Darcy Model Research Articles

Optimization of entropy generation and thermal mechanism of MHD hybrid nanoliquid flow in a sinusoidally heated porous cylindrical chamber

The present computational investigation explores the fluid and thermal characteristics along with entropy generation due to buoyancy-driven magnetohydrodynamic (MHD) convective flow of aqueous hybrid nanoliquid filled in a nonuniformly heated porous cylindrical chamber. The fluid motion in the enclosure is modeled by Brinkman — extended Darcy model. The modeled equations are resolved by finite difference approach. The computations are conducted for Rayleigh number (103–105), Hartmann number (0–50), Darcy number (10−5–10−1), different nanoparticle shapes and nanoparticle volume fraction (Ag/MgO: 0–0.05) to understand the characteristic of flow, thermal and irreversibility distribution. With vast numerical simulations, the outcomes reveal that though the buoyancy force is greater, the fluidity cannot be enhanced unless the permeability and magnetic field strength are optimally maintained. As Ra,Ha and Da is varied respectively from 103 to 105, 50 to 0 and 10−5 to 10−1, the fluidity has been enhanced by 99.39%,83.26% and 99.79%. Among all considered parametric combinations, it has been noticed that the choice of Ha=0,Ra=105,Da=10−1 with proper ratio of nanoparticles enhance the system efficiency. However, minimal entropy generation can be achieved with greater Hartmann and lower Darcy numbers. Furthermore, it has been found that blade shaped nanoparticles lead to increase the performance of thermal system.

A Revised Work on the Rayleigh-Bénard Instability of Nanofluid in a Porous Medium Layer

To reveal the mechanism of the enhanced heat transfer in nanofluids, Buongiorno (ASME J. Heat Transfer, vol. 128, 2006, pp. 240–250) developed a convective transport model by considering the slip mechanisms of nanoparticles migration. By now, many extended researches are based on his model. Among them, the study on porous medium flow pioneered by Nield & Kuznetsov (Int. J. Heat & Mass Transfer, vol. 52, 2009, pp.5796–5801) has received much attention. Their work employed the Darcy model and Buongiorno’s model to investigate the thermal instability in a horizontal porous medium layer saturated by a nanofluid. Through a sophisticated analysis, they obtained an approximate formula capable of predicting the stability threshold. However, a potential contradiction exists in their analysis owing to an improper assumption about the thermophoretic coefficient, which may lead to an unphysical result. To date, much of current works still adopted this improper assumption in various extended problems. To resolve this contradiction, the present study revises their work by considering the dependence of thermophoretic coefficient on the volume fraction of nanoparticles. A nonlinear basic-state solution of concentration is obtained and then used to implement the linear stability analysis. In comparison with Nield’s formula, the present result shows that the threshold of instability shifts to a lower concentration by more than one order of magnitude. The mechanism causing the shift is discussed and the novelty of the present study is stressed.

Thermal-hydraulic characteristics analysis of steam–air condensation in vertical porous-wall corrugated tubes

In the passive containment cooling systems (PCCS) of Generation III nuclear power plants, the condensation performance of steam containing non-condensable gas (NCG) in condensate tubes is critical for removing heat from the nuclear power plant containment. By applying a novel porous-wall corrugated structure in the condenser tubes of this system, it was found that under certain conditions, a double vortex is formed inside and outside the porous layer, which is conductive to the transportation and condensation of steam to the condensing wall. The VOF multiphase relation and Brinkman–Forchheimerextended Darcy model in combination of local heat balance, condensation and species transport equations are employed to describe the heat and mass transfer in the porous-wall corrugated tube during condensation. The numerical analysis are conducted to investigate the effects of waveform channel, porous layer and its thicknesses, subcooling of cooling wall and inlet air mass fractions on flow and condensation under different inlet velocities, in which simulations agree with the experimental data. The results show that the condensation heat transfer is greatly influenced by the vortex distribution and air accumulation. At inflowing velocity of 1 m/s, the waveform with amplitude of 1 mm and wavelength of 18 mm can achieve the highest performance evaluation factor, φ (about 67.5 % enhancement than the smooth tubes). The ratio of waveform amplitude to wavelength needs to be chosen properly in consideration of convection between solid matrix and steam–air mixture in porous layer, and non-condensation gas distribution near cooling wall of condensation tube.

