Boundary Conditions Research Articles

Viscosity models of tri-hybrid non-Newtonian nanofluid with Cattaneo–Christov heat flux, thermal radiation, Ohmic heating and convective boundary condition

PurposeThis study is to examine the impact of viscous dissipation, thermal radiation and Ohmic heating on the magnetohydrodynamic (MHD) flow with thermal and mass transport over a horizontally stretching surface. Cattaneo–Christov heat flux model on a non-Newtonian viscous fluid along with two viscosity models and convective boundary condition has been employed. Tri-hybrid nanofluid has been used to increase thermal performance.Design/methodology/approachGoverning mathematical model has been transposed into a dimensionless system of ordinary differential equations (ODEs) by applying suitable similarity transformation. Numerical solution has been found by applying the bvp4c shooting method in MATLAB software.FindingsVelocity and thermal profiles of Model-I dominate the profiles of Model-II whereas opposite behavior is noticed for concentration profiles. It is concluded that there is an increase in temperature due to thermal radiation, viscous dissipation and convective boundary condition.Originality/valueThe novelty of presented work is to examine the impact of Ohmic heating, viscous dissipation, thermal radiation, chemical reaction and two models of viscosity on Cattaneo–Christov heat flux model of tri-hybrid non-Newtonian nanofluid with convective boundary constraint. The accuracy and effectiveness of presented model have been compared with already published research.

Nonlinear vibration and parametric excitation of magneto‐thermo elastic embedded nanobeam using homotopy perturbation technique

AbstractThe present study focuses on the modeling and analyzing the nonlinear vibration patterns and parametric excitation of embedded Euler–Bernoulli nanobeams subjected to thermo‐magneto‐mechanical loads. The Euler–Bernoulli nanobeam is developed with external parametric excitation. The governing equation of motion is derived by utilizing nonlocal continuum theory and nonlinear von Karman beam theory. Subsequently, the homotopy perturbation technique is employed to determine the vibration frequencies. Finally, the modulation equation of Euler–Bernoulli nanobeams is derived for simply supported boundary condition. In order to validate our findings, we conduct a comparative analysis against existing literature, thereby underscoring the effectiveness and robustness of our proposed methodology. The influence of stress, magnetic potential, temperature, damping coefficient, Winkler coefficient, and nonlocal parameters are tested numerically on nonlinear frequency‐amplitude and parametric excitation–amplitude responses. The numerical examples indicate the significant impact of physical variables on the nonlinear frequency and parametric excitation. The primary objective of this study is to investigate the effects of external physical variables on the dynamic behavior of nanobeams, particularly in nonlinear regimes. This study provides insights into the design and control of nanostructures under complex load conditions, contributing to developing advanced materials and nanosystems.

Improving solar HVAC performance by incorporating sutterby SiO2–Cu/C3H8O2 hybrid nanofluid flow via a collocation based Gegenbauer wavelets technique: Effects of electromagnetic control and Smoluchowksi's temperature slippage

AbstractThe utilization of solar energy in heating, ventilation, and air conditioning (HVAC) systems has gained significant attention as a sustainable and environmentally friendly solution to meet the increasing energy demands. Therefore, this research work introduces a novel engineering study that explores solar‐HVAC systems. However, the study utilized hybrid nanofluids (HNFs) consisting of silicon dioxide and copper nanoparticles, with propylene glycol serving as the base fluid. Furthermore, this exploration features a magnetohydrodynamics (MHD) driven rotating flow with activation energy to enhance the heat transfer performance of solar‐HVAC systems. To increase the model novelty, 3D mathematical models were developed to characterize boundary conditions, which include the speed slippery and Smoluchowski temperature slippage. The partial differential equations in the model are transformed into ordinary differential equations (ODEs) through the use of similarity transformations. The Wavelets and Gegenbauer wavelets method in Mathematica was utilized to solve ODEs and investigate physical attributes such as plate friction, Nusselt number, Sherwood number, and mass flux. The findings show that the solar thermal radiation and magnetic field improve the thermal transfer efficiency of solar‐HVAC. Therefore, the findings of the research have practical applications in solar energy for HVAC systems and can contribute to technological improvements in the manufacturing industry.

