Boundary Conditions Research Articles

Entropy generation in newtonian vs non-newtonian nanofluid flow under vibration

Numerical investigation into the effects of vibration on heat transfer and entropy generation in Newtonian and Non-Newtonian nanofluid flows through pipes reveals enhanced heat transfer via intensified fluid agitation and improved particle dispersion. Thermal entropy generation analysis shows reduced irreversibility in vibrated flow, indicating improved flow mixing. Vibration enhances heat transfer by intensifying fluid agitation and promoting particle dispersion near the wall, resulting in a significantly more uniform temperature distribution along the pipe, approximately 100 times more than steady-state flow. This study underscores vibration’s potential to optimize heat transfer and reduce entropy generation in nanofluid systems, emphasizing velocity and rheological impacts. Comparison of vibrated flow to steady-state flow for Newtonian and non-Newtonian fluids reveals significant improvements under vibration, particularly at lower Reynolds numbers where non-Newtonian fluids exhibit pronounced effects. Future research directions include exploring thermal radiation’s impact on entropy generation, analyzing different nanofluid compositions, and investigating varied boundary conditions and geometries to advance understanding in this field. This study provides valuable insights into the complex interplay among vibration, fluid dynamics, and heat transfer in nanofluid flows. Its findings have practical implications for optimizing thermal management systems in diverse engineering applications.

Analysis of natural convection in a representative cavity of a room considering oscillatory boundary conditions: An experimental and numerical approach

Natural convection heat transfer in cavities commonly occurs in various engineering problems. Specifically, the problem of a differentially heated cavity with oscillatory boundary conditions arises in the design of energy-saving strategies or energy evaluations within the building sector. This work addressed numerically and experimentally the natural convection in a full-scale room subjected to diurnal heating and nocturnal cooling. The experiment was instrumented with temperature sensors and an air velocity sensor, inspired by works reported in the literature. The numerical model involved solving the equations governing natural convection, considering turbulent bi-dimensional and three-dimensional flow in a transient state. This research allowed the selection of an appropriate turbulence model and evaluated the performance of the two-dimensional and three-dimensional approaches in simulations. Results showed that the k-omega SST model performed best in predicting velocity, while the standard k-omega model performed best in predicting temperature for the two-dimensional simulation, and the RNG k-epsilon model performed best for the three-dimensional simulation. Additionally, the three-dimensional simulation more accurately reproduced the chaotic fluctuations observed in experimental velocity data, demonstrating up to 30 % better estimation during periods of high velocities. The study identified the reversal of convective cells in the cavity, with an approximate duration of 2 h and 40 min in a real case. This study contributes to improving the understanding of turbulent natural convection in a differentially heated cavity with oscillatory boundary conditions. These findings have significant implications for various environmental and engineering applications, including the design of thermally comfortable buildings.

Impact of double diffusion on solid particle dispersion in rotated cylinders with nano-enhanced phase change materials

This study introduces an innovative approach that combines the Incompressible Smoothed Particle Hydrodynamics method with Artificial Neural Networks to examine the dispersion of solid particles within rotated circular cylinders filled with nano-enhanced phase change materials. This method addresses the limitations of traditional numerical techniques by improving accuracy in complex geometries and dynamic boundary conditions. The various parameters are examined, including the lengths of low sources in boundary walls Lb, dimensionless time τ, Hartmann number (Ha), Darcy number (Da), thermal radiation parameter (Rd), and Rayleigh number (Ra). The solid particles are initially situated at the center gate between the two circular cylinders, maintained at elevated temperature Th and concentration Ch. Due to the upward direction of convection flow, the solid particles are consistently dispersed into the top circular cylinder. The findings offer valuable insights into the system's behavior. The dispersion of solid particles within the NEPCM is influenced by both τ and Lb, showcasing minimal dispersion for τ≤0.1 and intensified dispersion for τ≥0.2, particularly augmented by larger Lb. The heat capacity ratio (Cr) exhibits a decrease with increasing Lb at multiple time points. A decrease in the Darcy number significantly slows down the dispersion of solid particles because of the substantial resistance posed by the porous medium. As the Rayleigh number increases, there is an enhanced dispersion of solid particles into the upper circular cylinder and heightened temperature distributions. Additionally, the average Nusselt number Nu¯ and Sherwood number Sh¯ decrease with the increase in Lb due to the expansion of low-temperature and concentration source. When the length Lb was increased from 0.25 to 1, Nu¯ and Sh¯ decreased by approximately 76% and 67%, respectively, underscoring the impact of geometric configuration on heat and mass transfer efficiency. The study highlights the effectiveness of the MLP model in predicting Nu¯ and Sh¯ values through graphical analysis, showing significant agreement with the target values. The results demonstrated notable improvements in managing particle dispersion and heat/mass transfer, emphasizing the potential of this integrated approach for applications in thermal management and energy optimization.

