Boundary Perturbation Method Research Articles

Rheological analysis of pressure-driven Jeffrey fluid flow between corrugated porous curved walls with slip constraints

Pressure-driven movement is a fundamental concept with numerous applications in various industries, scientific disciplines, and fields of engineering. Its proper execution is vital for promoting revolutionary innovations and providing solutions in numerous sectors. Therefore, this article scrutinizes the pressure-driven flow of a magnetized Jeffrey fluid between two curved corrugated walls. The geometry of the channel is represented mathematically in an orthogonal curvilinear coordinate system. The corrugation grooves are described by sinusoidal functions with phase differences between the corrugated curved walls. The boundary perturbation method is used to find the analytical solution for the velocity and temperature taking the corrugation amplitude as the perturbation parameter. Furthermore, the volumetric flow rate, skin friction coefficient, and local Nusselt numbers are precisely calculated numerically for a variety of parameters, with the results presented comprehensively in tabular form. The impact of dissimilar parameters, such as the curvature parameter, wave number, magnetic parameter, Darcy number, thermal radiation, heat source/sink parameter, Jeffery fluid parameter, and amplitude parameter, on the flow fields is analyzed through graphical and tabular forms and discussed in detail. The results show that the velocity profile increases due to the curvature parameter and the Jeffrey fluid parameter. However, it decreases due to the magnetic parameter. The temperature distribution rises with the thermal slip and heat source/sink parameters. Meanwhile, it declined for the radiation parameter and the curvature parameter. The model can be used to simulate blood flow in arteries with varying geometries and magnetic fields, aiding in the study of cardiovascular diseases and the design of medical devices such as stents.

Rheological study of water-based Cu nanofluid between two corrugated curved walls under constant pressure gradient

Nanofluids have captured the attention of scientists due to their superior thermophysical properties compared to ordinary liquids. Consequently, nanofluids serve as suitable cooling agents applicable to systems requiring swift response to thermal changes, such as vehicle engines. Therefore, the current article scrutinizes the characteristics of heat transfer on the pressure-driven flow of magnetized nanofluid between two curved corrugated surfaces in the presence of heat generation/absorption. Copper oxide nanoparticles (Cu) have been combined with pure water to form a nanofluid called Cu/H2O. The geometry of the channel is represented mathematically in an orthogonal curvilinear coordinate system. The corrugation grooves are described by sinusoidal functions with phase differences between the corrugated curved walls. The boundary perturbation method is used to find the analytical solution for the velocity field, temperature field, and volumetric flow rate taking the corrugation amplitude as the perturbation parameter. The impact of dissimilar parameters such as the curvature parameter (0.5≤k≤10), wave number (1≤α≤3), magnetic parameter (1≤M≤5), and wave amplitude (0.1≤ε≤0.8) on the flow fields are analyzed through graphs and discussed in detail. The results show that the peak of the velocity increases with the radius of curvature and the width of the channel for a constant pressure gradient. If we increase the magnetic parameter from 1 to 4, the velocity profile at the specified point decreases by 30 %. If we increase the heat source/sink parameter from 2 to 5, the temperature profile at the specified point increases by approximately 17 %. The flow rate is increased by the corrugations for any phase difference between the corrugated curved walls depending on the corrugation wavenumber and the channel radius of curvature.

A study on the pressure‐driven flow of magnetized non‐Newtonian Casson fluid between two corrugated curved walls of an arbitrary phase difference

AbstractPressure‐driven movement is a fundamental concept with numerous applications in various industries, scientific disciplines, and fields of engineering. Its proper execution is vital for promoting revolutionary innovations and providing solutions in numerous sectors. Therefore, this article scrutinizes the pressure‐driven flow of magnetized Casson fluid between two curved corrugated walls. The geometry of the channel is represented mathematically in an orthogonal curvilinear coordinate system. The corrugation grooves are described by sinusoidal functions with phase differences between the corrugated curved walls. The boundary perturbation method is used to find the analytical solution for the velocity field and volumetric flow rate, taking the corrugation amplitude as the perturbation parameter. The results show that the peak of the velocity increases with the radius of curvature and the width of the channel for a constant pressure gradient. The velocity exhibited a declining trend due to an increase in the Casson fluid parameter. For a sufficiently large corrugation wavenumber, the flow rate decreases, and the phase difference becomes irrelevant. However, the reduction in flow can be minimized by decreasing the channel radius of curvature. In general, a smooth curved channel will give the maximum flow rate for a large corrugation wavenumber. The model can be used to simulate blood flow in arteries with varying geometries and magnetic fields, aiding in the study of cardiovascular diseases and the design of medical devices like stents.

