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The paper aims to clarify the relationship between the micro-structures of porous media and the coefficient of permeability. Most materials involve different types of defects like caves, pores and cracks, which are important characters of porous media and have a great influence on the physical properties of materials. To study the seepage mechanical characteristics of damaged porous media, the constitutive model of porous media dealing with coupled modeling of pores damage and its impact on permeability property of a deforming media was studied in this paper.

The paper opted for an exploratory study using the approach of continuum damage mechanics (CDM).

The paper provides some new insights on the fluid dynamics of porous media. The dynamic evolution model of permeability coefficient established in this paper can be used to model the fluid flow problems in damaged porous media. Moreover, the modified Darcy's law developed in this paper is considered to be an extension of the Darcy's law for fluid flow and seepage in a porous medium.

Owing to the limitations of time, conditions, funds, etc., the research results should be subject to multifaceted experiments before their innovative significance can be fully verified.

The paper includes implications for the development of fluid dynamics of porous media.

This paper fulfils an identified need to study the relationship between the micro-structures of porous media and the coefficient of permeability.

The purpose of this article is to analyse the effects of surface roughness on the magneto-hydrodynamic (MHD) squeeze-film characteristics between a sphere and a porous plane surface, which have not been studied so far.

The analytical model takes into account the effect of porosity by assuming that the flow in the porous matrix obeys modified Darcy's law. The stochastic MHD Reynold's type equation is derived by using the Christensen's stochastic method developed for hydrodynamic lubrication of rough surfaces. Two types of one-dimensional surface roughness (radial and azimuthal) patterns are considered.

The expressions for the mean MHD squeeze-film pressure and mean load-carrying capacity are obtained numerically. The results are shown graphically for selected representative parametric values. It is found that the response time increases significantly for the MHD case as compared to the corresponding non-conducting lubricants. The effect of roughness parameter is to increase/decrease the load-carrying capacity and the response time for azimuthal/radial roughness patterns as compared to the smooth case. Also, the effect of porous parameter is to decrease the load-carrying capacity and response time as compared to the solid case.

In this paper, an attempt has been made to analyse the combined effects of surface roughness and permeability on the MHD squeeze-film characteristics between a sphere and a plane surface.

The purpose of this study is to present a theoretical investigation of the effects of cavitation and couple stress on the squeeze film behavior between an anisotropic poroelastic rigid disc and a sinusoidally oscillating rigid disc.

Based on the microcontinuum theory of Vijay Kumar Stokes and the Elrod–Adam algorithm, the non-Newtonian Reynolds equation coupled with modified Darcy's law for lubricant flow through the porous disc is derived. This numerical study includes the continuity of tangential velocity at the porous–fluid interface and the effects of percolation of the polar additives into the anisotropic porous disc.

The effects of couple stress, oscillating amplitude, percolation additives, permeability and anisotropic permeability on the squeeze film characteristics are discussed. It is found that both the percolation effect of the lubricant additives and the anisotropic structure of the porous surface reduce the flow in the porous disc, resulting in a decrease in pressure. It is also observed that cavitation effects are more pronounced for Newtonian fluids than couple stress fluids.

The results of this study can be used to design a variety of engineering applications such as bearings, wet clutches and non-contact mechanical seals.

The analysis of enhanced oil recovery using surfactants is presented here. Surfactants lower the surface tension between oil and water and hence the capillary resistance to flow. The mathematical description of this problem requires modelling of multi‐phase flow in a porous medium. A pressure‐based formulation has been used in the present study. The governing partial differential equations have been solved by a finite difference method. Both Newtonian and non‐Newtonian (shear thinning) behaviour of oil are considered. Results clearly show an improvement in oil recovery in the presence of surfactants. A study of the ideal case where surface tension is reduced to zero shows that oil recovery can be very high.

The purpose of this paper is to investigate the flow and heat transfer of power-law fluids over a non-linearly stretching sheet with non-Newtonian power-law stretching features.

The governing non-linear partial differential equations are reduced to a series of ordinary differential equations by suitable similarity transformations and the numerical solutions are obtained by the shooting method.

As the temperature power-law index or the power-law number of the fluids increases, the dimensionless stream function, dimensionless velocity and dimensionless temperature decrease, while the velocity boundary layer and temperature boundary layer become thinner for other fixed physical parameters. The thermal diffusivity varying as a function of the temperature gradient can be used to present the characteristics of flow and heat transfer of non-Newtonian power-law fluids.

Unlike classical works, the effect of power-law viscosity on the temperature field is considered by assuming that the temperature field is similar to the velocity field with modified Fourier’s law heat conduction for power-law fluid media.

