Theory and Semi-Analytical Study of Micropolar Fluid Dynamics through a Porous Channel

In this work,We are looking at the characteristics of micropolar flow in a porous channel that’s being driven by suction or injection.The working of the fluid is described in the flowmodel.We can reduce the governing nonlinear partial differential equations(PDEs)to a model of coupled systems of nonlinear ordinary differential equations using similarity variables(ODEs).In order to obtain the results of a coupled system of nonlinear ODEs,we discuss a method which is known as the differential transform method(DTM).The concern transform is an excellent mathematical tool to obtain the analytical series solution to the nonlinear ODEs.To observe beast agreement between analytical method and numerical method,we compare our result with the Rung-Kutta method of order four(RK4).We also provide simulation plots to the obtained result by using Mathematica.Onthese plots,we discuss the effect of different parameters which arise during the calculation of the flow model equations.

Homotopy analysis solutions for the asymmetric laminar flow in a porous channel with expanding or contracting walls

In this paper, the asymmetric laminar flow in a porous channel with expanding or contracting walls is investigated. The governing equations are reduced to ordinary ones by using suitable similar transformations. Homotopy analysis method （HAM） is employed to obtain the expres- sions for velocity fields. Graphs are sketched for values of parameters and associated dynamic characteristics, especially the expansion ratio, are analyzed in detail.

Homotopy analysis solution for micropolar fluid flow through porous channel with expanding or contracting walls of different permeabilities

The flow of a micropolar fluid through a porous channel with expanding or contracting walls of different permeabilities is investigated. Two cases are considered, in which opposing walls undergo either uniform or non-uniform motion. In the first case, the homotopy analysis method （HAM） is used＇to obtain the expressions for the velocity and micro-rotation fields. Graphs are sketched for some parameters. The results show that the expansion ratio and the different permeabilities have important effects on the dynamic characteristics of the fluid. Following Xu＇s model, in the second case which is more general, the wall expansion ratio varies with time. Under this assumption, the governing equations axe transformed into nonlinear partial differential equations that can also be solved analytically by the HAM. In the process, both algebraic and exponential models are considered to describe the evolution of α（t） from the initial state α0 to the final state al. As a result, the time-dependent solutions are found to approach the steady state very rapidly. The results show that the time-dependent variation of the wall expansion ratio can be ignored because of its limited effects.

Analytic solution to the micropolar-fluid flow through a semi-porous channel with an expanding or contracting wall

The flow of a micropolar fluid in a semi-porous channel with an expanding or contracting wall is investigated. The governing equations are reduced to ordinary ones by using similar transformations. To get the analytic solution to the problem, the homotopy analysis method （HAM） is employed to obtain the expressions for velocity fields. Graphs are sketched and discussed for various parameters, especially the effect of the expansion ratio on velocity and micro-rotation fields.

Perturbation solution to unsteady flow in a porous channel with expanding or contracting walls in the presence of a transverse magnetic field

An incompressible flow in a porous channel with expanding or contacting walls in the presence of a transverse magnetic field is considered. Using similarity transformations, the governing equations are reduced to the nonlinear ordinary differential equations. The exact similar solutions for the different cases of the expansion ratio and the Hartmann number are obtained with a singular perturbation method, and the associated behavior is discussed in detail.

Asymptotic solutions for laminar flow in a channel with uniformly accelerating rigid porous walls

A theoretical investigation was done for the generalized Berman problem, which arises in steady laminar flow of an incompressible viscous fluid along a channel with accelerating rigid porous walls. The existence of multiple solutions and its conditions were established by taking into account exponentially small terms in matched asymptotic expansion. The correctness of the analytical predictions was verified by numerical results.

Application of Adomian decomposition method for micropolar flow in a porous channel

In this study the injective micropolar flow in a porous channel is investigated.The flow is driven by suction or injection on the channel walls,and the micropolar model is used to describe the working fluid.This problem is mapped into the system of nonlinear coupled differential equations by using Berman's similarity transformation.These are solved for large mass transfer via Adomian decomposition method(ADM).Also the numerical method is used for the validity of this analytical method and excellent agreement is observed between the solutions obtained from ADM and numerical results.Trusting this validity,effects of some other parameters are discussed.It can be seen that increasing in the value of N_(1) have different results in comparison with N_(2).

Asymptotic solutions for the asymmetric flow in a channel with porous retractable walls under a transverse magnetic field

The self-similarity solutions of the Navier-Stokes equations are constructed for an incompressible laminar flow through a uniformly porous channel with retractable walls under a transverse magnetic field. The flow is driven by the expanding or contracting walls with different permeability. The velocities of the asymmetric flow at the upper and lower walls are different in not only the magnitude but also the direction. The asymptotic solutions are well constructed with the method of boundary layer correction in two cases with large Reynolds numbers, i.e., both walls of the channel are with suction, and one of the walls is with injection while the other one is with suction. For small Reynolds number cases, the double perturbation method is used to construct the asymptotic solution. All the asymptotic results are finally verified by numerical results.

