studied in detail and presented in the form of graphs. The flow through porous boundaries has many applications in science and technology such as water waves over a shallow beach, mechanics of the cochlea in the human ear, aerodynamic heating, flow of blood in the arteries, and petroleum industry. Several authors have studied theoretically the laminar flow in porous channels. Berman [1] considered the viscous fluid and analyzed the flow characteristics when it passed through the porous walls. Later the same problem for different permeability was studied by Terril and Shrestha [2]. The theory of micropolar fluids was introduced by Eringen [3] which are considered as an extension of generalized viscous fluids with microstructure. Examples for micropolar fluids include lubricants, colloidal suspensions, porous rocks, aerogels, polymer blends, and microemulsions. The same Berman problem with micropolar fluid was discussed by Sastry and Rama Mohan Rao [4]. The flow and heat transfer of micropolar fluid between two porous parallel plates was analyzed by Ojjela and Naresh Kumar [5]. Srinivasacharya et al. [6] obtained an analytical solution for the unsteady Stokes flow of micropolar fluid between two parallel plates. The effect of buoyancy parameter on flow and heat transfer of micropolar fluid between two vertical parallel plates was investigated by Maiti [7].

Temporal stability of multiple similarity solutions for porous channel flows with expanding or contracting walls

In this paper, the temporal stability of multiple similarity solutions (flow patterns) for the incompressible laminar fluid flow along a uniformly porous channel with expanding or contracting walls is analyzed. This work extends the recent results of similarity perturbations of Sun et al. [“Temporal stability analysis for multiple similarity solutions of viscous incompressible flows in porous channels with moving walls,” Appl. Math. Modell. 77, 738–755 (2020)] by examining the temporal stability with perturbations of general form (including similarity and nonsimilarity forms). Based on the linear stability theory, two-dimensional eigenvalue problems associated with the flow equations are formulated and numerically solved by a finite difference method on the staggered grids. The linear stability analysis reveals that the stability of the solutions is same with that under the perturbations of a similarity form within the range of the wall expansion ratio α. [−5≤α≤3 as in Sun et al., “Temporal stability analysis for multiple similarity solutions of viscous incompressible flows in porous channels with moving walls,” Appl. Math. Modell. 77, 738–755 (2020)]. Further, it is found that the expansion ratio α has a great influence on the stability of type I flows: in the case of wall contraction (α<0), the stability region of the cross-flow Reynolds number (R) increases as the contraction ratio (|α|) increases; in the case of wall expansion and 0<α≤1, the stability region increases as the expansion ratio (α) increases; in the case of 1≤α≤3, type I flows are stable for all R where they exist. The flows of other types (types II and III with −5≤α≤3 and type IV with α = 3) are always unstable. As a nonlinear stability analysis or a validation of the linear stability analysis, the original nonlinear two-dimensional time-dependent problem with an initial perturbation of general form over those flow patterns is solved directly. It is found that the stability with the nonlinear analysis is consistent with the linear stability analysis.

Different-Scale Simulation of Flows in Porous Media

The paper considers the development of algorithms for an adequate description of processes of different scales in porous media. The choice of a computational technique is determined by the reference size of the problem being solved. Models of porous medium flow under Darcy’s law, neglecting the medium microstructure, are used for the simulation at macro-scale. While at micro-scale, a direct description of fluid flow in porous channels with complex geometry by means of gas dynamic equations is used. In the first case the proposed model of non-isothermal multiphase multicomponent flow in a porous medium includes the mass balance and total energy conservation equations modified by analogy to the known quasi-gas dynamic equations. The model features are the introduction of minimal reference scales in space and in time and the change of the system type from parabolic to hyperbolic to increase the stability of explicit difference schemes applied for approximation. In the second case the dimensionless form of the quasi-gas dynamic system with pressure decomposition, developed by the authors earlier, is adapted to the simulation of flows in the pore space. The fictitious domain method is proposed to reproduce the core microstructure. The developed approaches have been verified by test predictions.