Analyzing the pressure drop in spacer stacks for electrodialytic processes considering the effect of mechanical compression: Experimental vs. free and porous flow model prediction

There is a growing interest in using electromembrane processes in sustainable applications. However, it involves designing efficient cells with low pressure drops, which is particularly important in processes requiring high energy efficiency. In order to analyze the fluid dynamics in spacer-filled channels, manifolds and stacks used primarily in acid base flow batteries a free and porous flow model was developed. The predictive model composed by Navier-Stokes equations and Brinkman Forchheimer extended Darcy model closely follows the experimental pressure drop in a single spacer-filled channel. According to the model results, the entrance and exit zones of the spacer produce the highest pressure drop per axial longitude, highlighting the strong effect of the design of spacer in these zones. In the case of stacks the mechanical compression among spacers as revealed by measurement with compression film suggests some spacer deformation on entrance and exit zones that intensified the inlet and outlet effects.

Topology Optimization of Turbulent Flow Cooling Structures Based on the k-ε Model.

Topology optimization (TO) is an effective approach to designing novel and efficient heat transfer devices. However, the TO of conjugate heat transfer has been essentially limited to laminar flow conditions only. The present study proposes a framework for TO involving turbulent conjugate heat transfer based on the variable density method. Different from the commonly used and oversimplified Darcy model, this approach is based on the more accurate and widely accepted k-ε model to optimize turbulent flow channels. We add penalty terms to the Navier-Stokes equation, turbulent kinetic energy equation, and turbulent energy dissipation equation, and use interpolation models for the thermal properties of materials. A multi-objective optimization function, aiming to minimize the pressure drop and the average temperature, is set up to balance the thermal and hydraulic performance. A case study is conducted to compare various optimization methods in the turbulent regime, and the results show that the present method has substantially higher optimization effectiveness while remaining computationally inexpensive.

The Onset of Darcy–Brinkman Convection in a Porous Layer with Mutual Impact of Thermal Non-Equilibrium and Non-Uniform Temperature Gradients

The two-field thermal conditions of local thermal nonequilibrium (LTNE) were used to investigate linear stability of thermal convection in a liquid-saturated, porous layer via the extended Brinkman–Darcy model for different non-uniform basic thermal gradients. The critical values were numerically computed by the Galerkin method for rigid isothermal boundaries. The impact of LTNE and different forms of non-uniform basic temperature gradients on the onset of porous convection was examined. The porosity modified conductivity ratio has no influence on system stability at a small inter-phase heat transport coefficient limit. However, for higher values of the inter-phase heat transport coefficient, an increase in the porosity modified conductivity ratio hastens the onset of convection. An increase in the Darcy number delays the convective motions. The results for different basic temperature profiles are symmetric qualitatively. In addition, the possibility of control of convection by a basic temperature profile was studied in detail.

Numerical Method for Fractional-Order Generalization of the Stochastic Stokes–Darcy Model

This paper is aimed at efficient numerical implementation of the fractional-order generalization of the stochastic Stokes–Darcy model, which has important scientific, applied, and economic significance in hydrology, the oil industry, and biomedicine. The essence of this generalization of the stochastic model is the introduction of fractional time derivatives in the sense of Caputo’s definition to take into account long-term changes in the properties of media. An efficient numerical method for the implementation of the fractional-order Stokes–Darcy model is proposed, which is based on the use of a higher-order approximation formula for the fractional derivative, higher-order finite difference relations, and a finite element approximation of the problem in the spatial direction. In the paper, a rigorous theoretical analysis of the stability and convergence of the proposed numerical method is carried out, which is confirmed by numerous computational experiments. Further, the proposed method is applied to the implementation of the fractional-order stochastic Stokes–Darcy model using an ensemble technique, in which the approximation is carried out in such a way that the resulting systems of linear equations have the same coefficient matrix for all realizations. Furthermore, evaluation of the discrete fractional derivatives is carried out with the use of parallel threads. The efficiency of applying both approaches has been demonstrated in numerical tests.