A model of contact deep groove seals based on partition model and JFO boundary condition

Unlike nuclear main pump seals, deep groove seals in aero-engines operate on a contact basis. However, the precise working mechanism and accurate quantitative methods for assessing their sealing performance remain elusive. This paper introduces a fluid-solid-thermal coupling model for contact deep groove seals, utilizing a partition model and considering JFO boundary condition, mixed lubrication, and detailed heat calculations. The model significantly enhances accuracy compared to original approaches. It comprehensively accounts for contact effects, thermal deformations, convergence wedges, radial waviness, hydrodynamic pressures, groove drainage, and convection, revealing characteristics of contact deep groove seals such as high stiffness, effective heat dissipation, wear resistance, and prolonged service life. The proposed model and working mechanism provide theoretical guidance for designing diverse deep groove seal structures.

Fast fracture in toughened glass when impacted randomly by Ice

Modelling the triggering of fracture at a pre-existing flaw is an evolving method of predicting ultimate failure in glass. This fracture mechanics approach of modelling has been shown to give more reliable predictions than a calibrated probabilistic distribution model (as is commonly adopted) when dealing with hail impact which is highly transient in nature. The dynamic stress intensity factor controlling fast crack growth is sensitive to the complex stress state surrounding the critical flaw. Finite element simulations of localised stresses in 3D could incur high computation cost which is compounded by the need to repeat computations until convergence and to simulate multiple strikes in emulating a storm scenario. In this study, closed-form expressions were developed to waive away the need of any simulations. With hail impact, boundary conditions of the glass panel need not be factored into the modelling, as the highly transient stresses are wave controlled. Input parameters are the thickness and level of prestress in glass; offset of position of strike from the known crack and its depth; and the size, velocity, and temperature of the ice impactor. Results from 40 test scenarios involving 5 offset distances, 3 crack depths, 2 glass thicknesses, and 2 sizes of ice were used to validate the prediction, and to reveal the sensitivity of the outcome of the impact to changes in the impact position relative to the known crack.

Study on seismic failure mechanism and damage model of unconstrained adobe block walls

Through the quasi-static cyclic in-plane loading test of three kinds of unconstrained adobe block walls, namely plain adobe wall, modified mud adobe wall and modified adobe wall, the failure mode and seismic performance of each specimen were clarified. Using residual deformation and cumulative energy dissipation as failure parameters, a two-parameter seismic damage model of unconstrained adobe block walls was established. and a calculation method for the adjustment coefficients of energy consumption items was provided. The results showed that the failure mode of the typical unconstrained adobe block wall under earthquake action was not affected by the modification of adobe materials, and the final failure mode was shear failure along the mud crack and the inclined crack extending through the block. Furthermore, the proposed seismic damage model can well reflect the evolution law of earthquake damage of adobe block walls, and the recommended damage index boundary values for five performance levels were given, providing a reference for performance-based seismic design and damage assessment of adobe block walls.

