Shear-free Condition Research Articles

Lie symmetries in higher dimensional charged radiating stars

This study investigates the Lie symmetry properties of matter variables, spacetime dimension, and kinematic quantities in spherically symmetric radiating stars undergoing gravitational collapse in higher dimensional spacetimes. Our analysis explores how variations in functions and dependent variables influence the Lie algebra dimensionality and Lie symmetries of the boundary condition. Our study reveals the explicit dependence of charge and spacetime dimension in the Lie symmetry generators for the first time. We examine models with various kinematical features, such as shear, shear-free, geodesic, and non-expanding conditions with different matter variables. Using the Lie symmetries we obtain group invariant solutions to the models and observe how the kinematical features and matter variables affect the Lie symmetries. Additionally, we demonstrate the appearance of a linear equation of state. We recover known four-dimensional models from our results.

Stability and dynamic analyses of hybrid laminates using refined higher-order zigzag theory

This article presents a comparative study on the stability and dynamic response of hybrid laminated composite plates over monolithically produced laminated composite plates. A Refined Higher-order Zigzag Theory (RHZT) is formulated and implemented using finite element method for the analysis of hybrid laminates. This formulation considers both the interlaminar shear stress continuity and shear-free boundary conditions at surfaces of the plates. The numerical implementation employs C 0 continuous eight-noded isoparametric plate elements considering geometric nonlinearity. The element stiffness matrix is formulated to consider both the linear and nonlinear terms of the strain-displacement equations. Derivation of the consistent mass matrix for a plate element is presented following the approximation of total kinetic energy and utilising Hamilton’s principle. Numerical examples are provided to demonstrate buckling and free vibration analyses (as eigenvalue problems). The results are numerically verified and validated using data from published literature. Finally, parametric studies are presented to demonstrate the effectiveness of fibre hybridisation approach on the buckling and free vibration behaviour of laminated composites.

Numerical investigation of the drag reduction effect in turbulent channel flow by superhydrophobic grooved surfaces

Abstract Superhydrophobic surfaces (SHSs) are considered to be a promising technology for achieving skin-friction drag reduction. Development of more efficient techniques for simulating the turbulent boundary layer on SHSs continues to be a subject of interest. In this study, numerical simulations were carried out to capture near-wall behaviours due to the effect of the SHS on wall-bounded flows. To achieve this, high- to intermediate-fidelity turbulence models including Reynolds-averaged Navier–Stokes, detached eddy simulation and large eddy simulation were utilized. With regard to slip conditions, the well-known Navier slip velocity method was used over the SHS. For validating the numerical solutions, the slip velocity and skin friction over the SHS were compared with the experimental output. Results showed that the velocity profile and Reynolds stresses on the SHS were comparable to the reported results. Then, the developed models were further extended to investigate the drag reduction effect of SHSs with rectangular grooves. The subsequent results showed that the combination of superhydrophobicity and rectangular grooves led to a better performance with a maximum drag reduction of 46.1%. This is due to the surface slip caused by the SHS and the secondary vortex effect created by the grooves. Our results revealed that Reynolds stresses of the slippery grooved surface were higher than those of the case in which a shear-free condition was employed for the grooved surface. More importantly, the numerical results indicate the previous assumption of the shear-free condition is inaccurate for the geometrically simplified grooved SHSs. Therefore, geometry modifications rather than an overly simplified shear-free boundary condition should be applied in computational fluid dynamics simulations for SHSs with grooves or other complex structures.

Study of the radical polymerization mechanism and its application in the preparation of high-performance PMMA by reactive extrusion.