Radiative heat transfer enhancement in MHD porous channel flow of an Oldroyd-B fluid under generalized boundary conditions

This study explains the transient free convection phenomenon in a vertical porous channel subject to nonlinear thermal radiation. The infinite vertical channel encloses magnetohydrodynamic (MHD) flow of an Oldroyd-B fluid. The left channel wall possesses time-dependent velocity , while the right wall exhibits no motion. The momentum and temperature field equations are developed on the bases of momentum conservation law and Fourier’s principle of heat transfer. Laplace transformation technique and Durbin’s numerical inversion method are jointly incorporated to compute the solutions of the formulated problem. The influences of flow and material parameters on heat transfer and fluid velocity are graphically scrutinized with physical aspects. The numerical computations for skin friction and temperature gradient are tabularized to comprehensively examine the wall shear stress and heat transfer rate. Finally, velocity fields for Maxwell fluid, second grade fluid, and viscous fluid are traced out as limiting cases and their comparison is drawn with the velocity field of an Oldroyd-B fluid. Besides this, some newly published results are also deduced from the acquired solutions. It is observed that increasing the magnitude of radiation parameter Rd rapidly enhances the rate of heat transfer at the right channel wall while an inverse behavior of Nusselt number is witnessed at the left channel wall. The Maxwell fluid and second grade fluid indicate the swiftest and slowest channel flow rates respectively. The shear stress specifies dual nature for relaxation and retardation parameters subject to static and moving wall. Additionally, it is found that the flow of an Oldroyd-B fluid is retarded by a magnetic field.

Effects of Variable Viscosity on Asymmetric Flow of Non-Newtonian Fluid Driven Through an Expanding/Contracting Channel Containing Porous Walls

Flow in porous channel or pipe has attained significant attention in biophysics, especially when the walls are contracting or expanding. The purpose of this work is to explore the effects of variable viscosity on the asymmetric laminar flow of Casson fluid (CF) with thermal radiation in an expanding/contracting channel having porous walls. The flow equations, by using appropriate transformations, are reduced to ordinary differential equations (ODEs). The method of homotopy analysis (HAM) is used to obtain the expressions for the velocity field along with the temperature profile. Graphs are portrayed for different parametric values and analyzed in detail for the consequent dynamic attributes, especially the viscosity-dependent parameter, CF parameter, and the expansion ratio. CF parameter escalates the velocity of the fluid near the lower wall, but after mid-way, it starts decreasing. The fluid velocity due to temperature-dependent (TD) viscosity parameter is more noteworthy for Newtonian fluid (NF) relative to non-Newtonian (NN) fluid. As anticipated, the radiation parameter causes the fluid to heat up.

The effect of using nanofluid flow into a porous channel in the CPVT under transient solar heat flux based on energy and exergy analysis

Concentrator photovoltaic thermal system is one of the heat and power generation systems that have received special attention in recent decades. In this paper, concentrator photovoltaic thermal cell with the effect of Al2O3 nanofluid flow in porous channel has been investigated under transient heat flux. The system is analyzed from energy and exergy viewpoint, and also the first and second laws of thermodynamics efficiencies are calculated. The governing equations are continuity, Brinkman momentum and energy conservation equations considering the transient solar flux using parabolic dish concentrator over a day in Mashhad city. The numerical modeling is based on the finite element method. The numerical results show that the Nusselt number, normalized temperature and electrical efficiency of the presented model have an acceptable agreement with experimental data. Efficiency of the photovoltaic cell increases with increasing the Reynolds number as the difference between the highest and the lowest efficiency value is 5% at 12 p.m. In addition, with increasing Reynolds number, the first law of thermodynamics efficiency increases due to porosity and permeability effects of the porous channel cooling. The maximum difference between highest and the lowest value for first law efficiency is 49.4% at Re = 110. The second law of thermodynamics efficiency decrease as Reynolds number increases as the highest value is 4.2% and the lowest is 2.8% at Re = 20 and Re = 10, respectively.

Turbulence characteristics over k-type rib roughened porous walls

To understand the permeability effects on turbulent rib-roughened porous channel flows, particle image velocimetry measurements are performed at the bulk Reynolds number of 5000–20000. Solid impermeable and porous ribs are considered for the rib-roughness whose geometry is categorised in the k-type roughness whose pitch/rib-height is 10. Three isotropic porous media with nearly the same porosity: 0.8, and different permeabilities (0.004, 0.020, 0.033 mm2) are applied. It is observed that the recirculation between the ribs becomes weak and the recirculation vortex submerges into the porous wall as the wall permeability and Reynolds number increase for both solid and porous rib cases while the recirculation vanishes in high permeable cases. These phenomena result in characteristic difference in turbulence quantities. By fitting the mean velocity profiles to the log-law form, the permeability effects of both rib and bottom wall on the log-law parameters and the equivalent sand-grain roughness are discussed. It is concluded that the zero-plane displacement increases while the von Kármán constant and the equivalent sand-grain roughness decrease as the wall and rib permeability increases.