A weighted stabilized lagrange interpolation collocation method for boundary condition identification in 3D electromagnetic inverse scattering

The identification of boundary conditions in electromagnetic inverse scattering is of importance in various engineering applications, ranging from geophysical exploration to wireless communication. Conventional numerical methods solving this problem often suffer from the iterative process, leading to inefficiencies and non-convergence. This paper introduces a weighted scheme of the stabilized Lagrange interpolation collocation method (weighted SLICM) to resolve this problem. Weighted SLICM efficiently integrates governing equations, boundary conditions, and measurement conditions using a weighted least squares approach, offering a straightforward single-step solution and obviating the need for iterative processes in traditional methods like the finite element method. By incorporating regularization techniques, weighted SLICM decreases measurement errors which are unavoidable in engineering problems, thereby ensuring high efficiency and accuracy. In addition, characterized as a strong-form collocation method that relies solely on point information but not on grid connectivity, the weighted SLICM is readily extendible to complex three-dimensional applications in electromagnetic inverse scattering. Extensive simulations of benchmark problems show its ability to achieve accurate and stable results in boundary condition identification in electromagnetic inverse scattering problems including 1D, 2D, and 3D environments, highlighting the effectiveness of the weighted SLICM in navigating complex engineering challenges and substantially enriching research methodologies in this area.

Numerical analysis for nonlinear wave equations with boundary conditions: Dirichlet, Acoustics and Impenetrability

In this article, we present an error estimation in the L2 norm referring to three wave models with variable coefficients, supplemented with initial and boundary conditions. The first two models are nonlinear wave equations with Dirichlet, Acoustics, and nonlinear dissipative impenetrability boundary conditions, while the third model is a linear wave equation with Dirichlet, Acoustics, and linear dissipative impenetrability boundary conditions. In the field of numerical analysis, we establish two key theorems for estimating errors to the semi-discrete and totally discrete problems associated with each model. Such theorems provide theoretical results on the convergence rate in both space and time. For conducting numerical simulations, we employ linear, quadratic, and cubic polynomial basis functions for the finite element spaces in the Galerkin method, in conjunction with the Crank-Nicolson method for time discretization. For each time step, we apply Newton's method to the resulting nonlinear problem. The numerical results are presented for all three models in order to corroborate with the theoretical convergence order obtained.

Some basic theorems on the modified Green–Lindsay model of linear generalized thermoelasticity

The present paper is concerned with a theory of thermoelasticity based upon a newly developed temperature-rate-dependent thermoelastic model that was proposed by Yu et al. [Meccanica. 2018;53:2543–2554], which has eliminated the discontinuity observed in the displacement field during transient motion. The basic governing equations for a homogeneous and isotropic medium are formulated to deduce the significant theorems. Firstly, we prove the uniqueness theorem concerning a mixed initial and boundary value problem within the framework of linear thermoelasticity. Furthermore, we establish a reciprocity theorem utilizing the Laplace transform, which provides insight into the mutual influence between different aspects of the system under consideration. Consequently, we proved the Somigliana and Green theorems. This generalized theorem extends the applicability and versatility of the classical theorems and also assists the issue of thermal and mechanical fields as well as is beneficial for geophysics and mining.

Simulation study on heat and mass transfer characteristics within tubular moving bed heat exchangers

In the field of waste heat recovery, tubular moving bed heat exchangers (MBHEs) hold great promise as equipment capable of effectively handling large-sized granular materials with high temperature. To further clarify the heat and mass transfer characteristics within tubular MBHEs, this study firstly conducted detailed investigations on the contributions of different heat transfer mechanisms. The result shows that heat radiation (∼45 %) and gas film heat conduction (∼42 %) control the heat transfer processes involving tube walls, with an inlet particle temperature of 600 °C, tube wall temperature of 50 °C, and particle descent velocity of 2 mm/s. These contributions can be influenced by the inlet particle temperature and the tube wall temperature, rather than the particle descent velocity. Additionally, for a specific particle, its heat transfer state is highly depended on where it is located. Subsequently, the time-varying and space-varying characteristics of the heat transfer processes involving tube walls are studied. The results suggest that the time-varying and space-varying characteristics are inherent in tubular MBHEs due to the difficulty to achieve complete stability. Meanwhile, temporal fluctuations intensify with an increase in the inlet particle temperature, a decrease in wall temperature, or an increase in particle descent velocity. The result of power spectral density (PSD) indicates that the heat transfer processes exhibit a degree of chaotic behavior due to the nonlinear property of sub-models, as well as the randomness in particle feeding and contacts. The space-varying characteristic is mainly determined by the inlet particle temperature and the tube wall temperature, rather than the particle descent velocity. This characteristic can be observed in both the axial and circumferential directions, with the circumferential variation being more pronounced than the axial variation. Furthermore, a double-tube MBHE, a topic that has received scant attention in previous research, is investigated in comparison to a single-tube MBHE to explore the differences in heat and mass transfer between the two configurations. It indicates that under the same boundary conditions, there are differences in heat transfer results, which are attributed to the interactions between two vertically arranged tubes. These interactions are reflected in the reconstruction of particle flow patterns and the effect altering the temperature distribution for the particles or fluid surrounding the tubes. The obtained results provide valuable insights into the mass and heat transfer behaviors of particles and fluids within tubular MBHEs, laying a foundation for advancing the development of efficient tubular MBHEs.

