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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.

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.

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.

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.

The purpose of this paper is to develop a coupled lattice Boltzmann model for the simulation of the freezing process in unsaturated porous media.

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.

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.

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.

The purpose of this article is to present a mathematical model for the fully developed flow of Bi-viscous Bingham nanofluid through a uniform-width anisotropic porous channel. The model incorporates a generalized Brinkman-Darcy formulation for the porous layers while considering the motion of nanoparticles influenced by both Brownian diffusion and thermophoresis effects.

The similarity transformations derived through Lie group analysis are used to reduce the system from nonlinear partial differential equations to nonlinear ordinary differential equations. The finite difference method-based numerical routine bvp4c is employed to collect and graphically present the outcomes for velocity, temperature, and nanoparticle concentration profiles. The flow pattern is analyzed through streamlined plots. Furthermore, skin friction, heat, and mass transmission rates are investigated and presented via line plots.

It is observed that in anisotropic porous media, the temperature profile is stronger than in isotropic porous media. The thermal anisotropic parameter enhances the concentration profile while reducing the temperature.

Anisotropy arises in various industrial and natural systems due to factors such as preferred orientation or asymmetric geometry of fibers or grains. Hence, this study has applications in oil extraction processes, certain fibrous and biological materials, geological formations, and dendritic zones formed during the solidification of binary alloys.

1. The permeability and thermal conductivity are not constant; instead, they have different values in the x and y directions. 2. This study considers the dependency of thermophoresis on nanoparticle volume fraction and Brownian diffusion on the temperature in both the fluid flow equations and boundary conditions. 3. A novel similarity transformation is derived using Lie group analysis instead of using an existing transformation already available in the literature.

The purpose of this paper is to investigate computationally the hydrothermal characteristics for forced convective laminar flow of water through a channel with a top wavy wall and a flat bottom wall having metallic porous blocks.

The governing equations are solved computationally using a finite element method–based numerical solver COMSOL Multiphysics® for the following range of parameters: 10 ≤ Reynolds number (Re) ≤ 500 and 10^–4 ≤ Darcy number (Da) ≤ 10^–1.

The presence of porous blocks significantly influences the heat transfer rate, and the value of local Nusselt number increases with the increase in Da. The value of the average Nusselt number decreases with Da for the top wall and the same is enhanced for the bottom wall of the wavy channel with porous blocks (WCPB). The value of the average Nusselt number for WCPB is significantly higher than that of the wavy channel without porous block (WCWPB), plane channel without porous block (PCWPB) and plane channel with the porous block (PCPB) at higher Re. For PCPB, the performance factor (PF) is always higher than that of WCWPB and WCPB for Da = 10^–4 and Da = 10^–3. Also, PF for WCPB is higher than that of WCWPB for higher Re except for Da = 10^–4. Further, the value of for WCPB is higher than that of PCPB at Da = 10^–2 and 10^–1 at Re = 500.

The current study is useful in designing efficient heat exchangers for process plants, solar collectors and aerospace applications.

The analysis of thermo-hydraulic characteristics for laminar flow through a channel with a top wavy wall and a flat bottom wall having metallic porous blocks have been analyzed for the first time. Further, a comparative assessment of the performance has been performed with a wavy channel without a porous block, a plane channel without a porous block and a plane channel with porous blocks.

The purpose of the paper is to conduct a numerical and experimental investigation into the properties of nanofluids containing spherical nanoparticles of random sizes flowing through a porous medium. The study aims to understand how the thermophysical properties of the nanofluid are affected by factors such as nanoparticle volume fraction, permeability of the porous medium, and pore size. The paper provides insights into the behavior of nanofluids in complex environments and explores the impact of varying conditions on key properties such as thermal conductivity, density, viscosity, and specific heat. Ultimately, the research contributes to the broader understanding of nanofluid dynamics and has potential implications for engineering and industrial applications in porous media.

This paper investigates nanofluids with spherical nanoparticles in a porous medium, exploring thermal conductivity, density, specific heat, and dynamic viscosity. Studying three compositions, the analysis employs the classical Maxwell model and Koo and Kleinstreuer’s approach for thermal conductivity, considering particle shape and temperature effects. Density and specific heat are defined based on mass and volume ratios. Dynamic viscosity models, including Brinkman’s and Gherasim et al.'s, are discussed. Numerical simulations, implemented in Python using the Langevin model, yield results processed in Origin Pro. This research enhances understanding of nanofluid behavior, contributing valuable insights to porous media applications.

