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The work's goal is to learn more about how a magnetic field, Brownian motion, and thermophoresis diffusion influence convective heat transfer in a micropolar-nanofluid flow's laminar boundary layer. Near a vertically moving, permeable plate, the complex fluid is subjected to MHD. The MATLAB application bvp4c was utilized to simplify the governing nonlinear and coupled equations for the micropolar-nanofluid, leading to the solution of the ensuing ordinary differential equations (ODEs). Graphs have been used to analyze the effect of different relevant active factors on the flow field and temperature. The results demonstrate that the micro-rotation of the nanoparticles taken into account and in suspension becomes significant for the complex fluid in the presence of the magnetic field. Analysis of the generation entropy shows that the surface is a significant source of irreversibility. There is no discernible effect of micropolarity on the relationship between Brownian and thermophoresis numbers and entropy generation.

To investigate the consequence of thermophoresis and Brownian diffusion on convective boundary layer micropolar fluid flow over a stretching wedge-shaped surface. The effects of non-dimensional parameters namely coupling constant parameter (0.01 ≤ B1 ≤ 0.05), magnetic parameter (1.0 ≤ M ≤ 15.0), Grashof number (0.3 ≤ Gr ≤ 0.9), modified Grashof number (0.3 ≤ Gm ≤ 0.8), micropolar parameter (2.0 ≤ G2 ≤ 7.5), vortex viscosity constraint (0.02 ≤ G1 ≤ 0.2), Prandtl number (7.0 ≤ Pr ≤ 15.0), thermal radiation parameter (0.25 ≤ R ≤ 0.50), Brownian motion parameter (0.2 ≤ Nb ≤ 0.62), thermophoresis parameter (0.04 ≤ Nt ≤ 0.10), heat generation parameter (0.1 ≤ Q ≤ 0.5), Biot number (0.65 ≤ Bi ≤ 1.0), stretching parameter (0.2 ≤ A ≤ 0.5), Lewis number (3.0 ≤ Le ≤ 7.0), and chemical reaction parameter (0.2 ≤ K ≤ 0.7) on the steady MHD heat and mass transfer is investigated in the present study. The coupled non-linear partial differential equations are reduced into a set of non-linear ordinary differential equations employing similarity transformation. Furthermore, by using the Runge-Kutta method followed by the shooting technique, the transformed equations are solved. The main goal of this study is to investigate the numerical analysis of nanofluid flow within the boundary layer region with the effects of the microrotation parameter and velocity ratio parameter. The novelty of this paper is to propose a numerical method for solving third-order ordinary differential equations that include both linear and nonlinear terms. To understand the physical significance of this work, numerical analyses and tabular displays of the skin friction coefficient, Nusselt number, and Sherwood number are shown. The new approach of the present study contributes significantly to the understanding of numerical solutions to nonlinear differential equations in fluid mechanics and micropolar fluid flow. Micropolar fluids are becoming even more of a focus due to the desire for engineering applications in various fields of medical, mechanical engineering, and chemical processing. [ABSTRACT FROM AUTHOR]

A viscoelastic Timoshenko micro-beam is investigated using micropolar viscoelasticity theory. The governing equations are derived by applying the principle of virtual displacements, and can be used in a variety of problems. The equations are then reduced to the special case of a homogeneous uniform beam and solved for quasi-static elastic and viscoelastic cases. The viscoelastic material is modeled via standard linear solid model. For the elastic case, a closed-form solution is reached, but for the viscoelastic case, the inverse Laplace transform is calculated numerically by utilizing De Hoog's algorithm. It is shown that the proposed model can capture the size effects, and converges to the classical Timoshenko beam if the beam is thick enough. The model also converges to the micropolar Euler-Bernoulli model if the thickness of the beam is small. The role of distributed couple stress is also investigated in this paper. The results indicate that in a cantilever beam, the distributed couple stress has a high influence on the deflection of the beam, micro-rotation, stress components and couple stress. However, in a beam resting on three supports, it only affects the micro-rotation and the shear stress component in transverse direction (σ x z). Further investigation shows an extremum in some of the results over time, illustrating the importance of taking viscoelastic behaviour into account. [ABSTRACT FROM AUTHOR]