Analytical Model of Air‐Gap Magnetic Field for Eccentric Harmonic Magnetic Gear with Halbach Array

The eccentric harmonic magnetic gear (EHMG) has the characteristics of high torque density, high transmission ratio and high efficiency. The EHMG with Halbach array has better performance than the EHMG with traditional radial magnetization. Accurate calculation of its air‐gap magnetic field is of great significance for design and optimization. Based on the boundary perturbation method, a 2D analytical model of the air‐gap magnetic field of EHMG with Halbach array is established in this paper. The eccentric air‐gap magnetic field is calculated due to the permanent magnets of the eccentric rotor and the stator acting alone, and then the air‐gap magnetic field of the EHMG is obtained according to the superposition principle. The results of the air‐gap magnetic field are compared and evaluated by the regression evaluation indexes. The analytical results are consistent with the finite element results, which verifies the validity and accuracy of the analytical model. Comparing the EHMG with Halbach array and radial magnetization, the maximum static and dynamic electromagnetic torques of EHMG with Halbach array are increased by 59.1% and 55.6% compared with the EHMG with radial magnetization, which verifies the superior performance of EHMG with Halbach array. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

Robust structural optimization in presence of manufacturing uncertainties through a boundary-perturbation method

Most manufacturing processes are inevitably characterized by process tolerances that ultimately affect the way a component behaves and complies with the design requirements. These uncertainties determine the real performance of a structure, with their impact growing with increasing deviations from the nominal values. This work introduces a simple approach, applicable to both static and dynamic cases, to conduct robust structural topology optimization in presence of manufacturing uncertainties. This approach, based on the level set method, makes use of a computationally efficient boundary-perturbation technique to describe over- and under-etching errors. Compared to the existing methods, it does not require a frequent re-initialization of the level set function, nor does it require a mapping between the etched structures and the nominal one. Moreover, compared to the standard case with uniform uncertainty, the technique presented in this work allows dealing with arbitrary spatially varying errors without increasing the computational cost.

A quasi-solution on a lattice graph for an initial state reconstruction

This note considers a graph-based initial state reconstruction in image denoising. Our particular focus is on developing a quasi-model by a combination of boundary perturbation methods. The corresponding spectral quasi-solution enables one to stably approximate the original pixelated image after the standard forward–backward denoising process. Convergence estimates are derived with respect to the deterministic noise level. Some numerical examples are provided to verify the performance of the method.

On the role of interfacial elasticity in morphological instability of a heteroepitaxial interface

In this paper, we discuss a theoretical approach to morphological instability analysis of the coherent interphase boundaries in strained heterostructures. Taking into account the fact that, under certain conditions, the atomic arrangement of solid–solid interfaces is thermodynamically unstable, the evolution equation describing the kinetics of the relief formation is obtained. The considered process is controlled by interface diffusion activated by the nonuniform stress field which occurs due to mismatch between materials and the initial interface perturbation. To define the stress distribution along the curved interface, we use constitutive equations of bulk and surface/interface elasticity modeling the interphase domain as a negligibly thin layer adhering to the bulk phases. This allows us to take into account the surface energy variation related to the interface relief evolution and analyze, in addition to other parameters, the effect of elastic constants that characterize the mechanical behavior of the interphase layer. With the use of the first-order approximation of the boundary perturbation method, the solution of the linearized evolution equation leads to an estimation of equilibrium surface shape.

Coupled effect of curved surface and interface on stress state of wrinkled thin film coating at the nanoscale

AbstractIn this paper, we present the model of continuum mechanics for an analysis of the size‐dependent elastic state of the wrinkled thin film coating with the nanosized thickness. For this purpose, we formulate the two‐dimensional boundary value problem for the film‐on‐substrate system under plane strain conditions in terms of the complex variable. To analyse the effect of surface and interface elasticity, the surface and interphase domains are modelled as negligibly thin layers adhering to the bulk phases without slipping. The algorithm of deriving the expressions for the stress tensor components in the first‐order approximation of the boundary perturbation method is described. Based on this algorithm, the influence of the size of the wrinkles, film‐to‐substrate stiffness ratio and film thickness on the stress concentration in the film is examined.