In this study, the mechanism of radical polymerization was further explored by pre-dissolving different polymers and studying the kinetics of the bulk polymerization of methyl methacrylate (MMA) under shear-free conditions. Based on the analysis of the conversion and absolute molecular weight, it was found that, contrary to the shearing effect, the inert polymer with viscosity was the key factor to preventing the mutual termination of radical active species and reducing the termination rate constant k t. Therefore, pre-dissolving the polymer could increase the polymerization rate and molecular weight of the system simultaneously, making the polymerization system enter the automatic acceleration zone faster and greatly reducing the generation of small molecular weight polymers, leading to a narrower molecular weight distribution. When the system entered the auto-acceleration zone, k t decreased rapidly and greatly and entered the second steady-state polymerization stage. Then, with the increase in the polymerization conversion, the molecular weight gradually increased, while the polymerization rate gradually decreased. In shear-free bulk polymerization systems, k t can be minimized and radical lifetimes maximized, but the polymerization system is at best a long-lived polymerization rather than a living polymerization. On this basis, by using MMA to pre-dissolve ultrahigh molecular weight PMMA and core-shell particles (CSR), the mechanical properties and heat resistance of the PMMA with pre-dissolved polymer obtained by reactive extrusion polymerization were better than for pure PMMA obtained under the same conditions. Compared with pure PMMA, the flexural strength and impact strength of PMMA with pre-dissolved CSR were up to 166.2% and 230.5%. With the same quality of CSR, the same two mechanical properties of the samples obtained by the blending method were just improved by 29.0% and 20.4%. This was closely related to the distribution of CSR in the pre-dissolved PMMA-CSR matrix with a distribution of spherical single particles 200-300 nm in diameter, which enabled PMMA-CSR to exhibit a high degree of transparency. This one-step process for realizing PMMA polymerization and high performance shows extremely high industrial application prospects.

Higher order computational model considering the effects of transverse normal strain and 2-parameter elastic foundation for the bending of laminated panels

In this study, the authors analyze laminated composite panels supported on an elastic foundation considering the effects of transverse normal strain. A 2-parameter, i.e., Winkler and Pasternak foundation model is assumed to represent the interaction between the panels and the foundation. The theory presented here takes into account the effects of transverse shear and normal strains. The theory plots realistic distributions of the transverse shear stress through the plate thickness and satisfies the shear-free conditions at the extreme surfaces of the panel. The differential equations of the present model are obtained from the principle of virtual work. The laminated composite panel resting on the elastic foundation is analyzed for simply supported boundary conditions. For the verification purpose, the presented problems are also solved using the Reddy's model, Mindlin's model, and the classical model. Good agreement is observed between the numerical results obtained using the present model and the other models.

Investigation on free vibration behavior of laminated angle ply shell with numerical validation

This article attempts an investigation on the free vibration behavior of the laminated composite angle ply shell experimentally and the obtained results are validated by laminated shell model based on modified higher order zigzag theory. The angle ply shell is modeled by placing six layers of 45° glass fiber laminae. The mechanical properties such as Poisson’s ratio, Young’s modulus and shear modulus are determined experimentally. The experimental procedure is performed using a vibration testing instrument by Bruel and Kjaer. The theoretical laminated shell is modeled by taking thickness coordinate to radius of curvature of shell ratio in the strain displacement relationship with shear-free conditions at free surfaces. For the theoretical computations of natural frequencies, a C0 finite element model with nine-noded quadrilateral shell element with seven degrees of freedom at each node has been chosen. Theoretical findings have been compared with experimental results and also with relevant published results in the existing literature. Moreover, extensive parametric studies have been performed to investigate the effect of geometric configurations and lamination schemes with different boundary properties on free vibration behavior of laminated shells, which will serve as benchmark solutions for future researchers.

Dissipative charged homologous model for cluster of stars in f(R,T) gravity

In this paper, we discuss homologous model for cluster of stars in f ( R , T ) gravity. For this purpose, we use f ( R , T ) = R + K ( − T ) n model to incorporate exotic terms in the system. The quasi-static approximations are being imposed onto the shear-free dissipative relativistic self-gravitating charged fluid. It is found that non-dissipative case can easily be reduced to linear homology law in the Newtonian regime. In dissipative scenario, this condition exhibits that the linear homology law for a fluid element is applicable only if we apply the homology conditions on temperature, emission rate and charge associated to baryonic matter. For dark matter, it depends upon the emission of gravitational dissipation. We also deduce that the shear-free and homogeneous expansion rate conditions are equivalent to the homology conditions only in the Newtonian limit. Furthermore, the deviation from homology conditions leads to thermal peeling effects. We use PSR J 1614 − 2230 data with f ( R , T ) field equations for which the graphical analysis shows that the physical variables of baryonic matter like density, pressures and dissipation are suppressed in the presence of dark matter. Thus dark matter has a significant relevance in the emergence of homologous evolution of stellar cluster.

