Convection In Porous Medium Research Articles

A study on the combined effects of variable viscosity and thermal conductivity on forced convection in bidisperse porous medium

This research focuses on exploring the flow and temperature distribution of forced convection in a channel of horizontally placed parallel plate under the existence of a bidisperse porous medium (BDPM) emphasizing the consequences of viscous dissipation. The temperature-dependent thermal conductivity and viscosity are considered while maintaining the momentum slip and constant wall temperature at the channel walls. Analysis of the dynamics of fluid flow and the temperature distributions in both the fluid and solid phases is conducted by following the two-velocity and two-temperature models in this work. The model governing equations are non-dimensionalized following the relevant dimensionless parameters and the study calculates the temperature and velocity profiles for each phase using the Homotopy Analysis Method (HAM). The obtained temperature and velocity are discussed and explained with the help of graphs. Certain fluids exhibit varying behaviors at different temperatures. Therefore, it is crucial to consider the temperature-dependent physical properties of the fluid for specific applications. This highlights the importance of implementing temperature-dependent physical properties in the analysis. Throughout the investigation, it is discovered that the viscosity parameter has a greater influence on velocity as compared to temperature, the same for thermal conductivity on temperature. The impact of physical parameters including skin friction, volume flow rate, and Nusselt number on both plates are also examined in this study. The findings are discussed, and tables displaying numerical values for various physical characteristics are provided for both the liquid and solid phases. The results obtained were also compared with existing literature, revealing a strong alignment between them.

Transport scaling in porous media convection

We present a theory to describe the Nusselt number, $\operatorname {\mathit {Nu}}$ , corresponding to the heat or mass flux, as a function of the Rayleigh–Darcy number, $\operatorname {\mathit {Ra}}$ , the ratio of buoyant driving force over diffusive dissipation, in convective porous media flows. First, we derive exact relationships within the system for the kinetic energy and the thermal dissipation rate. Second, by segregating the thermal dissipation rate into contributions from the boundary layer and the bulk, which is inspired by the ideas of the Grossmann and Lohse theory (J. Fluid Mech., vol. 407, 2000; Phys. Rev. Lett., vol. 86, 2001), we derive the scaling relation for $\operatorname {\mathit {Nu}}$ as a function of $\operatorname {\mathit {Ra}}$ and provide a robust theoretical explanation for the empirical relations proposed in previous studies. Specifically, by incorporating the length scale of the flow structure into the theory, we demonstrate why heat or mass transport differs between two-dimensional and three-dimensional porous media convection. Our model is in excellent agreement with the data obtained from numerical simulations, affirming its validity and predictive capabilities.

REV-Scale study of miscible density-driven convection in porous media

Miscible density-driven convection in porous media has important implications for the long-term security of geological CO2 sequestration. In this study, a REV-scale lattice Boltzmann equation method based on the generalized Navier–Stokes equations was used to simulate density-driven convection in porous media, Thus, the effects of the Rayleigh number, the Darcy number, the Schmidt number, and the porosity of porous media can be discussed separately. The results show that density-driven convection only occurs when the Rayleigh–Darcy–Schmidt number RaD-S exceeds 102. The larger the Ra, the more disordered the concentration field, the earlier the convective phenomenon begins, and the more significant the convective mixing; The larger the Da, the finer the generated fingers. These findings provide important insights for the development of geological sequestration technologies.

Study of double-diffusive gravity modulated biothermal convection in porous media under internal heating effect

Study of double-diffusive gravity modulated biothermal convection in porous media under internal heating effect

Linear and weakly nonlinear analyses of double‐diffusive convection in porous media with chemical reaction using LTNE model

AbstractThe onset of convection in a horizontal porous layer with chemical reaction and local thermal nonequilibrium is investigated. The nondimensional governing equations have been solved using the normal mode technique, which results in an eigenvalue problem. The analytical expressions for both stationary and oscillatory Rayleigh numbers are obtained. The effect of different parameters has been investigated and presented. The amplitude equation is derived using weakly nonlinear theory. Nusselt number is calculated using an amplitude equation to investigate heat transport. When modeling a fluid‐saturated porous medium, previous research on double‐diffusive convection has uniformly operated under the assumption of local thermal equilibrium (LTE) between the fluid and solid phases at all points within the medium. This standard practice assumes a minimal temperature gradient between the phases at any given location. However, in practical scenarios involving high‐speed flows or significant temperature differentials between the fluid and solid phases, the LTE assumption proves insufficient.