Traveling wave vibration characteristic analysis of FRC sandwich cylindrical shells with FGP-GPLRC core under discontinuous elastic boundary conditions

In this study, a fiber-reinforced composite (FRC) sandwich cylindrical shell with a functionally graded porous graphene platelet reinforced composite (FGP-GPLRC) core is investigated, and the traveling wave vibration characteristics of this new sandwich cylindrical shell under discontinuous elastic boundary conditions are analyzed for the first time. The influences of centrifugal and Coriolis forces are introduced into the model. By employing the first-order shear deformation theory (FSDT) and the continuity assumption of the layerwise theory, the governing equations of the rotating sandwich shell are obtained. The artificial springs are implemented at the ends of the sandwich shell to represent the discontinuous elastic boundary conditions. The natural frequency of the shell is solved via the Rayleigh-Ritz method and the state space method. Then, the approach proposed is validated by comparing the present results with those reported in the literature and the finite element method. Finally, the effects of various parameters on the traveling wave frequency of the shell are evaluated. It was found that in practical engineering, the appropriate thickness of the FGP-GPLRC core should be selected according to the boundary conditions and other factors, and the ply angle should be adjusted to obtain more stability of vibration.

Investigation of the fast flux test facility transient behavior during a loss of flow without scram test

A Coordinated Research Project (CRP) on the benchmark analysis of Fast Flux Test Facility (FFTF) Loss of Flow Without Scram (LOFWOS) has been held under the sponsorship of the International Atomic Energy Agency. The CRP aims to improve understanding of loss of flow events in fast reactors, as well as to assess capabilities of existing computer codes against experimental data. FFTF is a 400 MWth Sodium-cooled Fast Reactor (SFR) owned by the U.S. Department of Energy, operated from 1980 to 1992. The CRP involves the LOFWOS Test #13, belonging to a series of unprotected transients performed as part of the Passive Safety Testing program. In this framework, the Nuclear Engineering Research Group of Sapienza University of Rome has developed an integrated multiphysics modelling based on a coupled approach with RELAP5-3D© (thermal-hydraulics) and PHISICS (neutron-kinetics) codes. The present paper discusses the results obtained by the authors after the participation in the benchmark open phase. As suggested by the organizers, a two-step methodology was followed. Firstly, calculations were run by imposing the reactor power as boundary condition and focusing on the FFTF thermal–hydraulic behaviour. A good accordance was detected between the numerical results and the experimental data, above all for what concerns the reference core outlet temperatures. Then, the simulations were repeated by using a coupled approach. Calculation outcomes demonstrated the capability of the selected code suite (PHISICS/RELAP5-3D®) to reproduce the reactor transient behavior and its suitability to be used as an effective numerical tool to simulate liquid metal fast reactors accidental scenarios where thermal–hydraulic and neutron-kinetic phenomena are strongly coupled.