Linear stability theory and molecular simulations of nanofilm dewetting with disjoining pressure, strong liquid–solid slip and thermal fluctuations

The dewetting of thin nanofilms is significantly affected by thermal fluctuations, liquid–solid slip and disjoining pressure, which can be described by lubrication equations augmented by appropriately scaled noise terms, known as stochastic lubrication equations. Here molecular dynamics simulations along with a newly proposed slip-generating method are adopted to study the instability of nanofilms with arbitrary slip. These simulations show that strong-slip dewetting is distinct from weak-slip dewetting by faster growth of perturbations and fewer droplets after dewetting, which cannot be predicted by the existing stochastic lubrication equation. A new stochastic lubrication equation considering the strong-slip boundary condition is thus derived using a long-wave approximation to the equations of fluctuating hydrodynamics. The linear stability analysis of this equation, i.e. surface spectrum, agrees well with molecular simulations. Interestingly, strong slip can break down the usual Stokes limits adopted in weak-slip dewetting and bring the inertia into effect. The evolution of the standard deviation of the film height $W^2(t)={\overline {h^2}-{\bar {h}}^2}$ at the initial stage of the strong-slip dewetting is found to be $W\sim t^{1/4}$ in contrast to $W\sim t^{1/8}$ for the weak-slip dewetting.

A model framework for atmosphere–snow water vapor exchange and the associated isotope effects at Dome Argus, Antarctica – Part 1: The diurnal changes

Abstract. Ice-core water isotopes contain valuable information on past climate changes. However, such information can be altered by post-depositional processing after snow deposition. Atmosphere–snow water vapor exchange is one such process, but its influence remains poorly constrained. Here we constructed a box model to quantify the atmosphere–snow water vapor exchange fluxes and the associated isotope effects at sites with low snow accumulation rates, where the effects of atmosphere–snow water vapor exchange are suspected to be large. The model reproduced the observed diurnal variations in δ18O, δD, and deuterium excess (d-excess) in water vapor at Dome C, East Antarctica. According to the same model framework, we found that under average summer clear-sky conditions, atmosphere–snow water vapor exchange at Dome A can cause diurnal variations in atmospheric water vapor δ18O and δD of 4.8 ‰ ± 2.6 ‰ and 29 ‰ ± 19 ‰, with corresponding diurnal variations in surface snow δ18O and δD of 0.80 ‰ ± 0.35 ‰ and 1.6 ‰ ± 2.7 ‰. The modeled results under summer cloudy conditions display similar patterns to those under clear-sky conditions but with much smaller magnitudes of diurnal variations. However, under winter conditions at Dome A, the model predicts few to no diurnal changes in snow isotopes, consistent with the stable boundary condition in winter that inhibits effective vapor exchange between the atmosphere and snow. In addition, after 24 h and continuous simulations of 11 d, the model predicts significant enrichments in snow isotopes under summer conditions, while in winter, the depletions also accumulate after each 24 h simulation but with a much smaller magnitude of change compared to the results from summer simulations. If the modeled snow isotope enrichments in summer conditions and the depletions in winter conditions represent the general situation at Dome A, this likely suggests that atmosphere–snow water vapor exchange tends to increase snow isotope seasonality, and the annual net effect would be overall enrichments in snow isotopes since the effects in summer appear to be greater than those in winter. This trend will need to be further explored in the future with more comprehensive model studies and/or field observations and experiments.

Finite-size corrections to the energy spectra of gapless one-dimensional systems in the presence of boundaries

We present the finite-size scaling theory of one-dimensional quantum critical systems in the presence of boundaries. While the finite-size spectrum in the conformal limit, namely of a conformal field theory with conformally invariant boundary conditions, is related to the dimensions of boundary operators by Cardy, the actual spectra of lattice models are affected by both bulk and boundary perturbations and contain non-universal boundary energies. We obtain a general expression of the finite-size energy levels in the presence of bulk and boundary perturbations. In particular, a generic boundary perturbation related to the energy-momentum tensor gives rise to a renormalization of the effective system size. We verify our field-theory formulation by comparing the results with the exact solution of the critical transverse-field Ising chain and with accurate numerical results on the critical three-state Potts chain obtained by Density-Matrix Renormalization Group.

Influence of Viscosity and Temperature on Rotational Dynamics of 3-(1H-benzo[d]Imidazol-2-yl)-7-(Diethyl Amino)-2H-chromen-2-one (Polar Laser dye) in Highly Viscous Solvent: Low and High Viscous Range.