Density-Driven CO2 Dissolution in Depleted Gas Reservoirs with Bottom Aquifers

Depleted gas reservoirs with bottom water show significant potential for long-term CO2 storage. The residual gas influences mass-transfer dynamics, further affecting CO2 dissolution and convection in porous media. In this study, we conducted a series of numerical simulations to explore how residual-gas mixtures impact CO2 dissolution trapping. Moreover, we analyzed the CO2 dissolution rate at various stages and delineated the initiation and decline of convection in relation to gas composition, thereby quantifying the influence of residual-gas mixtures. The findings elucidate that the temporal evolution of the Sherwood number observed in the synthetic model incorporating CTZ closely parallels that of the single-phase model, but the order of magnitude is markedly higher. The introduction of CTZ serves to augment gravity-induced convection and expedites the dissolution of CO2, whereas the presence of residual-gas mixtures exerts a deleterious impact on mass transfer. The escalation of residual gas content concomitantly diminishes the partial pressure and solubility of CO2. Consequently, there is an alleviation of the concentration and density differentials between saturated water and fresh water, resulting in the attenuation of the driving force governing CO2 diffusion and convection. This leads to a substantial reduction in the rate of CO2 dissolution, primarily governed by gravity-induced fingering, thereby manifesting as a delay in the onset and decay time of convection, accompanied by a pronounced decrement in the maximum Sherwood number. In the field-scale simulation, the injected CO2 improves the reservoir pressure, further pushing more gas to the producers. However, due to the presence of CH4 in the post-injection process, the capacity for CO2 dissolution is reduced.

Natural Convection in a Spherical Porous Annulus with Diathermal Partition Wall

The influence of the diathermal partition wall on natural convection in a fluid-saturated porous medium has been numerically studied in the present paper. A concentric diathermal wall of infinitesimal thickness is inserted in the fluid-saturated spherical porous annulus. Due to the flow symmetry along the vertical axis, only half of the sphere is considered for simulation. A Successive Accelerated Replacement Scheme has been used to solve the Darcy flow model using the finite difference method. The average Nusselt number value decreases with the presence of a partition wall within the fluid-saturated spherical porous annulus. The percentage decrease in average Nusselt number value depends upon the position of the diathermal wall within the width of the spherical annulus. There is about a 50% reduction in the average Nusselt number with a diathermal partition wall for the cases considered in this work. The results of the present investigation will help in the proper design of porous insulation in spherical porous containers for the storage of thermal energy.

Effects of vibration on natural convection in a square inclined porous enclosure filled with Cu-water nanofluid

PurposeThe purpose of this paper is to investigate the effects of gravitational modulation on natural convection in a square inclined porous cavity filled by a fluid containing copper nanoparticles.Design/methodology/approachThe present study uses a system of equations that couple hydrodynamics to heat transfer, representing the governing equations of fluid flow in a square domain. The Boussinesq–Darcy flow with Cu-water nanofluid is considered. The dimensionless partial differential equations are solved numerically using finite difference method based on alternating direction implicit scheme. The cavity is differentially heated by constant heat flux, while the top and bottom walls are insulated. The authors examined the effects of gravity amplitude (λ), vibration frequency (σ), tilt angle (α) and Rayleigh number (Ra) on flow and temperature.FindingsThe numerical simulations, in the form of streamlines, isotherms, Nusselt number and maximum stream function for different values of amplitude, frequency, tilt angle and Rayleigh number, have revealed an oscillatory behavior in the development of flow and temperature under gravity modulation. An increase of amplitude from 0.5 to 1 intensifies the flow stream (from |ψmax| = 21.415 to |ψmax| = 25.262) and improves heat transfer (from Nu¯ = 17.592 to Nu¯ = 20.421). Low-frequency vibration below 50 has a significant impact on the flow and thermal distributions. However, once this threshold is exceeded, the flow weakens, leading to a gradual decrease in heat transfer rate. The inclination angle is an effective parameter for controlling the flow and temperature characteristics. Thus, transitioning the tilt angle from 30° to 60° can increase the flow velocity (from 22.283 to 23.288) while reducing the Nusselt number (from 16.603 to 13.874). Therefore, by manipulating the combination of vibration and inclination, it is founded that for a fixed frequency value of σ = 100 and for increased amplitude (from 0.5 to 1), the flow intensity at inclination of 60° is boosted, and an increase of the heat transfer rate at inclination of 30° is also observed. Convective thermal instabilities may arise depending on the different key factors.Originality/valueTo the best of the authors’ knowledge, this study is original in its examination of the combined effects of modulated gravity and cavity inclination on free convection in nanofluid porous media. It highlights the crucial roles of these two important factors in influencing flow and heat transfer properties.

