当期目录

2021年 第42卷 第1期    刊出日期：2021-01-01

上一期    下一期

论文

Size-dependent thermoelasticity of a finite bi-layered nanoscale plate based on nonlocal dual-phase-lag heat conduction and Eringen's nonlocal elasticity

Zhangna XUE, Gongqi CAO, Jianlin LIU

2021, 42(1):  1-16.  doi:10.1007/s10483-021-2692-5

摘要 ( 395 )   HTML ( 26)   PDF (786KB) ( 227 )  

参考文献 | 相关文章 | 多维度评价

The size effects on heat conduction and elastic deformation are becoming significant along with the miniaturization of the device and wide application of ultrafast lasers. In this work, to better describe the transient responses of nanostructures, a size-dependent thermoelastic model is established based on nonlocal dual-phase-lag (N-DPL) heat conduction and Eringen's nonlocal elasticity, which is applied to the one-dimensional analysis of a finite bi-layered nanoscale plate under a sudden thermal shock. In the numerical part, a semi-analytical solution is obtained by using the Laplace transform method, upon which the effects of size-dependent characteristic lengths and material properties of each layer on the transient responses are discussed systematically. The results show that the introduction of the elastic nonlocal parameter of Medium 1 reduces the displacement and compressive stress, while the thermal nonlocal parameter of Medium 1 increases the deformation and compressive stress. These findings may be beneficial to the design of nano-sized and multi-layered devices.



Three-dimensional steady-state closed form solution for multilayered fluid-saturated anisotropic finite media due to surface/internal point source

Lianzhi YANG, Fanmin HE, Yang LI, Zhiyong SONG

2021, 42(1):  17-38.  doi:10.1007/s10483-021-2685-9

摘要 ( 353 )   HTML ( 14)   PDF (1029KB) ( 95 )  

参考文献 | 相关文章 | 多维度评价

A three-dimensional (3D) steady-state solution of fluid saturated anisotropic finite media is presented. The eigenequation method and the pseudo-Stroh formalism are used to obtain the exact solution for homogeneous saturated finite media. The propagator matrix method is introduced to deal with the corresponding multilayered poroelastic media. The poroelastic solutions due to surface or internal point fluid source are obtained. The comparison of the results of the saturated isotropic media in a half space and those obtained by the finite element method is given to illustrate the accuracy of the solution in a finite domain. Numerical solutions of a sandwich poroelastic medium are presented to analyze its hydromechanical behaviors. Two ratios of the horizontal permeability to vertical permeability and different source positions are investigated. The results show that the fluid parameters and source positions have great influence on the hydromechanical behaviors of the layered media.

Magnetophotothermal interaction in a rotating solid cylinder of semiconductor silicone material with time dependent heat flow

A. E. ABOUELREGAL

2021, 42(1):  39-52.  doi:10.1007/s10483-021-2682-6

摘要 ( 334 )   HTML ( 13)   PDF (823KB) ( 75 )  

参考文献 | 相关文章 | 多维度评价

A mathematical model linking thermoelasticity to photothermal experiments is proposed with the consideration of the photothermal effect. The system equations for coupled plasma, heat conduction with phase-lags (PLs), and motion equations are introduced and solved by using the Laplace transform technique. The photothermal, thermal, and elastic waves in a rotating solid cylinder of semiconductor material are analyzed with the proposed model. The cylinder surface is constrained and subjected to a time-dependent pulse heat flux. The sensitivity of the physical fields for the angular velocity, PLs, and thermal vibration parameters is investigated. In addition, the effects of the effective parameters on the physical quantities are graphically illustrated and discussed in detail.