Dissimilar Heat Transfer Enhancement in Turbulent Porous–Channel Flow

Dissimilar Heat Transfer Enhancement in Turbulent Porous–Channel Flow

Improved Eddy-Viscosity Modelling of Turbulent Flow around Porous–Fluid Interface Regions

The RANS modelling of turbulence across fluid-porous interface regions within ribbed channels has been investigated by applying double (both volume and Reynolds) averaging to the Navier–Stokes equations. In this study, turbulence is represented by using the Launder and Sharma (Lett Heat Mass Transf 1:131–137, 1974) low-Reynolds-number $$k-\varepsilon $$ turbulence model, modified via proposals by either Nakayama and Kuwahara (J Fluids Eng 130:101205, 2008) or Pedras and de Lemos (Int Commun Heat Mass Transf 27:211–220, 2000), for extra source terms in turbulent transport equations to account for the porous structure. One important region of the flow, for modelling purposes, is the interface region between the porous medium and clear fluid regions. Here, corrections have been proposed to the above porous drag/source terms in the k and $$\varepsilon $$ transport equations that are designed to account for the effective increase in porosity across a thin near-interface region of the porous medium, and which bring about significant improvements in predictive accuracy. These terms are based on proposals put forward by Kuwata and Suga (Int J Heat Fluid Flow 43:35–51, 2013), for second-moment closures. Two types of porous channel flows have been considered. The first case is a fully developed turbulent porous channel flow, where the results are compared with DNS predictions obtained by Breugem et al. (J Fluid Mech 562:35–72, 2006) and experimental data produced by Suga et al. (Int J Heat Fluid Flow 31:974–984, 2010). The second case is a turbulent solid/porous rib channel flow to examine the behaviour of flow through and around the solid/porous rib, which is validated against experimental work carried out by Suga et al. (Flow Turbul Combust 91:19–40, 2013). Cases are simulated covering a range of porous properties, such as permeability and porosity. Through the comparisons with the available data, it is demonstrated that the extended model proposed here shows generally satisfactory accuracy, except for some predictive weaknesses in regions of either impingement or adverse pressure gradients, associated with the underlying eddy-viscosity turbulence model formulation.

On the viscous core boundary layer of the injection and suction driven channel flows with expanding or contracting walls

AbstractThis work extends a sequence of studies devoted to the analysis of the laminar flow in porous channels with retracting walls. This problem was originally used to model slab propellant grain regression. After identifying a subtle endpoint singularity that affects the former solution in its third derivative, a stretched variable is introduced to capture the rapid variations in the channel's core. The core refers to the midsection plane where the shear layer is displaced due to hard blowing at the walls. Then using matched‐asymptotic expansions with logarithmic corrections, a composite solution is developed following successive integrations that start with the fourth derivative. In the process, the inner correction is retrieved from the fourth‐order equation governing the symmetric injection‐driven flow near the core. The resulting approximation is expressed in terms of generalized hypergeometric functions and is confirmed using numerics and limiting process verifications. The composite solution is shown to outperform the former, outer solution, as the core is approached or as the injection Reynolds number is increased. Without undermining the practicality of the former solution outside the thin core region, the development of a matched‐asymptotic approximation enables us to suppress the often overlooked singular terms, thus ensuring a uniformly valid outcome down to the third and fourth derivatives, which affect the pressure distribution and its normal gradients.

Low- and high-order accurate boundary conditions: From Stokes to Darcy porous flow modeled with standard and improved Brinkman lattice Boltzmann schemes