Numerical study on natural convection in a saturated non Darcian porous medium under radiation and entropy generation effects

This work focuses on analyzing fluid flow, generation of entropy, and heat transfer during natural convection in a cavity enclosed with a non-Darcian saturated porous medium. The influence of viscous dissipation and thermal radiation are considered. The Lattice Boltzmann method is adopted to simulate the governing equations. The study discusses the general effect of dimensionless parameters on the fluid structure interaction properties, entropy generation and the thermal field. The parameters investigated include the Grashof number, Eckert number, Rayleigh number, Forchheimer Resistance, inverse Darcy, radiation parameter, and Prandtl number. The combination of studying dimensionless parameters on non-Darcian porous medium, along with the consideration of thermal radiation, viscous dissipation, and entropy analysis, has made this research valuable and worth pursuing. The findings reveal that the areas of high entropy generation are primarily located along the walls (vertical) of the cavity. Moreover, it is observed that as the inverse Darcy and Forchheimer resistance increase, their effect on the average Nusselt number diminishes for varying parameters of radiation. As the Prandtl number increases, the isotherms cluster along the walls (vertical) of the porous cavity. With high Grashof values, convection becomes turbulent, and the temperature distribution becomes non-uniform. Additionally, the entropy caused by heat and fluid friction decreases as the Forchheimer resistance increases.

Lattice Boltzmann study on magnetohydrodynamic double-diffusive convection in Fe3O4–H2O nanofluid-filled porous media

Magnetohydrodynamic double-diffusive convection (MHD-DDC) in porous media has substantial significance in broad applications. However, due to the complexity of the DDC problems involving nanofluid, porous media, and external magnetic field at the same time, the MHD-DDC in nanofluid-filled porous media has rarely been studied. Besides, previous research on MHD convection problems usually focuses on magnetic fields or nanofluid effects. Effects of the thermal-to-mass properties, including the buoyancy radio (Br) and Lewis number (Le), on MHD-DDC problems have rarely been studied, seriously limiting the understanding and regulation of heat and mass transfer. Herein, we numerically study heat and mass transfer in the MHD-DDC within a square cavity containing a nanofluid of Fe3O4–H2O and a porous medium using a lattice Boltzmann method. A series of case studies are carried out to investigate the effects of Br, Le, and the medium porosity (ε) on the velocity, temperature, and nanoparticle concentration. Results indicate that Br determines the rotation pattern of the streamline, while Le and ε can be utilized to regulate the intensity of heat and mass exchange. The results of this paper present a quantitative insight into regulating heat and mass transfer patterns in MHD-DDC problems.

Magnetohydrodynamic influence on fractional nanofluid convection in infinite vertical porous media with constant heat flux

This study investigates the complex dynamics governing free convection flow in nanofluids under Magnetohydrodynamics (MHD) within a porous medium along an infinite vertical surface. We specifically focus on scenarios involving constant and uniform heat flux as well as heat sources. The governing equations, incorporating the Boussinesq approximation, continuity, and momentum equations, are formulated and solved using Caputo-Fabrizio derivatives and Laplace transforms. This comprehensive approach integrates the Boussinesq approximation and Caputo-Fabrizio fractional derivatives, while the use of Laplace transforms enables precise analytical solutions. Additionally, our investigation highlights the significant impact of nanometer-sized copper particles on fluid properties, transforming the behavior from Newtonian (water-like) to non-Newtonian. This transformation profoundly affects thermal conductivity and velocity behavior within the system. Overall, this research establishes a robust foundation for future studies and provides a framework for exploring non-Newtonian nanofluid systems in the context of MHD-driven free convection flow.

Asymptotic behaviour for convection with anomalous diffusion

We investigate the fully nonlinear model for convection in a Darcy porous material where the diffusion is of anomalous type as recently proposed by Barletta. The fully nonlinear model is analysed but we allow for variable gravity or penetrative convection effects which result in spatially dependent coefficients. This spatial dependence usually requires numerical solution even in the linearized case. In this work, we demonstrate that regardless of the size of the Rayleigh number, the perturbation solution will decay exponentially in time for the superdiffusion case. In addition, we establish a similar result for convection in a bidisperse porous medium where both macro- and microporosity effects are present. Moreover, we demonstrate a similar result for thermosolutal convection.