AbstractA theoretical study is carried out to explore the heat and mass transfer features in the flow of two types nanofluid, i.e., Al2O3/H2O micropolar nanofluid and (Al2O3+Ag)/H2O hybrid nanofluid, adjacent to a solid sphere. Furthermore, simultaneous effects of linear thermal radiation and chemical reaction are also explored on the heat and mass transfer characteristics. In mathematical formulation basic conservation laws are utilized along with the Soret and Doufer effects as a coupling agents in the energy and mass concentration equations. The normalized variables are used to transform the governing system of non-linear partial differential equations into the system of dimensionless partial differential equations. Stream function reduces the number of dependent variables and the resulting system is solved numerically by Keller box method. Several plots are presented to explore the impact of involved parameters on the different profiles and engineering interest quantities for both types of fluids. The temperature profile and Nusselt number are large in magnitude for hybrid nanofluid as compared to Al2O3/water based nanofluid. The heat transfer and mass transfer rates rises with thermal radiation parameter and chemical reaction parameter, respectively. [ABSTRACT FROM AUTHOR]

The goal of this paper is to learn more about how a magnetic field, Brownian motion, and thermophoresis diffusion influence convective heat transfer in a micropolar-nanofluid flow's laminar boundary layer. Near a vertically moving, permeable plate, the complex fluid is subjected to MHD. The MATLAB application bvp4c was utilized to simplify the governing nonlinear and coupled equations for the micropolar-nanofluid, leading to the solution of the ensuing ordinary differential equations (ODEs). Graphs have been used to analyze the effect of different relevant active factors on the flow field and temperature. The results demonstrate that the micro-rotation of the nanoparticles taken into account and in suspension becomes significant for the complex fluid in the presence of the magnetic field. Analysis of the generation entropy shows that the surface is a significant source of irreversibility. There is no discernible effect of micropolarity on the relationship between Brownian and thermophoresis numbers and entropy generation. [ABSTRACT FROM AUTHOR]

Viscous fluid can micro-rotate due to collisions between particles that affect viscous fluid's velocity and temperature.This study aims to determine the effect of viscosity parameters, micro-rotation materials, and heat sources on fluid velocity and temperature. The model of the laminar flow equation for viscous fluid in this study uses the laws of physics, namely, the law of conservation of mass, Newton II, and Thermodynamics I. The formed dimensional equations are converted into non-dimensional equations by using non-dimensional variables. Then, the non-dimensional equations are converted into similarity equations using stream function and similarity variables. The formed similarity equation was solved numerically by using the Gauss-Seidel method. The results of this study indicate that the velocity and temperature of the viscous fluid flow can be influenced by the parameters of viscosity, micro-rotation material, and heat source. The presence of collisions between particles causes heat to cause an increase in the variance of viscosity parameters, micro-rotation materials, and heat sources. Therefore, the viscous fluid's velocity decreases and its temperature increases.

The present study focuses on a crosswise stream of liquid-holding nano-sized particles over an elongating (stretching) surface. Tiny particles of copper are added into base liquid (water). The influence of the micro rotation phenomenon is also considered. By means of appropriate transformations non-linear coupled ordinary differential equations are attained that govern the flow problem. The Runge–Kutta–Fehlberg scheme, together with the shooting method, is engaged to acquire results numerically. Micropolar coupling parameter, microelements concentration and nanoparticles volume fraction effects are examined over the profiles of velocity, temperature and micro-rotation. Moreover, heat flux and shear stress are computed against pertinent parameters and presented through bar graphs. Outcomes revealed that material constant has increasing effects on normal components of flow velocity; however, it decreasingly influences the tangential velocity, micro-rotation components and temperature profile. Temperature profile appeared to be higher for weak concentration of microelements. It is further noticed that normal velocity profile is higher in magnitude for the case of strong concentration (n = 0) of microelements, whereas tangential velocity profile is higher near the surface for the case of weak concentration (n = 0.5) of microelements. An increase of 3.74% in heat flux is observed when the volume fraction of nanoparticles is increased from 1 to 5%. [ABSTRACT FROM AUTHOR]