Experimental investigation into the sensitivity of elastically coated piezoelectric polyvinylidene fluoride films to an impact force

This paper presents an experimental study on the effect of an elastic coating on the sensitivity to an impact force on a polyvinylidene fluoride (PVDF) film by using a model consisting of a top mass, a coated/uncoated PVDF film, and a base block. The sensitivity of the PVDF film is determined by measuring the voltage outputs from the PVDF film and an impact hammer, which is used to excite the top mass. The effects of the constraints at the top and bottom surfaces of an uncoated PVDF film on the sensitivity are examined first. Experimentally, the shear-free and perfectly bonded constraints are approximated by applying oil and epoxy glue to the interfaces between the PVDF film and the top mass/base block. The sensitivities of the PVDF film for these two constraints are determined analytically, thus explaining the roles of the stress components in the thickness and in-plane directions of the film in generating the voltage outputs. The approximated shear-free boundary condition using oil at the interface allows an experimental determination of the piezoelectric voltage constant of the PVDF film in the poling direction. Rubber and polyurethane are used for constructing the coated PVDF films. Even a thin layer of elastic coating is capable of significantly increasing the sensitivity of the PVDF film. For example, 3 mm rubber layers allow a 27 dB increase in the low-frequency sensitivity. A system including an elastically coated PVDF film provides an additional 10 dB increase at frequencies close to its first resonance frequency, resulting in a total 37 dB increase in the system sensitivity. The increased sensitivity may be explained as being due to the increased shear force between the elastic material and PVDF film as the thickness of the elastic layer increases. The dominating effect of the shear force is illustrated by the experimental and finite-element analysis as the thickness of the rubber coating gradually increases. The high rate of increase of the sensitivity as a function of rubber thickness can be observed when the thickness is under 0.8 mm.

Dynamics of perturbative Karmarkar collapse of radiating star in [formula omitted] gravity

The significance of the shear free condition on perturbative collapse of radiating anisotropic fluid with Karmarkar condition in the formalism of f(R,T) gravity is analyzed in this manuscript. The gravitational collapse of spherically symmetric radiating object proceeds from initially static regime satisfying the time dependent Karmarkar condition and further established by huge amount of energy dissipation in the form of heat flux. A perturbation approach is applied to get the collapse equation and the gravitational nature of our model is entirely governed by the Karmarkar condition and its boundary condition in scheme of f(R,T) gravity, where R is Ricci scalar and T is trace of energy momentum tensor. Vaidya’s time-like hypersurface is smoothly matched with the interior solution, which further entitles to examine physical viability of spherically symmetric source. Furthermore, a viable linear f(R,T) model is chosen to achieve the exact solution for anisotropic radiating fluid model. Stability tests are demonstrated, indicating that our model is well-behaved. Furthermore, General Relativity results have obtained by simply taking coupling parameter χ to zero.

Shear-free conditions of a Chaplygin-gas-dominated universe

In this work, we revisit the shear-free conjecture of general relativity and study the well-known shear-free condition in the context of the Chaplygin-gas cosmology. It had been shown in previous investigations that, in the general relativistic framework, the matter congruences of shear-free perfect fluid spacetimes should be either expansion-free or rotation-free. Our current investigation, however, indicates that a universe dominated by a Chaplygin-gas can allow a simultaneous expansion and rotation of the fluid provided that certain non-trivial conditions, which we derive and describe in what follows, are met. We also show that, in the appropriate limiting cases, our results reduce to the expected results of dust spacetimes which can only expand or rotate, but not both, at the same time.

Effect of interface curvature on isothermal heat transfer in a hydrophobic microchannel with transverse ribs and cavities