Stochastic simulation of magnetically controlled convection in porous media with random porosity via Karhunen-Loève expansion and intrusive polynomial chaos expansion

Understanding and quantifying uncertainty factors are crucial for accurately predicting thermomagnetic convection phenomena. This study presented a mathematical model and algorithm framework for uncertainty analysis of thermomagnetic convection in porous media with random porosity. The proposed method combined Karhunen-Loève expansion and intrusive polynomial chaos expansion to represent the input random parameters and output response, respectively. The Galerkin projection method was employed to decouple the stochastic governing equations of thermomagnetic convection into deterministic governing equations that can be efficiently solved using the finite volume method. By solving the polynomial chaos expansion of the output response and employing the stochastic projection method to solve the associated decoupled governing equations, the temporal evolution and statistical characteristics of the output response were obtained. The study revealed that porosity uncertainty in the porous medium affects the thermomagnetic convection of paramagnetic fluid, exhibiting significant chaos effects. Monte Carlo simulations were performed to validate the accuracy of the proposed approach and demonstrate its computational efficiency compared to traditional Monte Carlo methods. This research provides valuable insights into the uncertainty analysis of thermomagnetic convection and offers a promising methodology for analyzing heat transfer in various porous media applications.

Three-dimensional visualization of Rayleigh–Bénard convection in porous media

Investigating Rayleigh–Bénard convection, its onset, and its effect on mass transfer are crucial for understanding the effective dissolution processes between carbon-dioxide (CO2)-saturated and CO2-free brines in CO2 geological storage. However, most previous investigations on the onset of convection and mass transfer properties were conducted by 2D and 3D numerical simulations. Only a few 3D experimental studies of Rayleigh–Bénard convection were reported. In this study, we proposed a non-destructive experimental approach to visualize the three-dimensional (3D) fingering structure of Rayleigh–Bénard convection using a micro-focused X-ray computed tomography (X-ray CT) scanner. The experimental conditions covered the Rayleigh number (Ra) range between 3400 and 23000, which also includes the Ra value of the actual condition of gas reservoir field. Results show that fingers and coalescence dynamics significantly developed upon increasing Ra. At higher Ra, the finger concentration experienced greater dilution due to the combined effects of unsteady finger motion and enhanced dispersion strength. The maximum finger extension velocity is linearly proportional to Ra. The convective mass flux (Sh) correlated with Ra by a power-law relationship. The findings in this study provide a better understanding of the influence of Ra on mass transport properties and can be used as a reference for developing the convective mass transfer model of Rayleigh–Bénard convection in 3D porous media.

On the modelling of thermal convection in porous media through rate-type equations

AbstractThe paper investigates current models of flows in porous media from the viewpoint of the mixture theory. The constitutive equations are investigated for compressible, viscous, heat-conducting fluids subject to relaxation phenomena. The thermodynamic analysis is performed via the Clausius-Duhem inequality based directly on the peculiar fields of the mixture. The detailed analysis so developed involves the peculiar heat fluxes and stresses per se while the balance equations for energy and entropy of the whole body would involve also diffusion effects. Following the objectivity principle, the constitutive equations for stresses and heat fluxes are taken to be governed by objective rate equations.

A posteriori error analysis of a semi‐augmented finite element method for double‐diffusive natural convection in porous media

AbstractThis paper presents our contribution to the a posteriori error analysis in 2D and 3D of a semi‐augmented mixed‐primal finite element method previously developed by us to numerically solve double‐diffusive natural convection problem in porous media. The model combines Brinkman‐Navier‐Stokes equations for velocity and pressure coupled to a vector advection‐diffusion equation, representing heat and concentration of a certain substance in a viscous fluid within a porous medium. Strain and pseudo‐stress tensors were introduced to establish scheme solvability and provide a priori error estimates using Raviart‐Thomas elements, piecewise polynomials and Lagrange finite elements. In this work, we derive two reliable residual‐based a posteriori error estimators. The first estimator leverages ellipticity properties, Helmholtz decomposition as well as Clément interpolant and Raviart‐Thomas operator properties for showing reliability; efficiency is guaranteed by inverse inequalities and localization strategies. An alternative estimator is also derived and analyzed for reliability without Helmholtz decomposition. Numerical tests are presented to confirm estimator properties and demonstrate adaptive scheme performance.

