Flexible high-resolution thin micropolarizers for imaging polarimetry

More durable[with high impact force],lighter,and more compact flexible azo dye micropolarizers are attractive candidates for low-cost,simple polarization imaging systems.The liquid crystal polymer[LCP],as an emerging material developed by photo-alignment technology,is a potential material for organizing the long-range ordered structure of azo dyes.However,little research has been done on LCP aligned azo dyes.This paper points out and solves a key problem that restricts the fabrication of high-precision arrays in guest[azo dye]-host[LCP]systems:the doping of dyes leads to disorder of the LCP during curing.After solving the problem,the relationship between the thickness of the LCP and the extinction ratio of the polarizing film was investigated,which effectively improved the extinction ratio.Alignment of azo dye molecules in the range of 2μm[0°-180°]and arrays of micropolarizers[0°,45°,90°,-45°]with 8μm×8μm pixel pitch was achieved by laser direct writing technology.The bending cycle test demonstrates the mechanical stability of the ultrathin flexible polarizer.The flexible patterned polarizer with robust chemical and mechanical stabilities provides a flexible way to capture the polarization of the light and highly integrated advanced flexible optoelectronic devices.

Chemically Radiative MHD Flow of a Micropolar Nanofluid over a Stretching/ Shrinking Sheet with a Heat Source or Sink

This study examines the behavior of a micropolar nanofluidflowing over a sheet in the presence of a transverse magneticfield and thermal effects.In addition,chemical(first-order homogeneous)reactions are taken into account.A similarity transformation is used to reduce the system of governing coupled non-linear partial differ-ential equations(PDEs),which account for the transport of mass,momentum,angular momentum,energy and species,to a set of non-linear ordinary differential equations(ODEs).The Runge-Kutta method along with shoot-ing method is used to solve them.The impact of several parameters is evaluated.It is shown that the micro-rota-tional velocity of thefluid rises with the micropolar factor.Moreover,the radiation parameter can have a remarkable influence on theflow and temperature profiles and on the angular momentum distribution.

The Effects of Thermal Radiation and Viscous Dissipation on the Stagnation Point Flow of a Micropolar Fluid over a Permeable Stretching Sheet in the Presence of Porous Dissipation

In this paper,the effects of thermal radiation and viscous dissipation on the stagnation–point flow of a micropolar fluid over a permeable stretching sheet with suction and injection are analyzed and discussed.A suitable similarity transformation is used to convert the governing nonlinear partial differential equations into a system of nonlinear ordinary differential equations,which are then solved numerically by a fourth–order Runge–Kutta method.It is found that the linear fluid velocity decreases with the enhancement of the porosity,boundary,and suction parameters.Conversely,it increases with the micropolar and injection parameters.The angular velocity grows with the boundary,porosity,and suction parameters,whereas it is reduced if the micropolar and injection parameters become larger.It is concluded that the thermal boundary layer extension increases with the injection parameter and decreases with the suction parameter.

On complete and micropolar-based incomplete strain gradient theories for periodic lattice structures

The micropolar(MP) and strain gradient(SG) continua have been generally adopted to investigate the relations between the macroscopic elastic constants and the microstructural geometric parameters. Owing to the fact that the microrotation in the MP theory can be expressed in terms of the displacement gradient components, we may regard the MP theory as a particular incomplete SG theory called the MPSG theory,compared with the existing SG theories which are deemed complete since all the SGs are included. Taking the triangular lattice comprising zigzag beams as an example, it is found that as the angle of the zigzag beams increases, the bending of the beams plays a more important role in the total strain energy, and the difference between the results by the two theories gradually decreases. Finally, the models are verified with the pure bending and simple shear of lattices by comparing with the results obtained by the finite element method(FEM)-based structure analyses.

VANISHING VISCOSITY LIMIT FOR THE 3D INCOMPRESSIBLE MICROPOLAR EQUATIONS IN A BOUNDED DOMAIN

In this paper,we investigate the vanishing viscosity limit of the 3D incompressible micropolar equations in bounded domains with boundary conditions.It is shown that there exist global weak solutions of the micropolar equations in a general bounded smooth domain.In particular,we establish the uniform estimate of the strong solutions for when the boundary is flat.Furthermore,we obtain the rate of convergence of viscosity solutions to the inviscid solutions as the viscosities tend to zero(i.e.,(ε,χ,γ,κ)→0).

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.