Temperature-dependent rotational dynamics of 3-(1H-benzo[d]imidazol-2-yl)-7-(diethyl amino)-2H-chromen-2-one (3HBI-7D-2HChromen-2-one) has been studied in highly viscous glycerol solvent. Over the entire studied temperature range rotational reorientation time values vary linearly with temperature. Experimental obtained rotational results are analyzed using hydrodynamic and quasi-hydrodynamic models over the entire temperature range as well as low and high viscous range. 3HBI-7D-2HChromen-2-one rotational dynamics has been described using Stoke's-Einstein-Debye (SED) slip boundary conditions.

Compact Substrate Integrated Waveguide Cubical Dielectric Resonator Antenna for fifth-generation applications

A comprehensive analysis of a wideband Cubical Dielectric Resonator Antenna is presented, specifically designed for 5G-NR wireless communication applications, focusing on the N257, and N258 frequency bands. This antenna exhibits symmetrical radiation patterns, a wider bandwidth, improved efficiency, and substantial gain characteristics. The design employs a low-loss substrate-integrated waveguide structure to enhance gain while reducing cross-polarization effects. This is accomplished through an innovative approach of establishing boundary conditions using copper wire stitching for vias, superseding the conventional soldering iron method, which guarantees minimal radiation leakage, compact dimensions, and reduced losses. The perforated dielectric resonator antenna possesses higher mode excitations, and implementing metallic strips on two resonator surfaces facilitates the simultaneous excitation of fundamental and higher-order modes, thereby yielding a broadband response. The overall dimensions of the antenna are 15.29 × 8.42 × 3.8 mm3(1.3×0.7×0.3)λ03, which facilitates a measured impedance bandwidth of 8.2 GHz, spanning from 24.4 to 32.6 GHz (28.7%), accompanied by a high gain of 8.1 dBi and efficiency levels reaching up to 94%. The prototype is constructed utilizing the standard printed circuit board technique, and simulation outcomes are derived using the High-Frequency Structure Simulator (HFSS).

Contrasting the Penultimate Glacial Maximum and the Last Glacial Maximum (140 and 21 ka) using coupled climate–ice sheet modelling

Abstract. The configuration of the Northern Hemisphere ice sheets during the Penultimate Glacial Maximum differed to the Last Glacial Maximum. However, the reasons for this are not yet fully understood. These differences likely contributed to the varied deglaciation pathways experienced following the glacial maxima and may have had consequences for the interglacial sea level rise. To understand the differences between the North American Ice Sheet at the Last and Penultimate glacial maxima (21 and 140 ka), we perform two perturbed-physics ensembles of 62 simulations using a coupled atmosphere–ice sheet model, FAMOUS-ice, with prescribed surface ocean conditions, in which the North American and Greenland ice sheets are dynamically simulated with the Glimmer ice sheet model. We apply an implausibility metric to find ensemble members that match reconstructed ice extent and volumes at the Last and Penultimate glacial maxima. We use a resulting set of “plausible” parameters to perform sensitivity experiments to decompose the role of climate forcings (orbit, greenhouse gases) and initial conditions on the final ice sheet configurations. This confirms that the initial ice sheet conditions used in the model are extremely important in determining the difference in final ice volumes between both periods due to the large effect of the ice–albedo feedback. In contrast to evidence of a smaller Penultimate North American Ice Sheet, our results show that the climate boundary conditions at these glacial maxima, if considered in isolation, imply a larger Penultimate Glacial Maximum North American Ice Sheet than at the Last Glacial Maximum by around 6 m sea level equivalent. This supports the notion that the growth of the ice sheet prior to the glacial maxima is key in explaining the differences in North American ice volume.

Vibration analysis of shear actuated bi-directional FGP beam using generalized differential quadrature method

The primary objective of this study is to exhibit the shear mode vibrations of a bidirectional functionally graded piezoelectric beam. All material properties are assumed to vary bidirectional in accordance with an exponential law. Using Timoshenko beam theory, the governing equations and boundary conditions are derived using the Hamilton principle. The equations of motion are then solved using the generalized differential quadrature method. Since no previous solutions existed for the current problem, the obtained results are compared with the findings from a simplified case in previous research. The effects of exponent parameters, slenderness ratios, and boundary conditions on natural frequencies of the bidirectional FGP beam are discussed in detail.