Stress Distribution in Composites with Co-Phase Periodically Curved Two Neighboring Hollow Fibers

In this paper, stress distribution is examined in the case where infinite length co-phase periodically curved two neighboring hollow fibers are contained by an infinite elastic body. The midline of the fibers is assumed to be in the same plane. Using the three-dimensional geometric linear exact equations of the elasticity theory, research is carried out by use of the piecewise homogeneous body model. Moreover, the body is assumed to be loaded at infinity by uniformly distributed normal forces along the hollow fibers. On the inter-medium between the hollow fibers and matrix surfaces, complete cohesion conditions are satisfied. The boundary form perturbation method is used to solve the boundary value problem. In this investigation, numerical results are obtained by considering the zeroth and first approximations to calculate the self-equilibrium shear stresses and normal stress at the contact surfaces between the hollow fibers and matrix. Numerous numerical results have been obtained and interpreted about the effects of the interactions between the hollow fibers on this distribution.

Radiation of waves by a thin cap submerged in ice-covered ocean

SummaryThe present article is concerned with the radiation of flexural gravity waves due to a thin cap submerged in the ice-covered ocean. The problem is reduced to a system of hypersingular integral equations using the boundary perturbation method. The first-order approximation has only been considered. The effects of the rigidity of the ice sheet and depth of submergence on the added mass and damping coefficient have been analysed. Two types of caps (for example, concave upwards and concave downwards) have been considered for the numerical results. The effect of the concavity on added mass and damping coefficient has also been studied. The present study should be helpful to understand the nature of waves generated by a heaving submerged body in an ice-covered ocean.

Darcy–Brinkman Micropolar Fluid Flow through Corrugated Micro-Tube with Stationary Random Model

A boundary perturbation method is presented to investigate the modified micropolar Brinkman model. A slightly micro-corrugated cylindrical tube is filled with a porous medium in which a micropolar fluid flows through its pores. Stationary random model is used to mimic the surface roughness of the tube. The amplitude of the corrugations, which are perpendicular to the flow, is assumed to be small compared to the mean tube radius. The obtained solution is used for the evaluation of the influence of the corrugations on pressure gradient and the flow rate. The corrugation function depending on wavelength, permeability of the porous medium and micropolarity parameter is constructed. The limiting cases of Stokesian and Darcian micropolar fluid flows are investigated.

Magnetohydrodynamic flow through a wavy curved channel

The flow of an electrically conducting fluid through a curved channel with wavy boundaries is studied. The waviness of the curved boundaries is sinusoidal and periodic. The analytical results for the velocity field and the volumetric flow rate are obtained using the boundary perturbation method. The effects of the wavy boundaries, the channel radius of curvature, and the applied magnetic field on the flow field are analyzed. The study shows that the impact of the wavy boundaries on the flow decreases with the increase in the flow Hartmann number. However, the flow rate increases for any alignment of the wavy curved boundaries and for the wave numbers less than a threshold wavenumber (depending on the radius of curvature and the Hartmann number), and a further increase in the flow rate occurs with the increase in the phase difference between the wavy curved boundaries. On the other hand, the flow rate decreases with the increasing wavenumber, and for a sufficiently large wavenumber and Hartmann number, the phase difference between the wavy curved boundaries becomes irrelevant to the flow.

Analytical Method for Magnetic Field of Eccentric Magnetic Harmonic Gear

Eccentric magnetic harmonic gears (EMHG) can achieve high speed ratio transmission and large torque output by modulating the air gap length between permanent magnets (PM). The analytical method is based on the boundary perturbation method. The vector magnetic potential perturbation equation in the air gap region is established, and the general solution is obtained using the boundary conditions. According to the superposition principle, the air gap flux density of stator and rotor PMs acting alone is synthesized, and the electromagnetic torque and unbalanced magnetic pull are calculated. Last, we compare magnetic field distributions, electromagnetic torque and unbalanced magnetic pull computed by the analytical method with those obtained from finite-element method (FEM).

The effect of nonlinear terms in boundary perturbation method on stress concentration near the nanopatterned bimaterial interface

The effect of nonlinear terms in boundary perturbation method on stress concentration near the nanopatterned bimaterial interface

