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Purpose: Accurately evaluating fluid flow behaviors and determining permeability for deforming porous media is time-consuming and remains challenging. This paper aims to propose a novel machine-learning method for the rapid estimation of permeability of porous media at different deformation stages constrained by hydro-mechanical coupling analysis. Design/methodology/approach: A convolutional neural network (CNN) is proposed in this paper, which is guided by the results of finite element coupling analysis of equilibrium equation for mechanical deformation and Boltzmann equation for fluid dynamics during the hydro-mechanical coupling process [denoted as Finite element lattice Boltzmann model (FELBM) in this paper]. The FELBM ensures the Lattice Boltzmann analysis of coupled fluid flow with an unstructured mesh, which varies with the corresponding nodal displacement resulting from mechanical deformation. It provides reliable label data for permeability estimation at different stages using CNN. Findings: The proposed CNN can rapidly and accurately estimate the permeability of deformable porous media, significantly reducing processing time. The application studies demonstrate high accuracy in predicting the permeability of deformable porous media for both the test and validation sets. The corresponding correlation coefficients (R2) is 0.93 for the validation set, and the R2 for the test set A and test set B are 0.93 and 0.94, respectively. Originality/value: This study proposes an innovative approach with the CNN to rapidly estimate permeability in porous media under dynamic deformations, guided by FELBM coupling analysis. The fast and accurate performance of CNN underscores its promising potential for future applications. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to showcase the utilization of the magnetohydrodynamics-microrotating Casson's nanofluid flow model (MHD-MRCNFM) in examining the impact of an inclined magnetic field within a porous medium on a nonlinear stretching plate. This investigation is conducted by using neural networking techniques, specifically using neural networks-backpropagated with the Levenberg–Marquardt scheme (NN-BLMS). Design/methodology/approach: The initial nonlinear coupled PDEs system that represented the MRCNFM is transformed into an analogous nonlinear ODEs system by the adoption of similarity variables. The reference data set is created by varying important MHD-MRCNFM parameters using the renowned Lobatto IIIA solver. The numerical reference data are used in validation, testing and training sets to locate and analyze the estimated outcome of the created NN-LMA and its comparison with the corresponding reference solution. With mean squared error curves, error histogram analysis and a regression index, better performance is consistently demonstrated. Mu is a controller that controls the complete training process, and the NN-BLMS mainly concentrates on the higher precision of nonlinear systems. Findings: The peculiar behavior of the appropriate physical parameters on nondimensional shapes is demonstrated and explored via sketches and tables. For escalating amounts of inclination angle and Brinkman number, a viable entropy profile is accomplished. The angular velocity curve grows as the rotation viscosity and surface condition factors rise. The dominance of friction-induced irreversibility is observed in the vicinity of the sheet, whereas in the farthest region, the situation is reversed with heat transfer playing a more significant role in causing irreversibilities. Originality/value: To improve the efficiency of any thermodynamic system, it is essential to identify and track the sources of irreversible heat losses. Therefore, the authors analyze both flow phenomena and heat transport, with a particular focus on evaluating the generation of entropy within the system. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to investigate the hydrodynamic instability properties of a mixed convection flow of nanofluid in a porous channel. Design/methodology/approach: The treated single-phase nanofluid is a suspension consisting of water as the working fluid and alumina as a nanoparticle. The anisotropy of the porous medium and the effects of the inclination of the magnetic field are highlighted. The effects of viscous dissipation and thermal radiation are incorporated into the energy equation. The eigenvalue equation system resulting from the stability analysis is processed numerically by the spectral collocation method. Findings: Analysis of the results in terms of growth rate reveals that increasing the volume fraction of nanoparticles increases the critical Reynolds number. Parameters such as the mechanical anisotropy parameter and Richardson number have a destabilizing effect. The Hartmann number, permeability parameter, magnetic field inclination, Prandtl number, wave number and thermal radiation parameter showed a stabilizing effect. The Eckert number has a negligible effect on the growth rate of the disturbances. Originality/value: Linear stability analysis of Magnetohydrodynamics (MHD) mixed convection flow of a radiating nanofluid in porous channel in presence of viscous dissipation. [ABSTRACT FROM AUTHOR]