2D Skyrmion topological charge of spin textures with arbitrary boundary conditions: a two-component spinorial BEC as a case study

Abstract We derive the most general expression for the Skyrmion topological charge for a two-dimensional spin texture, valid for any type of boundary conditions or for any arbitrary spatial region within the texture. It reduces to the usual one for the appropriate boundary conditions. The general expression resembles the Gauss-Bonet theorem for the Euler-Poincaré characteristic of a 2D surface, but it has definite differences, responsible for the assignment of the proper signs of the Skyrmion charges. Additionally, we show that the charge of a single Skyrmion is the product of the value of the normal component of the spin texture at the singularity times the Index or winding number of the transverse texture, a generalization of a Poincaré theorem. We illustrate our general results analyzing in detail a two-component spinor Bose–Einstein condensate (BEC) in 2D in the presence of an external magnetic field, via the Gross-Pitaevskii equation. The condensate spin textures present Skyrmions singularities at the spatial locations where the transverse magnetic field vanishes. We show that the ensuing superfluid vortices and Skyrmions have the same value for their corresponding topological charges, in turn due to the structure of the magnetic field.

Singular Abreu equations and linearized Monge–Ampère equations with drifts

We study the solvability of singular Abreu equations which arise in the approximation of convex functionals subject to a convexity constraint. Previous works established the solvability of their second boundary value problems either in two dimensions, or in higher dimensions under either a smallness condition or a radial symmetry condition. Here, we solve the higher-dimensional case by transforming singular Abreu equations into linearized Monge–Ampère equations with drifts. We establish global Hölder estimates for linearized Monge–Ampère equations with drifts under suitable hypotheses, and then apply them to prove the regularity and solvability of the second boundary value problem for singular Abreu equations in higher dimensions. Many cases with general right-hand side are also discussed.

Examination of parameters affecting the free vibration frequency of 3D orthogonal woven composite rectangular plates

Three-dimensional orthogonal woven composites (3DOWC) can be widely used in various industries, including aerospace, automotive and military. This research examines the linear free vibration behavior of 3DOWC, focusing on the effects of important parameters, such as thickness, dimensional ratio, and binder fiber volume fraction under different boundary conditions. To achieve this, Ritz theory is utilized to calculate the natural frequency of the system. First, the governing equations for the linear free vibrations of 3DOWC are derived. After forming the energy function of the system and minimizing it, the frequency equations of the system are obtained.

On the boundary conditions for GFMxP high-order schemes on staggered grids in the simulation of incompressible multiphase flows

The simulation of incompressible multiphase flows through the so-called fractional step method needs to solve a variable coefficient Poisson equation for discontinuous functions. Recently, it has been shown how the solution of this equation may be found out through a novel coding of the Ghost Fluid Method (named GFMxP), by avoiding any fit to evaluate the interface position and providing, anyhow, a perfect sharp modeling of the same interface. Furthermore, the accuracy order of the numerical solutions exactly corresponds to the order of the adopted finite difference scheme. The effectiveness and reliability of the new procedure were successfully checked by a lot of tests; however, the a-priori knowledge of the unknown function allowed to elude a fundamental aspect of the numerical approach: the appropriate encoding of the boundary conditions. This topic has often been debated in the past, especially from a theoretical viewpoint, and still represents a rather thorny point in the whole simulation process. The paper shows how to handle the problem in practice and in the context of the GFMxP approach, i.e. by accounting for the presence of the discontinuity and the possible use of high-order solving schemes on a staggered grid.

Robustness and reliability of state-space, frame-based modeling for thermoacoustics

The Galerkin modal expansion is a well-known method used to develop reduced order models for thermoacoustics. A known issue is the appearance of Gibbs-type oscillations on velocity fluctuations at the interface between subdomains and at boundary conditions. Recent work of Laurent et al., Comb. and Flame, 206, (2019) and Laurent, Badhe and Nicoud, J. of Comp. Physics, 428 (2021) have shown that it is possible to overcome this issue by using an over-completed frame, instead of a Galerkin modal basis. However, the low-order modeling based on this frame modal expansion may generate spurious modes. In this paper, the origin of these non-physical modes is identified and a method is proposed to automatically remove them from the outcome. By preventing any interaction between the physical and non-physical components, the proposed methodology drastically improves the robustness and reliability of the frame modal expansion modeling for thermoacoustics.