Review of permeability evolution model for fractured porous media

The ability to capture permeability of fractured porous media plays a significant role in several engineering applications, including reservoir, mining, petroleum and geotechnical engineering. In order to solve fluid flow and coupled flow-deformation problems encountered in these engineering applications,both empirical and theoretical models had been proposed in the past few decades. Some of them are simple but still work in certain circumstances; others are complex but also need some modifications to be applicable. Thus, the understanding of state-of-the-art permeability evolution model would help researchers and engineers solve engineering problems through an appropriate approach. This paper summarizes permeability evolution models proposed by earlier and recent researchers with emphasis on their characteristics and limitations.

Freestanding film formed with Sb-nanoplates embedded in flexible porous carbon nanofibers as a binder-free anode for high-performance wearable potassium-ion battery

Antimony-based materials are considered as promising anodes for potassium ion batteries due to their high theoretical capacity and low electrode potential. However, the aggregation and bulk expansion of Sb particles in cycling will cause capacity attenuation and poor rate performance. In this paper, Sb nanoplates were designed to be embedded in flexible porous N-dopped carbon nanofibers(Sb@PCNFs)by a simple electrospinning deposition(ESD) method. In this structural design, Sb nanoplates of high capacity were employed as active materials, N-dopped carbon nanofibers were used to improve conductivity and structural stability. The introduction of pore-forming agent enables the nanofibers to possess porous structure, thus buffering the huge volume change and promoting the transfer of electrolyte/ions.More importantly, the freestanding film can be directly used as a working electrode, reducing the redundancy in the battery and the cost. Benefitting from the favorable structure, the freestanding flexible Sb@PCNFs electrode shows excellent potassium storage performance with a capacity of 314 m Ah/g after 2000 cycles at 500 m A/g. This strategy of employing active material with high capacity in porous and conductive flexible nanofibers represents an effective method of achieving binder-free electrode with good electrochemical performance towards wearable energy storage devices.

Fabrication of channeled scaffolds through polyelectrolyte complex (PEC) printed sacrificial templates for tissue formation

One of the pivotal factors that limit the clinical translation of tissue engineering is the inability to create large volume and complex three-dimensional (3D) tissues, mainly due to the lack of long-range mass transport with many current scaffolds. Here we present a simple yet robust sacrificial strategy to create hierarchical and per-fusable microchannel networks within versatile scaffolds via the combination of embedded 3D printing (EB3DP), tunable polyelectrolyte complexes (PEC), and casting methods. The sacrificial templates of PEC filaments (diameter from 120 to 500 μm) with arbitrary 3D configurations were fabricated by EB3DP and then incorpo-rated into various castable matrices (e.g., hydrogels, organic solutions, meltable polymers, etc.). Rapid disso-lution of PEC templates within a 2.00 M potassium bromide aqueous solution led to the high fidelity formation of interconnected channels for free mass exchange. The efficacy of such channeled scaffolds for in vitro tissue formation was demonstrated with mouse fibroblasts, showing continuous cell proliferation and ECM deposition. Subcutaneous implantation of channeled silk fibroin (SF) scaffolds with a porosity of 76% could lead to tissue ingrowth as high as 53% in contrast to 5% for those non-channeled controls after 4 weeks. Both histological and immunofluorescence analyses demonstrated that such channeled scaffolds promoted cellularization, vasculari-zation, and host integration along with immunoregulation.

Study of heat transfer and flow of nanofluid in permeable channel in the presence of magnetic field

In this paper,laminar fluid flow and heat transfer in channel with permeable walls in the presence of a transverse magnetic field is investigated.Least square method(LSM)for computing approximate solutions of nonlinear differential equations governing the problem.We have tried to show reliability and performance of the present method compared with the numerical method(Runge-Kutta fourth-rate)to solve this problem.The influence of the four dimensionless numbers:the Hartmann number,Reynolds number,Prandtl number and Eckert number on non-dimensional velocity and temperature profiles are considered.The results show analytical present method is very close to numerically method.In general,increasing the Reynolds and Hartman number is reduces the nanofluid flow velocity in the channel and the maximum amount of temperature increase and increasing the Prandtl and Eckert number will increase the maximum amount of theta.

A Study of Multiple Solutions for the Navier-Stokes Equations by a Finite Element Method

In this paper,a finite element method is proposed to investigate multiple solutions of the Navier-Stokes equations for an unsteady,laminar,incompressible flow in a porous expanding channel.Dual or triple solutions for the fixed values of the wall suction Reynolds number R and the expansion ratioαare obtained numerically.The computed multiple solutions for the symmetric flow are validated by comparing them with approximate analytic solutions obtained by the similarity transformation and homotopy analysis method.Unlike previous works,our method deals with the Navier-Stokes equations directly and thus has no similarity and other restrictions as in previous works.Finally we use the method to study multiple solutions for three cases of the asymmetric flow(which has not been studied before using the similarity-type techniques).