Micro-cracks, micro-voids and other such defects, which typically coalesce to form macroscopic cracks, could be represented through incompatible, local rotations of material points, i.e. micro-regions. Specifically, based on a micropolar or Cosserat continuum-like hypothesis that requires attaching directors to material points, we track the evolving frame rotation and hence the microstructural orientation during quasi-brittle damage. We introduce a critical energy release rate incorporating the wryness tensor, which in turn is a function of the micro-rotation field and its gradient within the damaged region. The (pseudo) rotation field appears as additional degrees of freedom to describe a frame field, whose evolution is particularly significant within a diffused region of evolving damage as obtained through a phase-field formulation of brittle fracture. We emphasize that, unlike micropolar continua where it contributes to elastic energy, the wryness tensor appears only in the fracture energy in our approach. Thus, without damage, the solid conforms to the classical continuum. By making suitable modifications to the terms within the elastic energy and applying the principle of virtual work, we arrive at the governing partial differential equations (PDEs). For assessing the proposed framework, we choose a specific form of energy density and demonstrate, through numerical examples, the effect of the newly introduced parameters. The classical phase-field model is readily recovered by switching off the micro-rotation. Additionally, we explore a potential application of this model in representing and propagating initial defects. • Geometrically transparent principle relating microcracks and macro-scopic response. • Relevance of the frame field in capturing the evolving damage. • The governing equations are derived using the principle of virtual work. • Classical phase field model is recovered when frame rotation is ignored. • Model effectively captures initial defect effects in 2D and 3D simulations. [ABSTRACT FROM AUTHOR]

Recently, metamaterials have driven advancements in wave propagation and polarization control. Chiral elastic metamaterials, in particular, have attracted considerable attention due to their distinctive properties, such as acoustical activity and auxeticity. Such characteristics arise from the additional degrees of freedom for tuning the embedded micro- and macro-rotations. In this study, we demonstrate an unusual energy exchange between longitudinal and in-plane shear waves in a 3D chiral mechanical metamaterial. The structural design is capable of inducing up to a 90 ^∘ rotation in the plane of polarization. Additionally, this capacity for conversion is achieved by employing both an arrangement of chiral cells and a single meta-atom. This peculiar behavior enables a seamless switch between the three polarization states existing within a solid material, namely, the longitudinal state, the shear horizontal state, and the shear vertical state. Furthermore, a 2D discrete mono-atomic mass-spring model featuring inclined connectors is used to characterize the distinctive energy exchange between modes. This characterization is based on the retrieval of the pertinent elastic coefficients. The engineered chiral metamaterial polarization converter stands as a promising device for momentum conservation conversions and applications in elasto-dynamic polarimetry.

Novel models for heat flux with laws of linear and angular momenta and convection-diffusion equation for heat are used for the formulation of system of problems associated with the flow of polymer (micropolar fluid) over a cylindrical heated body elongating in a radial direction with non-uniform velocity. Spin gradient and vortex effects with couple stresses are taken into account. Problems are solved using the finite element method (FEM) with Galerkin approximation. Grid-independent and convergent solutions are derived. The results for special cases are compared and validated with published benchmarks. Simulations are used to assess the impact of parameters on flow variables based on the convergent solutions. Simulated results are displayed in the form of velocity, temperature and concentration graphs. Thermal relaxation time corresponds to thermal elastic behaviour and is responsible to make the fluid to restore the thermal equilibrium. This thermal relaxation phenomenon helps in reducing the width of the thermal region. The angular motion of fluid particles has been shown to be affected less by vortex viscosity. Vortex viscosity has shown a greater impact on the motion of Cu−Ag− polymer relative that on Cu− polymer. Thermal performance of Cu−Ag− polymer is better than the thermal enhancement of Cu− polymer. Due to Joule heating, hybrid nanofluid dissipates more heat relative to the nanofluid. Vortex viscosity plays vital role in controlling the thermal region. Heat flux has shown an increase as a function of thermal relaxation time.