A comprehensive mathematical model for cardiac perfusion

The aim of this paper is to introduce a new mathematical model that simulates myocardial blood perfusion that accounts for multiscale and multiphysics features. Our model incorporates cardiac electrophysiology, active and passive mechanics, hemodynamics, valve modeling, and a multicompartment Darcy model of perfusion. We consider a fully coupled electromechanical model of the left heart that provides input for a fully coupled Navier–Stokes–Darcy model for myocardial perfusion. The fluid dynamics problem is modeled in a left heart geometry that includes large epicardial coronaries, while the multicompartment Darcy model is set in a biventricular myocardium. Using a realistic and detailed cardiac geometry, our simulations demonstrate the biophysical fidelity of our model in describing cardiac perfusion. Specifically, we successfully validate the model reliability by comparing in-silico coronary flow rates and average myocardial blood flow with clinically established values ranges reported in relevant literature. Additionally, we investigate the impact of a regurgitant aortic valve on myocardial perfusion, and our results indicate a reduction in myocardial perfusion due to blood flow taken away by the left ventricle during diastole. To the best of our knowledge, our work represents the first instance where electromechanics, hemodynamics, and perfusion are integrated into a single computational framework.

Computational analysis of nonsimilar electromagnetohydrodynamic radiative nanofluid flow across Darcy–Forchheimer–Brinkman porous media

This study develops nonsimilar analysis for the electrically conducting nanofluid flow over a vertically placed stretching surface adjacent to porous medium with transverse magnetic field assumption. The features of thermal radiations, viscous dissipation, and heat source factors are also incorporated to scrutinize the thermal prospective. The Brinkman–Forchheimer who extended Darcy model is considered for the porous medium and a Rosseland approximation is employed for thermal radiations. Titanium oxide and silica are considered nanoparticles, while kerosine oil and silicon ceramic serving as the base fluids in porous medium, respectively. Tiwari–Dass approach is used to derive the governing system. Appropriate transformations are deployed to render the governing partial differential equations into a dimensionless system. To address the transformed system, the local nonsimilarity technique in conjunction with the bvp4c (fourth-order method boundary value problem) is used. Variations in velocity and thermal distributions of nanofluids have been investigated in relation to developing dimensionless parameters such as nanoparticle concentration, Darcy porosity parameter, Darcy number, electric parameter, Hartmann number, radiation parameter, Richardson number, heat source/sink parameter, and Eckert number. Numerical findings are found to interpret the role of the emerging parameters on physical quantities. The obtained findings reveals that the surge in the estimations of Richardson number enhances the nanofluid velocity while it diminishes the temperature profile. The concentration of nanoparticles improves the thermal profile of both nanofluids under consideration, whereas the enhancement in Darcy porosity parameter reduces velocity and improves temperature distributions. Results found to be in excellent agreement with published results on a special case of the considered problem.

Multiphysics analysis of tramway geotechnical infrastructure: numerical modelling

Under realistic field conditions, geotechnical infrastructures are usually influenced by complex interactions of mechanical behaviour under the action of an internal water flow. This mechanism could be the main origin of damage to embankments. This study develops a new hydro-mechanical (HM) approach based on Darcy's law model and Biot's poroelastic concept to investigate the behaviour of soil with and without geotextile under realistic conditions. The problem's numerical solution is carried out using a finite-element method. The proposed two-dimensional model was implemented in Comsol Multiphysics Software. Under coupled HM behaviour, the stress in porous materials causes a volumetric change in strain, which causes fluid diffusion. Consequently, pore pressure dissipates through the pores. To discuss the advantages of coupled HM modelling and evaluate the geotextile performance, volumetric strain, pore-water pressure, storage and displacement are compared for a mechanical, hydraulic and HM model. These analyses were undertaken in connection with a tramway embankment project in a marshy area in Sidi Bel Abbes. The simulation results show better results for geotextile and embankment in HM coupled modelling.