This study involves a numerical examination of nanofluid properties, featuring spherical nanoparticles of varying sizes suspended in a base fluid with known density, flowing through a porous medium. Experimental findings reveal a notable increase in thermal conductivity, density, and viscosity as the volume fraction of particles rises. Conversely, specific heat experiences a decrease with higher particle volume concentration.xD; xA; The influence of permeability and pore size on particle volume fraction variation is a key focus. Interestingly, while the permeability of the medium has a significant effect, it is observed that it increases with permeability. This underscores the role of the medium’s nature in altering the thermophysical properties of nanofluids.

This paper presents a novel numerical study on nanofluids with randomly sized spherical nanoparticles flowing in a porous medium. It explores the impact of porous medium properties on nanofluid thermophysical characteristics, emphasizing the significance of permeability and pore size. The inclusion of random nanoparticle sizes adds practical relevance. Contrasting trends are observed, where thermal conductivity, density, and viscosity increase with particle volume fraction, while specific heat decreases. These findings offer valuable insights for engineering applications, providing a deeper understanding of nanofluid behavior in porous environments and guiding the design of efficient systems in various industrial contexts.

This study aims to numerically scrutinize the entropy generation minimization and mixed convective heat transfer of multi-walled carbon nanotubes–Fe₃O₄/water hybrid nanofluid flow in a lid-driven square enclosure with heat generation in the presence of a porous layer on inner surfaces, considering local thermal non-equilibrium (LTNE) approach and the non-Darcy flow model.

The dimensionless governing equations for hybrid nanofluid and solid phases are solved by applying the finite volume method and semi-implicit method for pressure-linked equations algorithm.

The roles of the internal heat generation in the porous layer, LTNE model and nanoparticles volume fraction on mixed convection phenomenon and entropy generation are introduced for lid-driven cavity hybrid nanofluid flow. Based on the investigation of entropy generation and heat transfer, the minimum total entropy generation and average Nusselt numbers are found at 1 ≤ Ri ≤ 10 where the effect of the forced and free convection flow directions being opposite each other is very significant. When considering various nanoparticle volume fractions, it becomes evident that the minimum entropy generation occurs in the case of φ = 0.1%. The outcomes of LTNE number reveal the operating parameters in which thermal equilibrium occurs between hybrid nanofluid and solid phases.

The analysis of entropy generation under various shear and buoyancy forces plays a significant role in the suitable thermal design and optimization of mixed convective heat transfer applications. This research significantly contributes to the optimization of design and the advancement of innovative solutions across diverse engineering disciplines, such as packed-bed thermal energy storage and thermal insulation.

This study aims to analyse the non-linear losses of a porous media (stack) composed by parallel plates and inserted in a resonator tube in oscillatory flows by proposing numerical correlations between pressure gradient and velocity.

The numerical correlations origin from computational fluid dynamics simulations, conducted at the microscopic scale, in which three fluid channels representing the porous media are taken into account. More specifically, for a specific frequency and stack porosity, the oscillating pressure input is varied, and the velocity and the pressure-drop are post-processed in the frequency domain (Fast Fourier Transform analysis).

It emerges that the viscous component of pressure drop follows a quadratic trend with respect to velocity inside the stack, while the inertial component is linear also at high-velocity regimes. Furthermore, the non-linear coefficient b of the correlation ax + bx² (related to the Forchheimer coefficient) is discovered to be dependent on frequency. The largest value of the b is found at low frequencies as the fluid particle displacement is comparable to the stack length. Furthermore, the lower the porosity the higher the Forchheimer term because the velocity gradients at the stack geometrical discontinuities are more pronounced.

The main novelty of this work is that, for the first time, non-linear losses of a parallel plate stack are investigated from a macroscopic point of view and summarised into a non-linear correlation, similar to the steady-state and well-known Darcy–Forchheimer law. The main difference is that it considers the frequency dependence of both Darcy and Forchheimer terms. The results can be used to enhance the analysis and design of thermoacoustic devices, which use the kind of stacks studied in the present work.