ANN-based deep collocation method for natural convection in porous media

ANN-based deep collocation method for natural convection in porous media

Modeling transient natural convection in heterogeneous porous media with Convolutional Neural Networks

Convolutional Neural Networks (CNNs) are gaining significant attention in applications related to coupled flow and transfer processes in porous media, especially when dealing with image-like data. In this context, the most important applications are related to surrogate modeling, where data obtained from simulators is used to train a CNN model. CNNs are also used as optimizers for inverse modeling or parameter estimation. For natural convection in porous media, applications of CNNs are scarce and limited to steady-state data. The main goal of this paper is to extend the applications of CNNs to transient data, by developing new CNN models that allow for integrating time-variant images. Thus, we suggest using an Encoder-Decoder CNN (ED-CNN) for surrogate modeling and a 3D-CNN for inverse modeling. Besides surrogate and inverse modeling, we suggest using CNN for time prediction by coupling it with long short-term memory (LSTM). The performances of these suggested approaches are investigated by applying them to the benchmark of natural convection in porous cavity with heterogeneous property fields, and by comparing the suggested approaches to other alternatives such as standard deep neural network (DNN) and 2D-CNN trained on steady-state data. The results show that, for surrogate modeling, with the same amount of data and equivalent training times, ED-CNN is more practical than DNN because it provides spatially distributed prediction while DNN is limited to local data. The transient data allows for improving the performance of CNN in inverse modeling because it provides more information about heat transfer across the different material zones and thus heterogeneity. The 3D-CNN approach is more efficient than 2D-CNN as it allows for considering the time progress in the training. For instance, the error with 3D-CNN and transient data is about 11 %, while it is about 18 % with 2D-CNN. Coupling CNN with LSTM allows for improving the performance of CNN in time series prediction.

Effects of rotation and temperature‐dependent viscosity on thermal convection in Oldroydian fluid saturating porous media: A modified stability analysis

AbstractThe onset of thermal convection in an incompressible Oldroydian fluid‐saturating porous media is examined to study the combined impact of uniform rotation and temperature‐dependent viscosity. A characteristic equation from the basic hydrodynamic equations governing the Brinkman–Oldroyd model is derived using linear stability theory and modified Boussinesq approximation. For various combinations of stress‐free and slip‐free boundaries, the expressions for the Darcy–Rayleigh numbers for both non‐oscillatory as well as oscillatory convection with linear and exponential temperature‐dependent viscosity are derived, using the “weighted residual method.” The effects of rotation, variable viscosity parameter, strain retardation and stress relaxation time parameters and other fluid parameters on non‐oscillatory and oscillatory convection are investigated numerically and the results are presented graphically. From the analysis, it is found that overstability is the preferred mode of onset of convection. The rotation, the coefficient of specific heat variations (due to temperature variation), and the strain retardation time have a stabilizing influence on the stability of the system, whereas the stress relaxation imparts a destabilizing effect. Additionally, it is noticed that the variable viscosity parameter and Brinkman‐Darcy number stabilize the system for each set of boundary conditions.

Lattice Boltzmann Simulations of Non-Homogeneous Li–O2 Battery Cathode: The Effect of Spatial and Temporal Porosity Variations

Abstract The porosity of the cathode in a lithium–oxygen battery is a crucial parameter that influences oxygen transport and active surface area availability. This study explores various cathode models with different initial porosity distributions and analyzes the porosity evolution during discharge. The objective is to maximize the active surface area utilization of the cathode and increase the battery’s discharge capacity. The simulations employ a recently developed lattice Boltzmann method (LBM) model proposed by Chen et al. (2017, “Simulation of Double Diffusive Convection in Fluid-Saturated Porous Media by Lattice Boltzmann Method,” Int. J. Heat Mass Transfer, 108, pp. 1501–1510), which is capable of handling spatial and temporal variations in diffusion coefficient values. The results demonstrate that a hierarchical porous cathode provides a better specific capacity than a uniform porous cathode with the same average initial porosity. The specific capacity increases as the magnitude of initial porosity variation in the domain increases. Furthermore, incorporating oxygen channels improves oxygen transport in the cathode and offers a better specific capacity than the hierarchical porous cathode. A combination of hierarchical porous media and oxygen channels delivers the best specific capacity among all the other cathode models, as it efficiently balances oxygen transport and active surface area.