Superhydrophobic microchannels have been found to deliver remarkable frictional flow resistance reduction owing to entrapped air on its surface micro texture. However, the entrapped air may adversely affect the heat transfer performance of the channel due to the increased thermal resistance offered by air. Hence the suitability of superhydrophobic microchannels in micro-scale heat transfer applications can only be ascertained through a combined thermo-hydraulic performance analysis which provides the trade-off between the decreased frictional resistance and increased thermal resistance. In this work, the thermo-hydraulic performance of a superhydrophobic microchannel consisting of transverse ribs and cavities is numerically investigated, at isothermal wall conditions, using CFD software Ansys-Fluent. The ribs and cavities that make up the channel wall can be represented by alternate no-slip (isothermal rib) and shear-free (adiabatic meniscus) zones. The liquid-gas interface formed at the cavity that separates the core flow and entrapped air forms convex, flat or concave menisci depending on the Laplace pressure. The effect of menisci shape on the combined thermo-hydraulic performance is studied for different gas-fractions and protrusion angles. The Nusselt number (Nu), Poiseuille number (fRe) and its ratio (Nu/fRe), are estimated for each case under convective heat transport settings. Increased shear-free fraction leads to an increase in the thermo-hydraulic performance. The concave menisci exhibited a uniform Nu irrespective of the protrusion angle, since the liquid near the interface is almost stagnant between successive no-slip riblets. In contrast, the convex interface demonstrated a drop in Nu with the rise in protrusion angle. The ribbed hydrophobic channel exhibited better performance than a no-slip classical channel having uniform heating for a protrusion angle range of -20°<0<+20° at different shear-free fractions. Moreover, the maximum thermo-hydraulic performance is observed for a nearly flat profile, which is in-line with the previous experimental observations. The thermal boundary layer development over the ribs and cavities is found to significantly influence the assessment of Nu and consequently the typical usage of a periodic boundary condition induces appreciable error in Nu estimation. For instance, a hydrophobic microchannel formed with 20 repeating units of ribs and cavities exhibited an error of 27% in Nu estimation in comparison with the asymptotic Nu, at a moderate Reynolds number of 100. Furthermore, two-phase VOF simulations are performed to compare the heat transfer characteristics of ribbed channels with and without the presence of entrapped air inside the cavities. Finally, the suitability of shear-free and adiabatic conditions is underscored through multi-phase simulations.

Exact third-order static and free vibration analyses of functionally graded porous curved beam

An exact solution based on refined third-order theory (TOT) has been presented for functionally graded porous curved beams having deep curvature. The displacement field of the refined TOT is derived by imposing the shear free conditions at the outer and inner surfaces of curved beams. The properties of the two phase composite are tailored according the power law rule and the effective properties are computed using Mori-Tanaka homogenization scheme. The equations of motion as well as consistent boundary conditions are derived using the Hamilton's principle. The curved beam stiffness coefficients (A, B, D) are obtained numerically using six-point Gauss integration scheme without compromising the accuracy due to deepness (1+z/R) terms. The porosity has been modeled assuming symmetric (even) as well as asymmetric (uneven) distributions across the cross section of curved beam. The programming has been performed in MATLAB and is validated with the results available in the literature as well as 2D finite element model developed in ABAQUS. The effect of inclusion of 1+z/R terms is studied for deflection, stresses and natural frequencies for FG curved beams of different radii of curvature. Results presented in this work will be useful for comparison of future studies.

Asymptotic Gluing of Shear-Free Hyperboloidal Initial Data Sets

We present a procedure for asymptotic gluing of hyperboloidal initial data sets for the Einstein field equations that preserves the shear-free condition. Our construction is modeled on the gluing construction in Isenberg et al. (Ann Henri Poincare 11(5):881–927, 2010), but with significant modifications that incorporate the shear-free condition. We rely on the special Holder spaces, and the corresponding theory for elliptic operators on weakly asymptotically hyperbolic manifolds, introduced by the authors in Allen et al. (Commun Anal Geom 26(1):1–61, 2018) and applied to the Einstein constraint equations in Allen et al. (Class Quantum Grav 33(11):115015, 2016).

Turbulent thermal convection driven by free-surface evaporation in cuboidal domains of different aspect ratios

In this paper, we present simulations of turbulent thermal convection driven by free-surface evaporation above and by a heated wall below. A novel algorithm is proposed for predicting evaporation rates at a free surface, which we then validate against experimental data. At the top of a cuboidal domain, a shear-free boundary condition acts as an approximation of the free surface. We first focus on a domain of aspect ratio Γ = 1, where a fully resolved direct numerical simulation is carried out at a moderate Rayleigh number, Ra = 1.2 × 107, and we compare flow statistics with a Large-Eddy Simulation (LES) on a coarse grid. Both the fully resolved simulation and the LES predict well the time- and area-averaged evaporation rate and free surface temperature when compared with the experimental data. Next, we carry out a series of LES with an increasing lower wall temperature and, consequently, Ra. We then validate the evaporation model by comparing LES predictions of the time- and area-averaged mass flux and temperature at the upper boundary against the experimental measurements. The aspect ratio of the domain is then reduced, and we show, for the first time, the transition to a dual-roll state of the large-scale circulation (LSC) at the aspect ratio of Γ = 1/4 in a cuboidal domain. The temperature and velocity distributions at the free surface are impacted by the state of the LSC. However, we find that the water-side turbulence and aspect ratio play a negligible role on the evaporation rate above, in accordance with experimental observations.