Non-constant functions with zero nonlocal gradient and their role in nonlocal Neumann-type problems

This work revolves around properties and applications of functions whose nonlocal gradient, or more precisely, finite-horizon fractional gradient, vanishes. Surprisingly, in contrast to the classical local theory, we show that this class forms an infinite-dimensional vector space. Our main result characterizes the functions with zero nonlocal gradient in terms of two simple features, namely, their values in a layer around the boundary and their average. The proof exploits recent progress in the solution theory of boundary-value problems with pseudo-differential operators. We complement these findings with a discussion of the regularity properties of such functions and give illustrative examples. Regarding applications, we provide several useful technical tools for working with nonlocal Sobolev spaces when the common complementary-value conditions are dropped. Among these, are new nonlocal Poincaré inequalities and compactness statements, which are obtained after factoring out functions with vanishing nonlocal gradient. Following a variational approach, we exploit the previous findings to study a class of nonlocal partial differential equations subject to natural boundary conditions, in particular, nonlocal Neumann-type problems. Our analysis includes a proof of well-posedness and a rigorous link with their classical local counterparts via Γ-convergence as the fractional parameter tends to 1.

A fast vibro-acoustic modeling method of plate-open cavity coupled systems

In this paper, a fast Chebyshev-Ritz method for vibro-acoustic analytical modeling of plate-open cavity coupled systems is developed for the first time. Based on the Chebyshev spectral method and the Rayleigh-Ritz solution procedure, the vibro-acoustic model of the open cavity coupled with a rectangular plate is established. The exterior acoustic field of the open cavity is expressed by the Rayleigh integral. Additionally, the Rayleigh integral is divided into a frequency-independent singular integral and a frequency-dependent non-singular integral, accelerating the calculation process. Furthermore, the Gauss-Chebyshev-Lobato sampling method is first developed for the plate-open cavity coupling model. By converting the integrals into tensor products, the method avoids complex quadruple integrals, increasing the efficiency of the entire integral operation. The vibration and acoustic responses from the proposed method agree well with existing literature and FEM analysis results, demonstrating the convergence and correctness of the current methodology. The mechanism of cavity depth on vibro-acoustic features of plate-open cavity systems is studied, which is less focused in the published literature. Other factors governing the plate-open cavity coupled model encompassed boundary conditions, fluid mediums, and plate thickness are fully examined. The results provide a theoretical foundation for the design and future research of plate-open cavity structures.

Analysis of energy dissipation in hyperbolic problems influenced by internal and boundary control mechanisms

ABSTRACT This article primarily focuses on the rational stabilisation of the wave equation, supplied with a second-order dynamical boundary condition of hyperbolic type, while considering an additional internal damping mechanism within the specified ring. To achieve rational decay rates of the associated energy, it is imperative to exponentially stabilise a portion of the domain using a global Ingham's-type estimate. This paper will subsequently illustrate how this partially localised exponential stabilisation, combined with a Bessel analysis, leads to a rational decrease in the overall energy of the system considered.

Gradient estimates for Yamabe type equations under different curvature conditions and applications

The aim of this paper is to give various aspects of gradient estimates for positive solutions to the Yamabe type equation ut=Δfu+au+buα. We study the problem in many different settings. As result, we obtain several types of gradient estimates for the solution. When the manifold is complete without boundary, we study gradient estimates of Shi type, and of Hamilton type. Moreover, we also derive gradient estimates if the manifold is evolved under the (k,m)-super Perelman-Ricci flows. Besides, we prove gradient estimates under the integral Ricci curvature bounds. Finally, when the manifold has compact boundary, we investigate gradient estimates with Dirichlet boundary conditions. Our theorems generalize and improve many previous works.

Combined electroosmotic and pressure driven flow through soft nanochannel grafted with partially ion-penetrable polyelectrolyte layers