The present contribution focuses on the accuracy of reflection-type boundary conditions in the Stokes–Brinkman–Darcy modeling of porous flows solved with the lattice Boltzmann method (LBM), which we operate with the two-relaxation-time (TRT) collision and the Brinkman-force based scheme (BF), called BF-TRT scheme. In parallel, we compare it with the Stokes–Brinkman–Darcy linear finite element method (FEM) where the Dirichlet boundary conditions are enforced on grid vertices. In bulk, both BF-TRT and FEM share the same defect: in their discretization a correction to the modeled Brinkman equation appears, given by the discrete Laplacian of the velocity-proportional resistance force. This correction modifies the effective Brinkman viscosity, playing a crucial role in the triggering of spurious oscillations in the bulk solution. While the exact form of this defect is available in lattice-aligned, straight or diagonal, flows; in arbitrary flow/lattice orientations its approximation is constructed. At boundaries, we verify that such a Brinkman viscosity correction has an even more harmful impact. Already at the first order, it shifts the location of the no-slip wall condition supported by traditional LBM boundary schemes, such as the bounce-back rule.For that reason, this work develops a new class of boundary schemes to prescribe the Dirichlet velocity condition at an arbitrary wall/boundary-node distance and that supports a higher order accuracy in the accommodation of the TRT-Brinkman solutions. For their modeling, we consider the standard BF scheme and its improved version, called IBF; this latter is generalized in this work to suppress or to reduce the viscosity correction in arbitrarily oriented flows. Our framework extends the one- and two-point families of linear and parabolic link-wise boundary schemes, respectively called B-LI and B-MLI, which avoid the interference of the Brinkman viscosity correction in their closure relations.The performance of LBM and FEM is thoroughly evaluated in three benchmark tests, which are run throughout three distinctive permeability regimes. The first configuration is a horizontal porous channel, studied with a symbolic approach, where we construct the exact solutions of FEM and BF/IBF with different boundary schemes. The second problem refers to an inclined porous channel flow, which brings in as new challenge the formation of spurious boundary layers in LBM; that is, numerical artefacts that arise due to a deficient accommodation of the bulk solution by the low-accurate boundary scheme. The third problem considers a porous flow past a periodic square array of solid cylinders, which intensifies the previous two tests with the simulation of a more complex flow pattern. The ensemble of numerical tests provides guidelines on the effect of grid resolution and the TRT free collision parameter over the accuracy and the quality of the velocity field, spanning from Stokes to Darcy permeability regimes. It is shown that, with the use of the high-order accurate boundary schemes, the simple, uniform-mesh-based TRT-LBM formulation can even surpass the accuracy of FEM employing hardworking body-fitted meshes.

A Semi-Analytical Solution for a Porous Channel Flow of a Non-Newtonian Fluid

A theoretical study of steady laminar two-dimensional flow of a non-Newtonian fluid in a parallel porous channel with variable permeable walls is carried out. Solution by Differential Transform Method (DTM) is obtained and the flow behavior is studied. The non-Newtonian fluid considered for the study is couple stress fluid. Thus, in addition to the effects of inertia and permeabilities on the flow, the couple stress effects are also analyzed. Results are presented and comparisons are made between the behaviour of Newtonian and non-Newtonian fluids.

Analysis of Thermal Flow in a Rotating Porous U-Turn Duct Using Lattice Boltzmann Method

The lattice Boltzmann method is carried out to investigate the heat transfer enhancement in a U-turn duct which is partially filled with a porous media. The porous layer is inserted at the core of the duct and is modeled using the Brinkman–Forchheimer assumptions. In order to validate the results, first a channel flow problem without any porous layer is compared with available data. Second, the porous Couette flow and partially porous channel flow are successfully compared with the studies of other researchers. Then, fluid flow in a clear U-turn duct is studied looking carefully at the velocity, curvature and rotation effects. Finally, the effects of porous layer thickness on the rate of heat transfer and pressure drop are investigated. Parametric studies are conducted to evaluate the effects of various parameters (i.e., Reynolds number, Darcy number, rotation number), highlighting their influences on the thermo-hydrodynamics behavior of the flow. The optimum values of porous layer thickness are presented for specific flow parameters.

POD analysis of low Reynolds turbulent porous channel flow

Snapshot proper orthogonal decomposition (POD) is utilized to understand the turbulent channel flow physics over permeable porous surfaces. Our aim is to study how the flow structures vary in different wall permeabilities. The data needed for POD algorithm are provided by large eddy simulation (LES). Utilizing Volume-Averaged Navier-Stokes (VANS) equations inside the permeable wall, eliminates the need for detailed knowledge of the pore microstructure and porous medium can be easily specified with global properties like porosity and permeability. The bulk mean Reynolds number is 5500 and simulations are carried out in three different porosities, 0, 0.8 and 0.95. The reasons why the quasi-streamwise vortices become shorter and absent above a permeable wall are discussed. POD analysis has revealed that permeability of wall amends the size and even shape of the large scale, energetic dominant structures of the flow and these alterations are more vivid in highly permeable walls in which large spanwise vortical structures that stem from the Kelvin-Helmholtz instability are dominant structures of the flow.