The interactive effect of products and consumption frequency on happiness in China

PurposeA substantial portion of existing literature on comparing experiential and material purchases on happiness indicates an experiential advantage. However, this advantage is presumed to occur in developed countries, with developing countries being overlooked. To address this gap in the literature, this paper examines the effect of consumption in China. It introduces a new perspective, consumption frequency (ordinary vs extraordinary), to investigate the interactive effect of consumption frequency (ordinary vs extraordinary) and product type (material vs experiential) on happiness and to explore the underlying mechanisms in China.Design/methodology/approachThe study constructs a model about the interactive effect of consumption frequency (ordinary vs extraordinary) and product type (material vs experiential) on happiness and takes self-expansion as the underlying mechanism. The authors employ two experiments and a nationwide secondary survey dataset to test the model.Findings(1) consumption frequency and product type can interactively improve happiness significantly in China; (2) extraordinary material consumption induces a higher level of happiness than extraordinary experiential consumption and (3) these effects are driven by self-expansion, which is an important character for people in developing countries.Research limitations/implicationsThis study is incomplete in its lack of investigation into the boundary conditions, such as materialism in the model.Originality/valueThis paper introduces a novel perspective, consumption frequency and integrates it with existing research variables (material vs experiential) to propose the interactive effect and the underlying mechanism, self-expansion. This paper contributes to the theory of consumption happiness by introducing the concept of consumption frequency in the comparison of material versus experiential products on happiness. Conversely, our findings contribute to the understanding of happiness in China.

Realization of a standing normal detonation for hypersonic propulsion

A standing normal detonation mode of combustion consisting of a normal shock coupled with heat release is realized in an experimental high-speed reacting-flow facility. The normal detonation is stabilized using a 2D ramp where the high-enthalpy freestream Mach number and reactant composition is equivalently matched to the Chapman-Jouguet (CJ) consumption speed of the detonation, at M∞/MCJ = 1.06. High resolution optical measurements of OH* chemiluminescence and density gradients from schlieren clearly show the close-coupling between the normal shock and the heat release of the standing detonation. A ZND analysis have been conducted using the boundary conditions where the induction length is found to closely matches the experimentally measured induction length. The agreement between the induction length scales and the freestream Mach number to detonation CJ Mach number confirm the realization of a standing detonation mode of combustion.

Strike a chord: How observed ostracism and perceived similarity affect observers' willingness to socialize

Research has shown that ostracism negatively affects the social willingness of those who are ostracized, but the impact of observers, who play an important role in ostracism situations, has been less studied. Three studies examined whether observed ostracism affects observers' willingness to socialize and the underlying mechanism. The results showed that (1) observed ostracism decreased observers' willingness to socialize; (2) perceived future rejection mediated the relationship between observed ostracism and observers' willingness to socialize; and (3) perceived similarity had a moderating effect on the mediation model. Specifically, the higher the perceived similarity between observers and ostracized individuals, the stronger the effect of observed ostracism on observers' perceived future rejection and willingness to socialize. These findings contribute to a more comprehensive, systematic understanding of how ostracism affects observers, including its underlying mechanisms and boundary conditions.

Stability analysis of a linear system coupling wave and heat equations with different time scales

In this paper we consider a system coupling a wave equation with a heat equation through its boundary conditions. The existence of a small parameter in the heat equation, as a factor multiplying the time derivative, implies the existence of different time scales between the constituents of the system. This suggests the idea of applying a singular perturbation method to study stability properties. In fact, we prove that this method works for the system under study. Using this strategy, we get the stability of the system and a Tikhonov theorem, which allows us to approximate the solution of the coupled system using some appropriate uncoupled subsystems.

A mechanics-based data-free Problem Independent Machine Learning (PIML) model for large-scale structural analysis and design optimization

Machine learning (ML) enhanced fast structural analysis and design recently attracted considerable attention. In most related works, however, the generalization ability of the ML model and the massive cost of dataset generation are the two most criticized aspects. This work combines the advantages of the universality of the substructure method and the superior predictive ability of the operator learning architecture. Specifically, using a novel mechanics-based loss function, lightweight neural network mapping from the material distribution inside a substructure and the corresponding continuous multiscale shape function is well-trained without preparing a dataset. In this manner, a problem machine learning model (PIML) that is generally applicable for efficient linear elastic analysis and design optimization of large-scale structures with arbitrary size and various boundary conditions is proposed. Several examples validate the effectiveness of the present work on efficiency improvement and different kinds of optimization problems. This PIML model-based design and optimization framework can be extended to large-scale multiphysics problems.