This article presents the interface shearing behaviour of a granular soil layer in contact with a bounding structure under motion. For this purpose, an elasto-plastic Cosserat continuum model (EPCCM) and finite element method (FEM) in the updated Lagrange frame are employed. Plane quasi-static shearing of a granular soil layer, bounded by upper and lower rigid boundaries with different surface roughness conditions, is simulated under free dilatancy and constant vertical pressure. Herein, the additional Cosserat kinematical boundary constraints along the bounding surfaces allow a more detailed description of the surface roughness. Specific emphasis is given to the effects of surface roughness as well as the boundary conditions of the entire system on the shear behaviour of layer. According to the obtained results, the shear band location is different in an infinite or finite shear layer depending on the adopted boundary constraints. Further numerical simulations of plane interface shearing are also carried out here using discrete element method (DEM), complementary to Cosserat FE analyses, to better understand the micro-mechanics of granular media near interfaces. FE results are compared with those of experiments as well as DEM simulations and reasonable agreements are seen. The evolution and distribution of state variables and polar quantities in DEM simulations are in proper accordance with the predictions of Cosserat FE model. [ABSTRACT FROM AUTHOR]

The inclusion of solid nano-structures in the liquid changes its rheology and hence its thermal performance. This article considers the impact of nano-solid structure on the ability of the polymer to transport heat. Mathematical models for nano-solid structures and conservation laws are finite element method. The impact of nano-solid structures on transportation of heat is studied via computed solutions. The micro-rotation field increases with an increase in vortex viscosity. The wall shear stress and wall couple stress are increased for vortex viscosity. However, the rate of heat transfer has shown decreasing behavior as a function vortex viscosity. [ABSTRACT FROM AUTHOR]

This paper presents a study of a hydromagnetic free convection flow of an electrically conducting micropolar fluid past a vertical plate through a porous medium with a heat source, taking into account the homogeneous chemical reaction of first order. A uniform magnetic field has also been considered in the study which acts perpendicular to the porous surface of the above plate. The analysis has been done by assuming varying permeability of the medium and the Rosseland approximation has been used to describe the radiative heat flux in the energy equation. Numerical results are presented graphically in the form of velocity, micro- rotation, concentration and temperature profiles, the skin-friction coefficient, the couple stress coefficient, the rate of heat and mass transfers at the wall for different material parameters. The study clearly demonstrates how a chemical reaction influences the above parameters under given conditions

The functional qualities of magneto-micropolar fluid with tiny particles allow for increased lubricating oil usage, increased industrial output, and the development of nanotechnology. However, in such a situation, little or nothing is known about the significance of Lorentz force associated with the behaviour of conducting fluids in magnetic fields, micro-rotation, and thermo-migration of particles as applicable to the control of liquid metals or plasmas. This study focuses on the combined impact of Lorentz force, micro-rotation, and thermo-migration of particles on the dynamics of micropolar fluids experiencing nonlinear thermal radiation and Arrhenius chemical reaction associated with the activation energy. The reactive non-Newtonian, magneto-micropolar nanoparticle fluid flows over a configured two-dimensional stretchy vertical plate. The flow is influenced by activation energy, Brownian movement of tiny particles, thermo-migration of particles and nonlinear thermal radiation. By means of suitable similarity quantities, the partial differential equations governing the flow equations are reduced to ordinary differential equations, and solved numerically using Fehlberg integrating Runge–Kutta scheme. It is worth concluding that the Lorentz force, micro-rotation, and thermo-migration of particles strongly affects the dynamics of micropolar fluids near the wall. A tiny number of particle spins produced by collisions with the boundary dominate the micro-rotation field. • Thermal radiation of reactive magneto-micropolar fluid conveying tiny particles subject to the activation energy. • Parameter sensitivities study of the tiny magneto-micropolar fluid particles for thermal system advancement. • Parameters that the enhances internal heat must be monitored to prevent chemical reaction nanofluid blowup. • A tiny number of particle spins produced by collisions with the boundary dominate the micro-rotation field. • The Lorentz force, micro-rotation, andthermo-migration of particles strongly affects the dynamics of micropolar fluids near the wall. [ABSTRACT FROM AUTHOR]