ABSTRACT This study explores the coupled effects of pressure-driven and electroosmotic flows in a soft nanochannel filled with non-Newtonian ionised liquid, where the inner walls are coated with a polymer layer. The ion partitioning effect occurs due to the Born energy, arising from the dielectric permittivity difference between the polyelectrolyte medium and the ionised liquid. The model incorporates the nonlinear Poisson-Boltzmann equation, the modified Darcy-Brinkman equation in the polyelectrolyte layer (PEL), the Cauchy momentum equation in the electrolyte domains and the continuity equation for incompressible fluids. Using the Debye-Hückel approximation for analytical results, the study validates numerical findings. The study considers the no-slip boundary condition on the walls and examines the impact of volume charge density of PEL, bulk electrolyte concentration, non-Newtonian fluid rheology and polymer layer characteristics and applied pressure gradient on flow modulation and ionic transport in the nanochannel. We provide rigorous mathematical results showing how electrohydrodynamic factors like charged PEL, flow behaviour index, EDL thickness, ion partitioning parameters, Debye-Hückel parameter and softness parameters influence the strength of the potential and the total flow modulation. We illustrate ion selectivity in the soft nanochannel and the friction factor across its walls, considering ion partitioning effects.

Per- and polyfluoroalkyl substances (PFAS) fate and transport across a groundwater-surface water interface

Per- and polyfluoroalkyl substances (PFAS) are emerging contaminants of concern whose fate and transport in environmental media are incompletely understood. In the 1960s, PFAS were dumped in the House Street Disposal Site, an unlined landfill on the crest of a glacial end moraine near Rockford, Michigan, USA. In 2017, PFAS were discovered in groundwater and subsequently, a network of monitoring wells delineated a 2 mi (3 km) PFAS plume migrating downgradient toward the Rogue River. Today, the Michigan Department of Natural Resources (MDNR) operates fish-rearing ponds in the area where the plume intersects the groundwater-surface water interface (GSI). Each year, the MDNR fills these man-made ponds using water from a nearby creek. Springs in the ponds prevent them from draining completely at the end of fish-rearing each fall.We sampled surface water and modeled groundwater flow to investigate PFAS transport across the GSI. Numerical models constructed with and without the fishponds did not substantially change MODFLOW model calibration curves or predicted MODPATH flow lines, indicating that PFAS transport is dominated by the regional flow system with limited influence from semiannual changes to boundary conditions at the GSI. Surface water samples collected from five locations within and adjacent to the fishponds were analyzed using EPA Draft Method 1633. PFAS were detected at all locations with the highest total PFAS >60 ng/L in the fishponds. Mixing models based on total PFAS indicate that approximately 10 % of the fishpond water is sourced by groundwater. However, similar analyses with perfluoroalkyl carboxylic acids (PFCA) and perfluoroalkyl sulfonic acids (PFSA) imply that groundwater comprises as much as 30 % of water in the ponds, suggesting differential movement of individual PFAS across the groundwater-surface water interface. Additional investigation of PFAS within the pond sediments is needed to better understand partitioning and differential transport behavior across the GSI.

Animal-Aided Design – planning for biodiversity in the built environment by embedding a species’ life-cycle into landscape architectural and urban design processes

There are suggestions of how to integrate biodiversity-friendly measures into both architecture and landscape architecture, however it is unclear how to systematically include the needs of other organisms such as animals. One particular challenge is the conflict between amenity and biodiversity, as the human designer aims for good design, which often appears to be incompatible with biodiversity-friendly measures. Here we describe ‘Animal-Aided Design’ (AAD) as a methodology to systematically include animals into the planning cycle of project-based planning. The basic idea of AAD is to make animals an integral part of the design and define their needs at the beginning of the planning process. The requirements of target species then set boundary conditions for the planning process, but also serve as an inspiration for the design itself. We illustrate our methodology using theoretical examples, mostly from Western Europe, in particular Germany.

An investigation of the asphalt blending during recycling using the analytical solutions of the binder diffusion models

Diffusion occurs during the blending process of asphalt recycling. The coefficient of diffusion between any two diffusing materials in asphalt recycling is estimated as a constant value, which is found to vary in the order of 10−9–10−16 m 2 / s in past studies. In this study, Fick’s law of diffusion is solved analytically and modelled to simulate asphalt binder diffusion. A comparative study is performed among the models used to study the variability in asphalt binder diffusion. It is observed that the binder concentration gradients are inconsistent with similar initial and parametric values with the change in the boundary conditions adopted in the binder diffusion models. Similarly, the coefficient of diffusion predicted by the models varies for the models adopted under a constant time. From a comparative study of the models, it is observed that the complete blending condition may not be achieved in some cases.