Multi-resonator coupled metamaterials for broadband vibration suppression

Pengcheng ZHAO, Kai ZHANG, Cheng ZHAO, Zichen DENG

2021, 42(1):  53-64.  doi:10.1007/s10483-021-2684-8

摘要 ( 383 )   HTML ( 9)   PDF (1643KB) ( 202 )  

参考文献 | 相关文章 | 多维度评价

In this study, multi-resonator coupled metamaterials (MRCMs) with local resonators are proposed to obtain the multiple and wide band gaps. Kinetic models of the MRCMs are established, and the boundary conditions of the unit cell are obtained with Bloch's theorem. The effects of structural parameters, including the mass of the resonator and the spring stiffness, on the distributions of the band gaps are studied. Furthermore, the frequency domain responses and the time domain responses are calculated for analyzing the structural vibration characteristics and the effects of damping on structural vibration. The results show that the frequency domain response can accurately express the distributions of the band gaps of the MRCMs, and we can increase the number and the width of the band gaps by using the MRCMs for the superior vibration suppression capability.

Quantifying the parameter dependent basin of the unsafe regime of asymmetric Lévy-noise-induced critical transitions

Jinzhong MA, Yong XU, Yongge LI, Ruilan TIAN, Shaojuan MA, J. KURTHS

2021, 42(1):  65-84.  doi:10.1007/s10483-021-2672-8

摘要 ( 310 )   HTML ( 7)   PDF (2300KB) ( 87 )  

参考文献 | 相关文章 | 多维度评价

In real systems, the unpredictable jump changes of the random environment can induce the critical transitions (CTs) between two non-adjacent states, which are more catastrophic. Taking an asymmetric Lévy-noise-induced tri-stable model with desirable, sub-desirable, and undesirable states as a prototype class of real systems, a prediction of the noise-induced CTs from the desirable state directly to the undesirable one is carried out. We first calculate the region that the current state of the given model is absorbed into the undesirable state based on the escape probability, which is named as the absorbed region. Then, a new concept of the parameter dependent basin of the unsafe regime (PDBUR) under the asymmetric Lévy noise is introduced. It is an efficient tool for approximately quantifying the ranges of the parameters, where the noise-induced CTs from the desirable state directly to the undesirable one may occur. More importantly, it may provide theoretical guidance for us to adopt some measures to avert a noise-induced catastrophic CT.

Dynamic quasi-continuum model for plate-type nano-materials and analysis of fundamental frequency

Chunxiao XIA, Wenlong XU, Guohua NIE

2021, 42(1):  85-94.  doi:10.1007/s10483-021-2688-8

摘要 ( 267 )   HTML ( 4)   PDF (1140KB) ( 62 )  

参考文献 | 相关文章 | 多维度评价

A dynamic quasi-continuum model is presented to analyze free vibration of plate-type cubic crystal nano-materials. According to the Hamilton principle, fundamental governing equations in terms of displacement components and angles of rotations are given. As an application of the model, the cylindrical bending deformation of the structure fixed at two ends is analyzed, and a theoretical formula evaluating the fundamental frequency is obtained by using Galerkin's method. Meanwhile, the solution for the classical continuous plate model is also derived, and the size-dependent elastic modulus and Poisson's ratio are taken in computation. The frequencies corresponding to different atomic layers are numerically presented for the plate-type NaCl nano-materials. Furthermore, a molecular dynamics (MD) simulation is conducted with the code LAMMPS. The comparison shows that the present quasi-continuum model is valid, and it may be used as an alternative model, which reflects scale effects in analyzing dynamic behaviors of such plate-type nano-materials.

Irreversibility investigation of Casson fluid flow in an inclined channel subject to a Darcy-Forchheimer porous medium: a numerical study

A. ROJA, B. J. GIREESHA, B. NAGARAJA

2021, 42(1):  95-108.  doi:10.1007/s10483-021-2681-9

摘要 ( 289 )   HTML ( 6)   PDF (907KB) ( 114 )  

参考文献 | 相关文章 | 多维度评价

The heat transfer and entropy generation characteristics of the magnetohydrodynamic Casson fluid flow through an inclined microchannel with convective boundary conditions are analyzed. Further, the effects of the viscous forces, Joule heating, heat source/sink, and radiation on the flow are taken into account. The non-dimensional transformations are used to solve the governing equations. Then, the reduced system is resolved by the fourth-fifth order Runge-Kutta-Fehlberg method along with the shooting technique. The effects of different physical parameters on the heat transfer and entropy generation are discussed in detail through graphs. From the perspective of numerical results, it is recognized that the production of entropy can be improved with the Joule heating, viscous dissipation, and convective heating aspects. It is concluded that the production of entropy is the maximum with increases in the Casson parameter, the angle of inclination, and the Hartmann number. Both the Reynolds number and the radiation parameter cause the dual impact on entropy generation.