Strain localization of Mohr-Coulomb soils with non-associated plasticity based on micropolar continuum theory

To address the problems of strain localization, the exact Mohr-Coulomb (MC) model is used based on second-order cone programming (mpcFEM-SOCP) in the framework of micropolar continuum finite element method. Using the uniaxial compression test, we focused on the earth pressure problem of rigid wall segment involving non-associated plasticity. The numerical results reveal that when mpcFEM-SOCP is applied, the problems of mesh dependency can be effectively addressed. For geotechnical strain localization analysis involving non-associated MC plasticity, mpcFEM-SOCP in conjunction with the pseudo-time discrete scheme can improve the numerical stability and avoid the unreasonable softening issue in the pressure-displacement curves, which may be encountered in the conventional FEM. It also shows that the pressure-displacement responses calculated by mpcFEM-SOCP with the pseudo-time discrete scheme are higher than those calculated by mpcFEM-SOCP with the Davis scheme. The inclination angle of shear band predicted by mpcFEM-SOCP with the pseudo-time discrete scheme agrees well with the theoretical solution of non-associated MC plasticity.

Unsteady Flow and Heat Transfer of a Casson Micropolar Nanofluid over a Curved Stretching/Shrinking Surface

We present the results of an investigation into the behavior of the unsteady flow of a Casson Micropolar nanofluid over a shrinking/stretching curved surface,together with a heat transfer analysis of the same problem.The body force acting perpendicular to the surface wall is in charge of regulating the fluid flow rate.Curvilinear coordinates are used to account for the considered curved geometry and a set of balance equations for mass,momentum,energy and concentration is obtained accordingly.These are turned into ordinary differential equations using a similarity transformation.We show that these equations have dual solutions for a number of different combinations of various parameters.The stability of such solutions is investigated by applying perturbations on the steady states.It is found that high values of the Micropolar and Casson parameters cause the flow to move more slowly.However,when compared to a shrunken surface,a stretched surface produces a greater Micro-rotation flux.

NCCT for Micropolar Solid and Fluid Media Based on Internal Rotations and Rotation Rates with Rotational Inertial Physics: Model Problem Studies

This paper presents model problem studies for micropolar thermoviscoelastic solids without memory and micropolar thermoviscous fluid using micropolar non-classical continuum theories (NCCT) based on internal rotations and rotation rates in which rotational inertial physics is considered in the derivation of the conservation and balance laws (CBL). The dissipation mechanism is due to strain rates as well as rotation rates. Model problems are designed to demonstrate and illustrate various significant aspects of the micropolar NCCT with rotational inertial physics considered in this paper. In case of micropolar solids, the translational and rotational waves are shown to coexist. In the absence of microconstituents (classical continuum theory, CCT) the internal rotations are a free field, hence have no influence on CCT. Absence of gradients of displacements and strains in micropolar thermoviscous fluid medium prohibits existence of translational waves as well as rotational waves even though the appearance of the mathematical model is analogous to the solids, but in terms of strain rates. It is shown that in case of micropolar thermoviscous fluids the BAM behaves more like time dependent diffusion equation i.e., like heat conduction equation in Lagrangian description. The influence of rotational inertial physics is demonstrated using BLM as well as BAM in the model problem studies.

Computational Dynamics of Stagnation Point Flow of Micropolar Fluid Past Vertical Porous Plates

This work examines the flow of a micropolar fluid over a vertical porous plate at the MHD stagnation point under viscous dissipation, convective boundary conditions, and thermal radiation. The governing partial differential equations and a set of similarity parameters were used to transform them into ordinary differential equations. The Runge-Kutta fourth-order algorithm is used in conjunction with the Newton Raphson shooting technique to numerically solve the generated self-similar equations. Results were tabulated both numerically and graphically, and examples for different controlling factors are quantitatively analyzed. According to the study, the vortex viscosity parameter (k) causes the velocity profiles to rise while the magnetic parameter, suction parameter, and radiation parameter cause them to fall. In contrast, as the flow’s suction and prandtl values rise, so do the magnetic parameter, radiation, and vortex viscosity, while the thickness of the thermal boundary layer decreases. .

The micropolar fluid model for blood flow through a tapered artery with a stenosis

A micropolar model for axisymmetric blood flow through an axially nonsymmetreic but radially symmetric mild stenosis tapered artery is presented. To estimate the effect of the stenosis shape, a suitable geometry has been considered such that the axial shape of the stenosis can be changed easily just by varying a parameter （referred to as the shape parameter）. The model is also used to study the effect of the taper angle Ф. Flow parameters such as the velocity, the resistance to flow （the resistance impedance）, the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis （stenosis throat） have been computed for different values of the shape parameter n, the taper angle Ф, the coupling number N and the micropolar parameter m. It is shown that the resistance to flow decreases with increasing the shape parameter n and the micropolar parameter m while it increases with increasing the coupling number N. So, the magnitude of the resistance impedance is higher for a micropolar fluid than that for a Newtonian fluid model. Finally, the velocity profile, the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis are discussed for different values of the parameters involved on the problem.