Three-dimensional transient CFD modeling of multiple finned aluminum foam heat sinks in a horizontal channel

Finned metal foam heat sinks are well-known because of their excellent performance in cooling of powered electronics. In this study, three-dimensional transient numerical simulations of finned aluminum foam heat sinks in a forced convection of air were carried out using commercial COMSOL. The geometry under consideration consists of an array of finned aluminum foam heat sinks mounted on heater blocks and placed on a plate in a horizontal channel. Heat sink aluminum foam regions were considered as porous media with a local non-equilibrium thermal model to evaluate thermal characteristics, while the Forchheimer-Brinkman extended Darcy model is considered for the flow analysis. Our main concern in the present study is to evaluate the transient thermal–hydraulic behavior and the cooling performance under constant flux heat sources while varying the Reynolds number and variable morphological parameters of the aluminum foam, i.e., porosity (ε) varied from 0.85 to 0.95. The thermal performance ratio and the average Nusselt number of the finned aluminum foam heat sinks are 23.14% and 30%, respectively, larger than the finned aluminum heat sinks. As the Reynolds number increases, the thermal characteristics are enhanced, and the pressure drop is increased. An increase in porosity causes a reduction in heat transfer rate and an elevation of pressure drop.

Oscillatory Modes on the Onset of Electrohydrodynamic Instability in Oldroydian Nanofluid Saturated Anisotropic Porous Layer

This work deals with an analytical study on the initiation of oscillatory convection in a rheological nanofluid saturating anisotropic porous layer with inclusion of vertical AC electric field using modified boundary conditions with negligible flux of volume fraction of nanoparticles. The rheological properties of the nanofluid are described using Oldroyd model. The Darcy model extended by Brinkman model is deployed to characterize the solid matrix behavior. The used model for nanofluid with inclusion of electric field integrates the additional effect of electrophoresis with that of thermophoresis and Brownian motion in the conservation equations of motion. The partial differential equations are simplified to non-dimensional linear equations using infinitesimal perturbations, Boussinesq approximation, normal mode technique and linearized stability theory. The characteristic equation is solved analytically for stress-free boundary conditions and the expressions for Rayleigh number of non-oscillatory and oscillatory modes initiation are determined. The oscillatory modes are found to occur for both the cases of top-/bottom-heavy nanoparticles distributions. The electric Rayleigh number, thermal Prandtl number and stress relaxation parameter advances whereas the Brinkman-Darcy number are found to delay initiation of both stationary and oscillatory convection.

Natural convection in a differentially heated cavity filled with a Brinkman bidisperse porous medium

PurposeThe purpose of this work is the study of the steady free convection in a square differentially heated cavity filled by a Brinkman bidisperse porous medium. An appropriate mathematical model considering the Brinkman, momentum and energy interphase terms is proposed. The dependence of the stream functions, isotherms and of the Nusselt numbers on the governing parameters is analysed.Design/methodology/approachThe both phases of flow and heat transfer are solved numerically using a modified finite difference technique. The algebraic system obtained after discretization is solved using the SOR method. The results are found to be in a significant agreement with the ones presented by the literature for a Darcy bidisperse porous medium and a Brinkman monodisperse porous medium.FindingsThe effects of the governing parameters on stream functions, isotherms and Nusselt numbers are discussed. It has been found that in the case of the Brinkman bidisperse model, the Nusselt numbers decrease compared to the Darcy model, and this behaviour is significant in comparison to the Brinkman monodisperse case.Originality/valueA mathematical model for the free convection inside a cavity filled by a non-Darcy bidisperse porous medium, based on the Brinkman equation, is used. The effect of Darcy number, Rayleigh number, modified inter-phase heat transfer parameter, modified thermal conductivity ratio and the inertial parameters is studied. To the best of the authors’ knowledge, this problem has not been studied before, and the results are new and original.