Purpose: Natural gas leak from underground pipelines could lead to serious damage and global warming, whose spreading in soil should be systematically investigated. This paper aims to propose a three-dimensional numerical model to analyze the methane–air transportation in soil. The results could help understand the diffusion process of natural gas in soil, which is essential for locating leak source and reducing damage after leak accident. Design/methodology/approach: A numerical model using finite element method is proposed to simulate the methane spreading process in porous media after leaking from an underground pipe. Physical models, including fluids transportation in porous media, water evaporation and heat transfer, are taken into account. The numerical results are compared with experimental data to validate the reliability of the simulation model. The effects of methane leaking direction, non-uniform soil porosity, leaking pressure and convective mass transfer coefficient on ground surface are analyzed. Findings: The methane mole fraction distribution in soil is significantly affected by the leaking direction. Horizontally and vertically non-uniform soil porosity has a stronger effect. Increasing leaking pressure causes increasing methane mole flux and flow rate on the ground surface. Originality/value: Most existing gas diffusion models in porous media are for one- or two-dimensional simulation, which is not enough for predicting three-dimensional diffusion process after natural gas leak in soil. The heat transfer between gas and soil was also neglected by most researchers, which is very important for predicting the gas-spreading process affected by the soil moisture variation because of water evaporation. In this paper, a three-dimensional numerical model is proposed to further analyze the methane–air transportation in soil using finite element method, with the presence of water evaporation and heat transfer in soil. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to develop a coupled lattice Boltzmann model for the simulation of the freezing process in unsaturated porous media. Design/methodology/approach: In the developed model, the porous structure with complexity and disorder was generated by using a stochastic growth method, and then the Shan-Chen multiphase model and enthalpy-based phase change model were coupled by introducing a freezing interface force to describe the variation of phase interface. The pore size of porous media in freezing process was considered as an influential factor to phase transition temperature, and the variation of the interfacial force formed with phase change on the interface was described. Findings: The larger porosity (0.2 and 0.8) will enlarge the unfrozen area from 42 mm to 70 mm, and the rest space of porous medium was occupied by the solid particles. The larger specific surface area (0.168 and 0.315) has a more fluctuated volume fraction distribution. Originality/value: The concept of interfacial force was first introduced in the solid–liquid phase transition to describe the freezing process of frozen soil, enabling the formulation of a distribution equation based on enthalpy to depict the changes in the water film. The increased interfacial force serves to diminish ice formation and effectively absorb air during the freezing process. A greater surface area enhances the ability to counteract liquid migration. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to explore the double diffusive magneto-hydrodynamic (MHD) squeezed flow of (Cu–water) nanofluid between two analogous plates filled with Darcy porous material in existence of chemical reaction and external magnetic field. Design/methodology/approach: The governing nonlinear equations are transformed into ordinary differential equations by means of similarity transforms, and the coupled mass and heat transference equations are resolved analytically with the application of differential transform method (DTM). The effects of different relevant parameters on velocity, temperature and concentration, including the squeeze number, magnetic parameter, Biot number, Darcy number and chemical reaction parameter, are illustrated with figures. In addition, for various parameters, the local skin friction coefficient, local Nusselt number and local Sherwood number are computed and are graphically displayed. Findings: It is observed that the squeeze number has a direct relationship with Sherwood number and an inverse relationship with skin friction as Biot number increases. With enhanced Biot numbers, the temperature value increases during both squeeze and non-squeeze moments, but the temperature values are higher for squeeze moments compared to the other case. Practical implications: This research has potential applications in various large-scale enterprises that might benefit from increased productivity. Social implications: The results are useful to thermal science community. Originality/value: Unique and valuable insights are provided by studying the impact of chemical reaction on double diffusive MHD squeezing copper–water nanofluid flow between parallel plates filled with porous medium. In addition, this research has potential applications in various large-scale enterprises that might benefit from increased productivity. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to present a numerical study that investigates the flow of MgO-Al2O3/water hybrid nanofluid inside a porous elliptical-shaped cavity, in which we aim to examine the performance of this thermal system when exposed to a magnetic field via heat transfer features and entropy generation. Design/methodology/approach: The configuration consists of the hybrid nanofluid out layered by a cold ellipse while it surrounds a non-square heated obstacle; the thermal structure is under the influence of a horizontal magnetic field. This problem is implemented in COMSOL multiphysics, which solves the related equations described by the "Darcy-Forchheimer-Brinkman" model through the finite element method. Findings: The results illustrated as streamlines, isotherms and average Nusselt number, along with the entropy production, are given as functions of: the volume fraction, and shape factor to assess the behaviour of the properties of the nanoparticles. Darcy number and porosity to designate the impact of the porous features of the enclosure, and finally the strength of the magnetic induction described as Hartmann number. The outcomes show the increased pattern of the thermal and dynamical behaviour of the