The purpose of this study is to provide that porous media and viscous dissipation are crucial considerations when working with hybrid nanofluids in various applications.Recent years have witnessed significant progress in optimizing these fluids for enhanced heat transfer within porous (Darcy–Forchheimer) structures, offering promising solutions for various industries seeking improved thermalmanagement and energy efficiency.

The first step is to transform the original partial differential equations into a system of first-order ordinary differential equations (ODEs). The fourth-order Runge–Kutta method is chosen for its accuracy in solving ODEs. The present study investigates the free convective boundary layer flow of hybrid nanofluids over a moving thin inclined needle with the slip flow brought about by inclined Lorentz force and Darcy–Forchheimer porous matrix, viscous dissipation.

It is found that slip conditions (velocity and Thermal) exist for a range of the natural convection boundary layer flow. In the hybrid nanofluid flow, which consists of Al₂O₃ and Fe₃O₄ are nanoparticles, H₂O − C₂H₆O₂ (50:50) are considered as the base fluid. The consequence of the governing parameter on the momentum and temperature profile distribution is graphically depicted. The range of the variables is 1 ≤ M ≤ 4, 1 ≤ d ≤ 2.5, 1 ≤ δ ≤ 4, 1 ≤ Fr ≤ 7, 1 ≤ Kr ≤ 7 and 0.5≤λ ≤ 3.5. The Nusselt number and skin friction factors are used to calculate the numerical values of various parameters, which are displayed in Table 4. These analyses elucidate that upsurges in the value of the Fr noticeably diminish the momentum and temperature. It is investigated to see if the contemporary results are in outstanding promise with the outcomes reported in earlier works.

The results can be very helpful to improve the energy efficiency of thermal systems.

The hybrid nanofluids in heat transfer have the potential to improve the energy efficiency and performance of a wide range of systems.

This study proposes that in the combined effects of hybrid nanofluid properties, the inclined Lorentz force, the Darcy–Forchheimer model for porous media and viscous dissipation on the boundary layer flow of a conducting fluid over a moving thin inclined needle. Assessing the potential practical applications of the hybrid nanofluids in inclined needles, this could involve areas such as biomedical engineering, drug delivery systems or microfluidic devices. In future should explore the benefits and limitations of using hybrid nanofluids in these applications.

The 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.

The 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.

The 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.

A 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.

Thermo-magnetic convective flow analysis under the impact of thermal radiation for heat and entropy generation phenomena is an active research field for understanding the efficiency of thermodynamic systems in various engineering sectors. This study aims to examine the characteristics of convective heat transport and entropy generation within an inverted T-shaped porous enclosure saturated with a hybrid nanofluid under the influence of thermal radiation and magnetic field.

The mathematical model incorporates the Darcy-Forchheimer-Brinkmann model and considers thermal radiation in the energy balance equation. The complete mathematical model has been numerically simulated through the penalty finite element approach at varying values of flow parameters, such as Rayleigh number (Ra), Hartmann number (Ha), Darcy number (Da), radiation parameter (Rd) and porosity value (e). Furthermore, the graphical results for energy variation have been monitored through the energy-flux vector, whereas the entropy generation along with its individual components, namely, entropy generation due to heat transfer, fluid friction and magnetic field, are also presented. Furthermore, the results of the Bejan number for each component are also discussed in detail. Additionally, the concept of ecological coefficient of performance (ECOP) has also been included to analyse the thermal efficiency of the model.

The graphical analysis of results indicates that higher values of Ra, Da, e and Rd enhance the convective heat transport and entropy generation phenomena more rapidly. However, increasing Ha values have a detrimental effect due to the increasing impact of magnetic forces. Furthermore, the ECOP result suggests that the rising value of Da, e and Rd at smaller Ra show a maximum thermal efficiency of the mathematical model, which further declines as the Ra increases. Conversely, the thermal efficiency of the model improves with increasing Ha value, showing an opposite trend in ECOP.

Such complex porous enclosures have practical applications in engineering and science, including areas like solar power collectors, heat exchangers and electronic equipment. Furthermore, the present study of entropy generation would play a vital role in optimizing system performance, improving energy efficiency and promoting sustainable engineering practices during the natural convection process.

To the best of the authors’ knowledge, this study is the first ever attempted detailed investigation of heat transfer and entropy generation phenomena flow parameter ranges in an inverted T-shaped porous enclosure under a uniform magnetic field and thermal radiation.