Mathematical modeling of unsteady convective flow analysis of water and nano-encapsulated phase change particles in composite enclosure subject to rotation

Free convection heat transfer in water and hybrid particles in an enclosure is studied. A layer of porous material with various thickness and permeability is attached to the enclosure. Both fluid and porous layers rotate with a specific speed. Hybrid particles are formed by a polyurethane (PU) and an N-nonadecane (ND). PU acts as shell and ND goes through a phase change and it capables of preserving and releasing a considerable amount of latent heat. The enclosure movement can be controlled through a rotation speed. The Brinkman-Forchheimer extended Darcy model is used for governing the flow within a fully saturated porous layer. The governing equations for the convective flow and phase change heat transfer, including specific heat capacity and permeability, were introduced and solved by FEM. The impact of the porous thickness, permeability, fusion temperature and rotation speed on the heat capacity ratio, streamline and isotherms structures were investigated. The results showed that a high Darcy number and thin porous thickness were a good candidate for the improvement of average heat transfer rate since reinforcing the melting process and heat transmitting.

Heat Transfer and Performance Enhancement of Porous Split Elliptical Fins

To augment the heat transfer phenomenon, the infusion of various fin geometry over the heated plate is being investigated by various researchers. Solid fins of the porous medium can enhance the convective heat transfer, providing a higher surface area-to-volume ratio for heat transfer. In this work, the fluid flow pattern and thermodynamic analysis of porous-based split elliptical fins mounted staggered over a heated base plate is numerically studied with the Reynolds numbers in the range of 783 to 1839, which is dependent on the fin dimension. The variable parameters were dimensionless transverse offset ( TO ∗ = transverse offset / diameter ), which varied from 0 to 0.5; dimensionless longitudinal offset ( L O ∗ = longitudinal offset / diameter ), which varied from 0 to 0.25; porosity (ɸ), which varies from 0.8 to 0.92; pores per inch (PPI), which was 10; permeability ( P n ); and inertial parameter ( F ). To count the viscous and inertial effect inside the porous zone, the Forchheimer–Brinkman extended Darcy model was adopted. The associated parameters, the Nusselt number (Nu), frictional coefficient ( C f ), and performance evaluation criteria (PEC), are thoroughly analyzed over the TO ∗ and LO ∗ combination. The results of the investigation revealed that the highest value of Nu and PEC was obtained by TO ∗ = 0.5 and L O ∗ = 0 at ɸ = 0.92 , which were approximately 54% and 79% higher than the solid circular fin at Re = 1839 . Additionally, a response function based on Nu was obtained using the response surface method, and cuckoo optimization was assessed to identify the optimal Nu. The optimal Nu is established at TO ∗ = 0.4141 and L O ∗ = 0 ( ɸ = 0.92 and Re = 1839 ) and was validated with the present investigation with an accuracy of 1.20%.

A novel mathematical model of MHD boundary layer flow of an activated micropolar nanofluid over a stretching surface under the effect of electro-osmosis forces

The major objective of this research is to create a novel mathematical model for the flow of an electro-osmotic boundary layer in a micropolar Williamson nanofluid. This development is achieved by considering the influence of electro-osmotic force on an incompressible micropolar Williamson nanofluid through a Darcian flow (Darcy model) when combined with a binary chemical reaction and the energy of activation over a linearly stretching sheet. The constituent parts of the energy equation include heat radiation, thermal and mass transport, along with joule-based heating and dissipation of viscous fluids. The problem is computationally analyzed using an equation set of nonlinear partial differential equations (PDEs), which are then similarly converted into a system of ordinary differentiation equations (ODEs). The obtained ODEs system is solved numerically using the built-in command (Parametric ND Solve) via MATHEMATICA software. A series of figures are used to demonstrate numerically and graphically the influence of physical characteristics on the fluid behavior. The behavior of flow is obtained by studying the streamlines around the plate in contour and three-dimensional form. In the case of non-Newtonian fluid, the results indicated that the boundary layer velocity is slower compared with the Newtonian fluid case. It is also mentioned that the graphic representation of the results shows that increasing the radiation parameter enhances thermal distribution, which means that the rate of heat transfer improved. The main findings revealed that the upward trend in the Williamson number diminishes the nanofluid flow while enhancing the skin friction coefficient. Also, it is discovered that as [Formula: see text] rises, the fluid’s velocity distributions in the boundary layer rise. Consequently, this type of research’s significance stems from its potential uses in biomedical engineering since it could be used to dewater liquids and solids from infected human tissues.