Bubble Complex Finite Strip Method in the Stability and Vibration Analysis of Orthotropic Laminated Composite Plates

In this study, a bubble complex finite strip method (BCFSM) with the higher-order zigzag theory is formulated for mechanical buckling and free vibration analysis of laminated composite plates, including cross-ply and angle-ply laminates. Few studies have been done to obtain the analytical solutions for clamped and free boundary conditions in the longitudinal and transverse edges. Therefore, this study, for the first time, investigates the effects of various boundary conditions on the stability and vibration results of laminated composite plates subjected to axial or pure shear forces with the use of higher-order zigzag theory and BCFSM. Following this, both the interlaminar continuity conditions of transverse shear stresses and the shear-free surface conditions are satisfied by applying a cubic displacement and a zigzag linear varying displacement with the same number of unknowns as the first-order shear deformation theories. Moreover, the effects of width-to-thickness ratio, fiber orientation, number of modes, different dimensional ratios of the plate, and finally, the number of layers are investigated through numerical examples. The bubble shape functions are exploited in the transverse direction to improve the convergence of the method. Finally, the shearing and axial interaction diagrams of composite laminated plates are presented for various types of boundary conditions.

Evaporation-driven turbulent convection in water pools

Abstract

Rolling of non-wetting droplets down a gently inclined plane

Abstract

Free vibration of radially graded hollow cylinders subject to axial force via a higher-order shear deformation beam theory

The dynamic behavior of radially functionally graded tubes is studied when subjected to axial tensile and compressive forces. Differing from the Euler–Bernoulli/Timoshenko beam theories, a higher-order shear beam deformation model that does neither require a shear correction factor nor need a planar cross-section assumption after deformation. The cross-section’s warping is constructed to meet the shear-free condition on tube’s inner and outer surfaces. A governing partial differential equation is derived. Exact characteristic equations for determining the natural frequencies are given. For typical end supports including hinged-hinged, clamped–clamped, clamped-free, and clamped-hinged ends, the natural frequencies are calculated. By letting the frequency vanish, the critical buckling loads under compression can be exactly determined by solving the characteristic equation. A comparison of the present buckling loads and the natural frequencies with the classical ones and with finite element results is made and verifies the efficiency of the proposed model. The frequency-load interaction is plotted for typical boundary conditions. Axial tensile force causes the natural frequencies to increase and axial compressive force decreases the natural frequencies. The effects of the radial gradient, tube’s thickness and length, and the cross-sectional warping shape on the buckling loads and the natural frequencies are elucidated.

Exact solution considering layerwise mechanics for laminated composite and sandwich curved beams of deep curvatures

In this work, a third-order efficient layerwise theory (ELWT) has been developed for laminated composite and sandwich curved beams of deep curvatures. The circumferential displacement is assumed to have global third-order variation in thickness (radial) coordinate with a linear layerwise variation. The number of independent variables is reduced to 3 by imposing the continuity of displacement and transverse shear stress at interfaces and shear free conditions on the outer and inner surfaces. Equations of the motion are derived using Hamilton’s principle. Navier type analytical solution is obtained for simply supported ends. Results for static deflection, stresses, and natural frequencies are presented for laminated composites and sandwich curved beams of different radii of curvature and thicknesses. The importance of inclusion of the deepness terms (1+z/R) in the formulation for the static and free vibration responses are discussed by comparing with the exact 2D elasticity solution. It is shown that the results predicted by the present ELWT are more accurate than equivalent single layer theories having same number of variables. For sandwich curved beams, the predictions of third-order theory (TOT) are extremely poor in comparison with ELWT. The results presented in the paper will be useful for assessing the accuracy of other simplified 1D theories.

Tilted shear-free axially symmetric fluids in f(R) gravity

Some physical properties of the irrotational axially symmetric fluid distributions, which is evolving along geodesics, are studied in this work. With shear-free conditions, the effects of f(R) gravity are analyzed for the case of non-tilted and tilted observers in the dynamics of relativistic system. For the comoving congruence of observers, the purely electric Weyl tensor indicates that no gravitational radiation is produced during the evolution of the system. Though, the case is quite different for tilted congruences.