Laminar flow of micropolar fluid in rectangular microchannels

Compared with the classic flow on macroscale, flows in microchannels have some new phenomena such as the friction increase and the flow rate reduction. Papautsky and co-workers explained these phenomena by using a micropolar fluid model where the effects of micro-rotation of fluid molecules were taken into account. But both the curl of velocity vector and the curl of micro-rotation gyration vector were given incorrectly in the Cartesian coordinates and then the micro-rotation gyration vector had only one component in the z-direction. Besides, the gradient term of the divergence of micro-rotation gyration vector was missed improperly in the angular moment equation. In this paper, the governing equations for laminar flows of micropolar fluid in rectangular microchannels are reconstructed. The numerical results of velocity profiles and micro-rotation gyrations are obtained by a procedure based on the Chebyshev collocation method. The micropolar effects on velocity and micro-rotation gyration are discussed in detail.

A revised Cattaneo-Christov micropolar viscoelastic nanofluid model with combined porosity and magnetic effects

The dynamics of non-Newtonian fluids along with nanoparticles is quite interesting with numerous industrial applications. The current predominately predictive modeling deals with the flow of the viscoelastic micropolar fluid in the presence of nanoparticles. A progressive amendment in the heat and concentration equations is made by exploiting the Cattaneo-Christov(C-C) heat and mass flux expressions. Besides, the thermal radiation effects are contributed in the energy equation and aspect of the radiation parameter, and the Prandtl number is specified by the one-parameter approach.The formulated expressions are converted to the dimensionless forms by relevant similarity functions. The analytical solutions to these expressions have been erected by the homotopy analysis method. The variations in physical quantities, including the velocity,the temperature, the effective local Nusselt number, the concentration of nanoparticles,and the local Sherwood number, have been observed under the influence of emerging parameters. The results have shown good accuracy compared with those of the existing literature.

Slip flow of Maxwell viscoelasticity-based micropolar nanoparticles with porous medium: a numerical study

This article presents the mass and heat transport aspects in viscoelastic nanofluid flows under the presence of velocity slip conditions. To explore the nonNewtonian behavior, a Maxwell viscoelasticity-based micropolar is considered. Moreover, a porous medium saturates the stretching sheet. A set of similarity variables is introduced to derive the dimensionless ordinary differential equations of velocity, concentration, and temperature profiles. The numerical solution is computed by using the MATLAB bvp4c package. The salient flow features of velocity, concentration, and temperature profiles are described and discussed through various graphs. It is observed that with an increase in the slip parameter, the micro-rotation velocity also increases. The temperature of nanoparticles gets maximum values by varying the viscoelastic parameter and the porosity parameter while an opposite trend is noted for the micro-rotation parameter. The local Nusselt number and the local Sherwood number increase by increasing the viscoelastic parameter, the porosity parameter, and the slip velocity parameter. The graphical computation is performed for a specified range of parameters, such as 0 ≤ M ≤ 2.5, 0 ≤σm ≤ 2.5, 0 ≤ K1 ≤ 1.5, 0.5 ≤ Pr ≤ 3.0, 0 ≤σ≤ 1.5, 0.5 ≤ Sc ≤ 2.0, 0.2 ≤ Nb ≤ 0.8, and 0.2 ≤ Nt ≤ 0.8.

Bending of small-scale Timoshenko beams based on the integral/differential nonlocal-micropolar elasticity theory: a finite element approach

A novel size-dependent model is developed herein to study the bending behavior of beam-type micro/nano-structures considering combined effects of nonlocality and micro-rotational degrees of freedom. To accomplish this aim, the micropolar theory is combined with the nonlocal elasticity. To consider the nonlocality, both integral (original) and differential formulations of Eringen’s nonlocal theory are considered. The beams are considered to be Timoshenko-type, and the governing equations are derived in the variational form through Hamilton’s principle. The relations are written in an appropriate matrix-vector representation that can be readily utilized in numerical approaches. A finite element (FE) approach is also proposed for the solution procedure. Parametric studies are conducted to show the simultaneous nonlocal and micropolar effects on the bending response of small-scale beams under different boundary conditions.