Variational Data Assimilation and its Decoupled Iterative Numerical Algorithms for Stokes–Darcy Model

Variational Data Assimilation and its Decoupled Iterative Numerical Algorithms for Stokes–Darcy Model

Impact of titling angle and density extremum on transient convection in a porous chamber with sinusoidal heating

The aim of the present study is to investigate numerically the 2D unsteady transient convection of cold water near its highest density value in an inclined square porous enclosed space. The horizontal walls are kept in adiabatic condition. The temperature of left sidewall varies in sinusoidal manner whereas the opposing right sidewall is sustained with constant lower temperature. The range of angle of inclination is considered from 0° to 90°. The finite volume method (FVM) was applied to portray all mathematical equations. The special outcome of inclination angle, Darcy number, maximum density parameter and porosity are obtained in the present study with the use of Brinkmann–Forchheimer extended Darcy model. The change in the angle of inclination is noteworthy in the structure and direction of the flow of the fluid. The bicellular structure of the fluid is identified because of the density inversion effect. Increasing Darcy number and porosity values enhance the average rate of energy transport across the chamber. The lowest heat transfer is noticed for due to supreme density effect. Here the energy transfer from one cell to another cell is by conduction mode due to the existence of dual cell structure.

Thermal performance of stretching/shrinking fully wet porous cylindrical and conical pin fin structures by differential transformation approach

In this paper, the thermal behavior of cylindrical and conical pin fin structures operating in a convective–radiative environment has been examined. The fully wet porous fin structures are assumed to be mounted with a stretching/shrinking mechanism similar to a conveyer belt. The conical pin fin has been comparatively analyzed with the cylindrical one for three distinct cases of stretching, stagnant, and shrinking. Further, the Darcy model has been employed to analyze the fluid–solid interactions. The differential transformation method (DTM) has been used to solve the resulting second-order nonlinear ordinary differential equations. On the thermal performance of conical and cylindrical pin fin structures, the effects of the stretching/shrinking parameter, Peclet number, wet porous parameter, convective parameter, and radiative parameter have been established graphically. The conical pin fin is found to aid the heat transmission process better than the cylindrical one. The work is also helpful in the realm of microelectronics, particularly in the development of micro-pin-fin structures.

Ensemble Domain Decomposition Algorithm for the Fully Mixed Random Stokes–Darcy Model with the Beavers–Joseph Interface Conditions

In this paper, an efficient ensemble domain decomposition algorithm is proposed for fast solving the fully mixed random Stokes–Darcy model with the physically realistic Beavers–Joseph interface conditions. We utilize the Monte Carlo method for the coupled model with random inputs to derive some deterministic Stokes–Darcy numerical models and use the idea of the ensemble to realize the fast computation of multiple problems. One remarkable feature of the algorithm is that multiple linear systems share a common coefficient matrix in each deterministic numerical model, which significantly reduces the computational cost and achieves comparable accuracy with the traditional methods. Moreover, by domain decomposition, we can decouple the Stokes–Darcy system into two smaller subphysics problems naturally. Both mesh-dependent and mesh-independent convergence rates of the algorithm are rigorously derived by choosing suitable Robin parameters. Optimized Robin parameters are derived and analyzed to accelerate the convergence of the proposed algorithm. Especially, for small hydraulic conductivity in practice, the almost optimal geometric convergence can be obtained by finite element discretization. Finally, two groups of numerical experiments are conducted to validate the exclusive features of the proposed algorithm.