Asymptotics for filtration of polydisperse suspension with small impurities

L. I. KUZMINA, Y. V. OSIPOV, T. N. GORBUNOVA

2021, 42(1):  109-126.  doi:10.1007/s10483-021-2690-6

摘要 ( 270 )   HTML ( 3)   PDF (780KB) ( 177 )  

参考文献 | 相关文章 | 多维度评价

A model for deep bed filtration of a polydisperse suspension with small impurities in a porous medium is considered. Different suspended particles move with the same velocity as the carrier water and get blocked in the pore throats due to the size-exclusion mechanism of particle retention. A solution of the model in the form of a traveling wave is obtained. The global exact solution for a multiparticle filtration with one high concentration and several low concentrations of suspended particles is obtained in an explicit form. The analytic solutions for a bidisperse suspension with large and small particles are constructed. The profiles of the retained small particles change monotony with time. The global asymptotics for the filtration of a polydisperse suspension with small kinetic rates is constructed in the whole filtration zone.

Regular perturbation solution of Couette flow (non-Newtonian) between two parallel porous plates: a numerical analysis with irreversibility

M. NAZEER, M. I. KHAN, S. KADRY, Yuming CHU, F. AHMAD, W. ALI, M. IRFAN, M. SHAHEEN

2021, 42(1):  127-142.  doi:10.1007/s10483-021-2677-9

摘要 ( 385 )   HTML ( 5)   PDF (1457KB) ( 115 )  

参考文献 | 相关文章 | 多维度评价

The unavailability of wasted energy due to the irreversibility in the process is called the entropy generation. An irreversible process is a process in which the entropy of the system is increased. The second law of thermodynamics is used to define whether the given system is reversible or irreversible. Here, our focus is how to reduce the entropy of the system and maximize the capability of the system. There are many methods for maximizing the capacity of heat transport. The constant pressure gradient or motion of the wall can be used to increase the heat transfer rate and minimize the entropy. The objective of this study is to analyze the heat and mass transfer of an Eyring-Powell fluid in a porous channel. For this, we choose two different fluid models, namely, the plane and generalized Couette flows. The flow is generated in the channel due to a pressure gradient or with the moving of the upper lid. The present analysis shows the effects of the fluid parameters on the velocity, the temperature, the entropy generation, and the Bejan number. The nonlinear boundary value problem of the flow problem is solved with the help of the regular perturbation method. To validate the perturbation solution, a numerical solution is also obtained with the help of the built-in command NDSolve of MATHEMATICA 11.0. The velocity profile shows the shear thickening behavior via first-order Eyring-Powell parameters. It is also observed that the profile of the Bejan number has a decreasing trend against the Brinkman number. When η_i → 0 (i=1, 2, 3), the Eyring-Powell fluid is transformed into a Newtonian fluid.

Analysis of a two-grid method for semiconductor device problem

Ying LIU, Yanping CHEN, Yunqing HUANG, Qingfeng LI

2021, 42(1):  143-158.  doi:10.1007/s10483-021-2696-5

摘要 ( 333 )   HTML ( 6)   PDF (2007KB) ( 85 )  

参考文献 | 相关文章 | 多维度评价

The mathematical model of a semiconductor device is governed by a system of quasi-linear partial differential equations. The electric potential equation is approximated by a mixed finite element method, and the concentration equations are approximated by a standard Galerkin method. We estimate the error of the numerical solutions in the sense of the L^q norm. To linearize the full discrete scheme of the problem, we present an efficient two-grid method based on the idea of Newton iteration. The main procedures are to solve the small scaled nonlinear equations on the coarse grid and then deal with the linear equations on the fine grid. Error estimation for the two-grid solutions is analyzed in detail. It is shown that this method still achieves asymptotically optimal approximations as long as a mesh size satisfies H=O(h^1/2). Numerical experiments are given to illustrate the efficiency of the two-grid method.