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES(Ⅸ)—THERMOMECHANICS

The existing fundamental laws of thermodynamics for micropolar continuum field theories are restudied and their incompleteness is pointed out. New first and second fundamental laws for thermostatics and thermodynamics for micropolar continua are postulated. From them all equilibrium equations and the entropy inequality of thermostatics as well as all balance equations and the entropy rate inequalities are naturally and simultaneously deduced. The comparisons between the new results presented here and the corresponding results demonstrated in existing monographs and textbooks concerning micropolar continuum mechanics are made at any time. It should be emphasized to note that, the problem of why the local balance equation of energy and the local entropy inequality could not be obtained from the existing fundamental laws of thermodynamics for micropolar continua, is believed to be clarified.

Modeling natural convection boundary layer flow of micropolar nanofluid over vertical permeable cone with variable wall temperature

This paper discusses the natural convection boundary layer flow of a micropo- lax nanofluid over a vertical permeable cone with variable wall temperatures. Non-similax solutions are obtained. The nonlineaxly coupled differential equations under the boundary layer approximations governing the flow axe solved numerically using an efficient, itera- tive, tri-diagonal, implicit finite difference method. Different experimental correlations for both nanofluid effective viscosity and nanofluid thermal conductivity are considered. It is found that as the vortex-viscosity parameter increases, both the velocity profiles and the local Nusselt number decrease. Also, among all the nanoparticles considered in this investigation, Cu gives a good convection.

Melting heat transfer effects on stagnation point flow of micropolar fluid saturated in porous medium with internal heat generation(absorption)

The effect of melting heat transfer on the two dimensional boundary layer flow of a micropolar fluid near a stagnation point embedded in a porous medium in the presence of internal heat generation/absorption is investigated. The governing non-linear partial differential equations describing the problem are reduced to a system of non-linear ordinary differential equations using similarity transformations solved numerically using the Chebyshev spectral method. Numerical results for velocity, angular velocity and temperature profiles are shown graphically and discussed for different values of the inverse Darcy number, the heat generation/absorption parameter, and the melting parameter. The effects of the pertinent parameters on the local skin-friction coefficient, the wall couple stress, and the local Nusselt number are tabulated and discussed. The results show that the inverse Darcy number has the effect of enhancing both velocity and temperature and suppressing angular velocity. It is also found that the local skin-friction coefficient decreases, while the local Nusselt number increases as the melting parameter increases.

Hydrodynamic and heat transfer properties of magnetic fluid in porous medium considering nanoparticle shapes and magnetic field-dependent viscosity

The purpose of this paper is to study the characteristics of the combined convection heat transfer and a micropolar nanofluid flow passing through an impermeable stretching sheet in a porous medium.The nanofluid flow field is affected by a magnetic field perpendicular to the sheet.The dynamic viscosity of the micropolar nanofluid changes under the influence of the magnetic field.The continuity,linear momentum,angular momentum,and energy equations are first simplified using the order of magnitude technique that,along with the applied boundary conditions and the definition of the appropriate parameters,are transferred to the similarity space using the similarity analysis.Then the resulting equations are solved using the Runge–Kutta method.The distinction of the macroscale and microscale flow fields and temperature fields resulting from different nanoparticle shapes was clarified.Increasing the Hartmann number,the vortex viscosity parameter,the magnetic parameter,the nanoparticle volume fraction,and the permeability parameter of the porous media increased the surface friction on the sheet.Increasing the vortex viscosity parameter,the magnetic parameter,and the volume fraction of the nanoparticles increases the Nusselt number.

Heat Absorption and Joule Heating Effects on Transient Free Convective Reactive Micropolar Fluid Flow Past a Vertical Porous Plate

Mathematical model for an unsteady,incompressible,electrically conducting micropolar fluid past a vertical plate through porous medium with constant plate velocity has been investigated in the present study.Heat absorption,Joulian dissipation,and first-order chemical reaction is also considered.Under the assumption of low Reynolds number,the governing transport equations are rendered into non-dimensional form and the transformed first order differential equations are solved by employing an efficient finite element method.Influence of various flow parameters on linear velocity,microrotation velocity,temperature,and concentration are presented graphically.The effects of heat absorption and chemical reaction rate decelerate the flow is particularly near the wall.Skin friction and wall couple stress increases as heat absorption increases but the reverse phenomenon is observed in the case of chemical reaction rate.Wall mass transfer rate increases for chemical reaction and Sherwood number increases for heat absorption.Finite element study is very versatile in simulating unsteady micropolar rheo-materials processing transport phenomena.However,a relatively simple reaction effects restricted to first order.