The purpose of this paper is to consider magnetohydrodynamic (MHD) squeeze film characteristics between finite porous parallel rectangular plates with surface roughness.

Based upon the MHD theory, this paper analyzes the surface roughness effect squeeze film characteristics between finite porous parallel rectangular plates lubricated with an electrically conducting fluid in the presence of a transverse magnetic field.

It is found that the magnetic field effects characterized by the Hartmann number produce an increased value of the load carrying capacity and the response time as compared to the classical Newtonian lubricant case. The modified averaged stochastic Reynolds equation governing the squeeze film pressure is derived.

The present study has considered both Newtonian fluids and non-Newtonian liquids.

The work represents a very useful source of information for researchers on the subject of MHD squeeze film with finite porous parallel rectangular plates lubricated with an electrically conducting fluid.

This paper is relatively original and illustrates the squeeze film characteristics between finite porous parallel rectangular plates with MHD effects.

The purpose of this paper is to study the amalgamated consequences of nonNewtonian fluid and permeability for nonporous journal spinning with constant tangential velocity inside a rough porous bearing.

The flow is assumed to have developed under low Reynolds number, and the flow is governed by reduced Navier–Stokes equations. Based on Stokes theory for couple-stress fluid, a closed form of nonNewtonian Reynolds equation is obtained. Finite difference based multigrid method is adopted to study the various parameters of journal bearings.

It is found that bearing attributes such as pressure distribution and weight carrying capacity are commanding for nonNewtonian couple-stress fluid compared to the classical Newtonian case.

The multigrid method for the Reynolds equation is used, which accelerates the convergence rate of the solution and is independent of the grid size. The effects of couple-stress fluid promote the enhanced pressure distribution in the fluid. Both increased weight bearing capacity and delayed squeezing time reduce the skin-friction and hence take longer time to come in contact with each other.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-02-2020-0051/

The purpose of this paper is to discuss the natural convection flow of an incompressible third grade fluid between two parallel plates. The basic equations governing the flow are reduced to a nonlinear ordinary differential equation.

The resulting nonlinear ordinary differential equation is solved by multi‐step differential transform method (MDTM).

The obtained solutions in comparison with the numerical solutions (fourth‐order Runge‐Kutta) admit a remarkable accuracy.

The analysis illustrates the validity and the great potential of the MDTM in solving nonlinear differential equations.

The purpose of this article is to understand the current research status and future development trends in the field of numerical simulation on rock mass grouting.

This article first searched the literature database (EI, Web of Science, CNKI, etc.) for keywords related to the numerical simulation of rock mass grouting to obtain the initial literature database. Then, from the initial database, several documents with strong relevance to the numerical simulation theme of rock mass grouting and high citation rate were selected; some documents from the references were selected as supplements, forming the sample database of this review study (a total of 90 articles). Finally, through sorting out the relationship among the literature, this literature review was carried out.

The numerical simulation of rock mass grouting is mainly based on the porous media model and the fractured media model. It has experienced the development process from Newtonian fluid to non-Newtonian fluid, from time-invariant viscosity to time-varying viscosity, and from generalized theoretical model to engineering application model. Based on this, this article summarizes four scientific problems that need to be solved in the future in this research field: the law of grout distribution at the cross fissures, the grout diffusion mechanism under multi-field coupling, more accurate grouting theoretical model and simulation technology with strong engineering applicability.

This research systematically analyzes the current research status and shortcomings of numerical simulation on rock mass grouting, summarizes four key issues in the future development of this research field and provides new ideas for the future research on numerical simulation on rock mass grouting.

Particular attention is given to the viscous damping force parameter, stiffness parameter, rigidity parameter, and Brinkman number and plotted their graph for thermal distribution, momentum profile and concentration profile.

In the field of engineering, biologically inspired propulsion systems are getting the utmost importance. Keeping in view their developmental progress, the present study was made. The theoretical analysis explores the effect of heat and mass transfer on non-Newtonian Sisko fluid with slip effects and transverse magnetic field in symmetric compliant channel. Using low Reynolds number, so that the authors neglect inertial forces and for keeping the pressure constant during the flow, channel height is used largely as compared to the ratio of wavelength. The governing equations of fluid flow problem are solved using the perturbation analysis.

Results are considered for thickening, thinning and viscous nature of fluid models. It is found that the velocity distribution profile is boosted for increasing values of the Sisko fluid parameter and porous effect, while thermal profile is reducing for Brinkman number (viscous dissipation effects) for all cases. Moreover, shear-thicken and shear-thinning behavior of non-Newtonian Sisko fluid is also explained through the graphs.

Hear-thicken and shear-thinning behavior of non-Newtonian Sisko fluid is also explained through the graphs.