Elastic field at a rugous interface of a bimaterial with surface effects

The two-dimensional problem of elasticity incorporating surface effect at a rugous interface of bimaterial is considered. The current study is directed towards developing the theoretical model for analysing the stress distribution along nanosized interface irregularities of isotropic bimaterial systems, as the fracture of heterogeneous materials is strongly influenced by the stress concentrations around topological defects in an interface region. Based on the simplified Gurtin-Murdoch model of surface elasticity and the boundary perturbation method combined with the complex variable technique, the original boundary value problem is reduced to the sequence of hypersingular integral equations for any-order approximation. For the first-order approximation and periodic shape of the interface, the solution is obtained in an explicit form of Fourier series. The closed form expression for the hoop stress at the interface is derived in the case of the harmonic shape of the interface. Some detailed numerical investigations of the influence of mechanical characteristics of the interface, the shape and the size of interface asperities, and the elastic properties of the bimaterial components on the hoop stress and stress concentration are presented. It is shown that the incorporation of an interfacial energy exhibits properties that cannot be obtained using classical approach. For instance, the size effect is revealed, namely, the stress concentration depends on the deviation amplitude of the interface undulation at the nanoscale when the ratio of this amplitude to the period is constant; allowing for the interface elasticity reduces the concentration of the hoop stresses if the interface tension is neglected; if external loading is absent or relatively small, the elastic field at the interphase region is determined by the value of the interface tension and depends on geometric and elastic properties of the interface.

Stress concentration analysis of nanosized thin-film coating with rough interface

The boundary perturbation method combined with the superposition principle is used to calculate the stress concentration along the arbitrary curved interface of an isotropic thin film coherently bonded to a substrate. In the case of plane strain conditions, the boundary value problem is formulated for a four-phase system involving two-dimensional constitutive equations for bulk materials and one-dimensional equations of Gurtin–Murdoch model for surface and interface. Static boundary conditions are formulated in the form of generalized Young–Laplace equations. Kinematic boundary conditions describe the continuous of displacements across the surface and interphase regions. Using Goursat–Kolosov complex potentials, the system of boundary equations is reduced to a system of the integral equations via first-order boundary perturbation method. Finally, the solution of boundary value problem is obtained in terms of Fourier series. The numerical analysis is then carried out using the practically important properties of ultra-thin-film materials.

Fluid motion in a corrugated curved channel

In this paper, pressure driven flow between two corrugated curved walls is analyzed. The combined effects of the corrugations and the radius of curvature of the channel on the fluid flow are investigated using the boundary perturbation method. The results show that the peak of the velocity increases with the radius of curvature and the width of the channel for a constant pressure gradient. The flow rate is increased by the corrugations for any phase difference between the corrugated curved walls depending on the corrugation wavenumber and the channel radius of curvature. For a sufficiently large corrugation wavenumber, the flow rate decreases, and the phase difference becomes irrelevant. However, the reduction in flow can be minimized by decreasing the channel radius of curvature. In general, a smooth curved channel will give the maximum flow rate for large corrugation wavenumber. The results of this study are consistent with those of a corrugated straight channel flow for sufficiently large radius of curvature.

Reaction-driven almost frictionless transport of neutrino

We adopt a verified theory of absolute reaction or transition-state theory as well as the boundary perturbation method to demonstrate the possible almost frictionless transport of reaction-driven (electron) neutrino (condensate) considering the carbon–nitrogen–oxygen cycle. The calculation of resistance as well as the shear viscosity depends crucially on the temperature, selection of activation energy and activation volume.

Optimal Form for Compliance of Membrane Boundary Shift in Nonlinear Case

In this work, we search the existence shifting compliance optimal form of some boundary membrane, which is not elastic and not isotropic, generating nonlinear PDE. An optimal form of the elastic membrane described by the p-Laplacian is investigated. The boundary perturbation method due to Hadamard is applied in Sobolev spaces.

Analysis of electro-osmotic flow over a slightly bumpy plate

The present study is aimed to investigate the effects of wavy roughness on electro-osmotic (EO) flow over a wavy plate. The waviness of the plate is modeled by the product of two cosinoidal functions, and the roughness (ε) is defined to be the ratio of the wavy amplitude to the Debye length. The effects are examined with respect to the roughness ε and different wave numbers (α and β) of the plate waviness. The analysis of the EO flow over the wavy plate is carried out for the applied electric potential, the potential for the electric double layer, as well as the EO flow velocity and pressure field under the Debye-Hückel approximation by using a boundary perturbation method. It is found that the velocity component along the direction of the applied electric field is modified by a second-order term of the roughness, though the same velocity component near the wavy wall exhibits periodic behaviors in phase with the plate waviness. The mean flow rate deficit (ε2μ2) due to the surface roughness presents a sophisticated dependence on the longitudinal wave number (α) and transverse wave number (β) of the plate waviness, yet the flow deficit is linear in α for small α at β = 0, and shows a long wavelength limit singularity at β = 0 for α ≠ 0.