hybrid nanofluid when augmenting the concentration, shape factor, porosity and Darcy number; however, it also engenders increased formations of irreversibilities in the system that were revealed to enhance with the permeability and the great properties of the nanofluid. Nevertheless, this thermal enhanced pattern is shown to degrade with strong Hartmann values, which also reduced both thermal and viscous entropies. Therefore, it is advised to minimize the magnetic influence to promote better heat exchange. Originality/value: The investigation of irreversibilities in nanofluids heat transfer is an important topic of research with practical implications for the design and optimization of heat transfer systems. The study's findings can help improve the performance and efficiency of these systems, as well as contribute to the development of sustainable energy technologies. The study also offers an intriguing approach that evaluates entropy growth in this unusual configuration with several parameters, which has the potential to transform our understanding of complicated fluid dynamics and thermodynamic processes, and at the end obtain the best thermal configuration possible. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to review previous research studies on mathematical models for entropy generation in the magnetohydrodynamics (MHD) flow of nanofluids. In addition, the influence of various parameters on the velocity profiles, temperature profiles and entropy generation was studied. Furthermore, the numerical methods used to solve the model equations were summarized. The underlying purpose was to understand the research gap and develop a research agenda. Design/methodology/approach: This paper reviews 141 journal articles published between 2010 and 2022 on topics related to mathematical models used to assess the impacts of various parameters on the entropy generation, heat transfer and velocity of the MHD flow of nanofluids. Findings: This review clarifies the application of entropy generation mathematical models, identifies areas for future research and provides necessary information for future research in the development of efficient thermodynamic systems. It is hoped that this review paper can provide a basis for further research on the irreversibility of nanofluids flowing through different channels in the development of efficient thermodynamic systems. Originality/value: Entropy generation analysis and minimization constitute effective approaches for improving the performance of thermodynamic systems. A comprehensive review of the effects of various parameters on entropy generation was performed in this study. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to study the magneto-radiative gas (water vapor) on an unsmooth boundary. Design/methodology/approach: This paper provided a numerical treatment via the implicit Chebyshev pseudo-spectral method to investigate unsteady compressible magneto-radiative gas (water vapor Pr = 1) flow near a heated vertical wavy wall through porous medium in the presence of inclined magnetic field. The impacts of viscous dissipation, temperature-dependent fluid properties, thermal conductivity and viscosity in the presence of nonlinear thermal radiation are studied. The sinusoidal surface is transformed into a flat one using a suitable transformation. The comparison figures of published data with the present outcomes illustrate a good match. The present steady-state outcomes are presented for the temperature, velocity, Nusselt number and the shearing stress through figures for several interested physical parameters, namely, compressibility, magnetic, radiation, viscosity–temperature variation, thermal conductivity–temperature variation, surface sinusoidal waveform and porous parameters. Findings: The present numerical outcomes confirm the importance of applying nonlinear thermal radiation cases in all studies that investigate heat transfer under the influence of thermal radiation. Originality/value: A mathematical model is established for a wavy boundary, and Chebyshev pseudo-spectral method is adopted for the numerical study. [ABSTRACT FROM AUTHOR]

The publishers of the International Journal of Numerical Methods for Heat and Fluid Flow have retracted an article titled "Simulation of water/FMWCNT nanofluid forced convection in a microchannel filled with porous material under slip velocity and temperature jump boundary conditions." An internal investigation revealed that the peer review process was compromised, and as a result, the findings of the article cannot be trusted. The authors of the paper disagree with this decision, and the publishers apologize to the readers. The retracted article can still be accessed through the provided link. [Extracted from the article]

Purpose: The purpose of this paper is to investigate the effects of Ha and the Nanoparticles (NP) volume fraction over the irreversibility and heat transport in Darcy–Forchheimer nanofluid saturated lid-driven porous medium. Design/methodology/approach: The present paper highlights entropy generation because of mixed convection for a lid-driven porous enclosure filled through a nanoliquid and submitted to a uniform magnetic field. The analysis is achieved using Darcy–Brinkman–Forchheimer technique. The set of partial differential equations governing the considered system was numerically solved using the finite element method. Findings: The main observations are as follows. The results indicate that the movement of horizontal wall is an important factor for the entropy generation inside the porous cavity filled through Cu–water nanoliquid. The variation of the thermal entropy generation is linear through NPs volume fraction. The total entropy generation reduces when the Darcy, Hartmann and the nanoparticle volume fraction increase. The porous media and magnetic field effects reduce the total entropy generation. Practical implications: Interest in studying thermal interactions by convective flow within a saturating porous medium has many fundamental considerations and has received extensive consideration in the literature because of its usefulness in a large variety of engineering applications, such as the energy storage and solar collectors, crystal growth, food processing, nuclear reactors and cooling of electronic devices, etc. Originality/value: By examining the literature, the authors found that little attention has been paid to entropy generation encountered during convection of nanofluids. Hence, this work aims to numerically study entropy generation and heat transport in a lid-driven porous enclosure filled with a nanoliquid. [ABSTRACT FROM AUTHOR]