A numerical study is carried out in order to investigate the multiple solutions of micropolar fluid in a channel with changing walls. Mathematical modeling of laws of conservation of mass, momentum, angular momentum and energy is performed and governing partial differential equations are converted into self-similar ordinary differential equations by applying suitable similarity transformation and then solved numerically by shooting method. A new branch of solutions is found and presented graphically and numerically for the various values of parameters, which has never been reported. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to study the reflection of a plane harmonic wave at the interface of thermo-microstretch elastic half space. The modulus of elasticity is taken as a linear function of reference temperature. The formulation is applied to generalized thermoelasticity theories, the Lord-Shulman and Green-Lindsay theories, as well as the classical dynamical coupled theory. Using potential function, the governing equations reduce to ten-order differential equation. Design/methodology/approach – Coefficient ratios of reflection of different waves with the angle of incidence are obtained using continuous boundary conditions. By numerical calculations, the variation of coefficient ratios of reflection with the angle of incidence is illustrated graphically for magnesium crystal micropolar material under three theories. Findings – The effect of different temperature-dependent constants and frequency on the coefficient ratios of reflection is illustrated graphically in context of Lord-Shulman theory. Originality/value – The reflection coefficient ratios are given analytically and illustrated graphically. The effects of thermal relaxation times are very small on reflection coefficient ratio. The temperature-dependent constant and wave frequency have a strong effect on the reflection coefficient ratios. [ABSTRACT FROM AUTHOR]

Magnetic fields have been shown to achieve excellent fabrication control and manipulation of conductive bio-polymer characteristics. To simulate magnetohydrodynamic effects on non-Newtonian electroconductive bio-polymers (ECBPs) we present herein a theoretical and numerical simulation of free convection magneto-micropolar biopolymer flow over a horizontal circular cylinder (an "enrobing" problem). Eringen's robust micropolar model (a special case of the more general micro-morphic or "microfluid" model) is implemented. The transformed partial differential conservation equations are solved numerically with a powerful and new code based on NSM (Network Simulation Method) i.e. PSPICE. An extensive range of Hartmann numbers, Grashof numbers, micropolar parameters and Prandtl numbers are considered. Excellent validation is also achieved with earlier non-magnetic studies. Furthermore the present PSPICE code is also benchmarked with an implicit tridiagonal solver based on Nakamura's method (BIONAK) again achieving close correlation. The study highlights the excellent potential of both numerical methods described in simulating nonlinear biopolymer micro-structural flows. [ABSTRACT FROM AUTHOR]

Abstract: The boundary layer flow of a micro-polar fluid due to a linearly stretching sheet is investigated. The influence of various flow parameters like ‘suction and injection velocity through the porous surface’, ‘viscosity parameter causing the coupling of the micro-rotation field and the velocity field’ and ‘vortex viscosity parameter’ on ‘shear stress at the surface’, ‘fluid velocity’ and ‘micro-rotation’ are studied. The governing equations of the transformed boundary layer are solved analytically using homotopy analysis method (HAM). The convergence of the obtained series solutions is explicitly studied and a proper discussion is given for the obtained results. Comparison between the HAM and numerical solutions showed excellent agreement. [Copyright &y& Elsevier]