Purpose: The classical advection-dispersion equation (ADE) model cannot accurately depict the gas transport process in natural geological formations. This paper aims to study the behavior of CO2 transport in fractal porous media by using an effective Hausdorff fractal derivative advection-dispersion equation (HFDADE) model. Design/methodology/approach: Anomalous dispersion behaviors of CO2 transport are effectively characterized by the investigation of time and space Hausdorff derivatives on non-Euclidean fractal metrics. The numerical simulation has been performed with different Hausdorff fractal dimensions to reveal characteristics of the developed fractal ADE in fractal porous media. Numerical experiments focus on the influence of the time and space fractal dimensions on flow velocity and dispersion coefficient. Findings: The physical mechanisms of parameters in the Hausdorff fractal derivative model are analyzed clearly. Numerical results demonstrate that the proposed model can well fit the history of gas production data and it can be a powerful technique for depicting the early arrival and long-tailed phenomenon by incorporating a fractal dimension. Originality/value: To the best of the authors' knowledge, first time these results are presented. [ABSTRACT FROM AUTHOR]

Purpose Analytical methods are widely used in heat and fluid flow; the purpose of this paper is to couple Taylor series method and Bubbfil algorithm to solve nonlinear differential equations.Design/methodology/approach A series solution is obtained with some unknown constants, which can be determined by incorporating boundary conditions, and the constants are calculated by the Bubbfil algorithm.Findings This paper gives an analytical approach to a nonlinear equation arising in porous catalyst using Taylor series and Bubbfil algorithm, and a high accuracy can be achieved.Research limitations/implications The coupled method of Taylor series and Bubbfil algorithm is a powerful method for nonlinear differential equations.Practical implications The proposed technology can be used in various numerical methods.Originality/value A new analytical method is proposed based on Taylor series and Bubbfil algorithm, which is a development of Newton’s iteration method and an ancient Chinese algorithm. The solution process is simple and easy to follow. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to solve the local problem involving strong contrast heterogeneous conductive material, with application to gas-filled porous media with both perfect and imperfect Kapitza boundary conditions at the bi-material interface. The effective parameters like the dynamic conductivity and the thermal permeability in the acoustics of porous media are also derived from the cell solution. Design/methodology/approach: The Fourier transform method is used to solve frequency-dependent heat transfer problems. The periodic Lippmann–Schwinger integral equation in Fourier space with source term is first formulated using discrete Green operators and modified wavevectors, which can then be solved by iteration schemes. Findings: Numerical examples show that the schemes converge fast and yield accurate results when compared with analytical solution for benchmark problems. Originality/value: The formulation of the method is constructed using static and dynamic Green operators and can be applied to pixelized microstructure issued from tomography images. [ABSTRACT FROM AUTHOR]

Purpose: A combination of highly conductive porous media and nanofluids is an efficient way for improving thermal performance of relevant applications. For precisely predicting the flow and thermal transport of nanofluids in porous media, the purpose of this paper is to explore the inter-phase coupling numerical methods. Design/methodology/approach: Based on the lattice Boltzmann (LB) method, this study combines the convective flow, non-equilibrium thermal transport and phase interactions of nanofluids in porous matrix and proposes a new multi-phase LB model. The micro-scale momentum and heat interactions are especially analyzed for nanoparticles, base fluid and solid matrix. A set of three-phase LB equations for the flow/thermal coupling of base fluid, nanoparticles and solid matrix is established. Findings: Distributions of nanoparticles, velocities for nanoparticles and the base fluid, temperatures for three phases and interaction forces are analyzed in detail. Influences of parameters on the nanofluid convection in the porous matrix are examined. Thermal resistance of nanofluid convective transport in porous structures are comprehensively discussed with the models of multi-phases. Results show that the Rayleigh number and the Darcy number have significant influences on the convective characteristics. The result with the three-phase model is mildly larger than that with the local thermal non-equilibrium model. Originality/value: This paper first creates the multi-phase theoretical model for the complex coupling process of nanofluids in porous structures, which is useful for researchers and technicians in fields of thermal science and computational fluid dynamics. [ABSTRACT FROM AUTHOR]