Abstract: In this paper, a linear theory for the analysis of beams based on the micropolar continuum mechanics is developed. Power series expansions for the axial displacement and micro-rotation fields are assumed. The governing equations are derived by integrating the momentum and moment of momentum equations in the micropolar continuum theory. Body couples and couple stresses can be supported in this theory. After some simplifications, this theory can be reduced to the well-known Timoshenko and Euler–Bernoulli beam theories. The nature of flexural and longitudinal waves in the infinite length micropolar beam has been investigated. This theory predicts the existence of micro-rotational waves which are not present in any of the known beam theories based on the classical continuum mechanics. Also, the deformation of a cantilever beam with transverse concentrated tip loading has been studied. The pattern of deflection of the beam is similar to the classical beam theories, but couple stress and micro-rotation show an oscillatory behavior along the beam for various loadings. [Copyright &y& Elsevier]

Abstract: A generalized boundary condition in the Stokes regime is developed for modeling wall bounded flows of fluids with homogeneous internally rotating structures. The governing equations are solved to obtain a universal scaling behavior of the micro-rotation boundary condition at the walls. These observations are supported by molecular dynamics simulation predictions. [Copyright &y& Elsevier]

Abstract: The present study is concerned with the wave propagation in an electro-microelastic solid. The reflection phenomenon of plane elastic waves from a stress free plane boundary of an electro-microelastic solid half-space is studied. The condition and the range of frequency for the existence of elastic waves in an infinite electro-microelastic body are investigated. The constitutive relations and the field equations for an electro-microelastic solid are stemmed from the Eringen’s theory of microstretch elasticity with electromagnetic interactions. Amplitude ratios and energy ratios of various reflected waves are presented when an elastic wave is made incident obliquely at the stress free plane boundary of an electro-microelastic solid half-space. It has been verified that there is no dissipation of energy at the boundary surface during reflection. Numerical computations are performed for a specific model to calculate the phase speeds, amplitude ratios and energy ratios, and the results obtained are depicted graphically. The effect of elastic parameter corresponding to micro-stretch is noticed on reflection coefficients, in particular. Results of Parfitt and Eringen [Parfitt, V.R., Eringen, A.C., 1969. Reflection of plane waves from a flat boundary of a micropolar elastic half-space. J. Acoust. Soc. Am. 45, 1258–1272] have also been reduced as a special case from the present formulation. [Copyright &y& Elsevier]

Novel nonlinear power-law flux models were utilized to model the heat transport phe-nomenon in nano-micropolar fluid over a flexible surface. The nonlinear conservation laws (mass, momentum, energy, mass transport and angular momentum) and KKL cor-relations for nanomaterial under novel flux model were solved numerically. Computed results were used to study the shear-thinning and shear-thickening nature of nano pol-ymer suspension by considering n-diffusion theory. Normalized velocity, temperature and micro-rotation profiles were investigated under the variation of physical parame-ters. Shear stresses at the wall for nanoparticles (CuO and Al2O3) were recorded and dis-played in the table. Error analyses for different physical parameters were prepared for various parameters to validate the obtained results. [ABSTRACT FROM AUTHOR]

In the most recent decade, the CORDIC calculation has drawn wide consideration from the industry and scholarly community for different applications, for example, DSP, SDR, bio-signal processing, Machine Learning, and communication systems, etc. This approach is an iterative calculation, and it involves effortless shift-add tasks, for logic cell utilization of fundamental, rudimentary capacities, present large calculations, and requires huge power. The key prospects for achieving overall output at a faster rate, less power, and minimal area is to modify the adder used. In this paper, the significance of low power Approximate Adder based Repetitive Iteration CORDIC (LP-ARICO) technique that obtains sine/cosine value. The algorithmic quality decreases system, which prompts a decrease in implementation difficulty through misusing the importance. This modifies be actualized in favor of the decrease in power utilization and area effective plan for the iterative procedure. The proposed LP-ARICO architecture achieves higher throughput and decreases idleness. The obtained results show that the proposed system accomplishes delay, power, and area reduction of 45.13%, 4.02%, and 31.12% individually beyond the other techniques at the expense of a 5.3% increase in throughput. [ABSTRACT FROM AUTHOR]