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2020年 第41卷 第8期    刊出日期：2020-08-01

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论文

Non-axisymmetric Homann MHD stagnation point flow of Al₂O₃-Cu/water hybrid nanofluid with shape factor impact

M. KHAN, J. AHMED, F. SULTANA, M. SARFRAZ

2020, 41(8):  1125-1138.  doi:10.1007/s10483-020-2638-6

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The heat transfer of Homann flow in the stagnation region of the Al₂O₃-Cu/water hybrid nanofluid is investigated by adopting the Tiwari-Das model over a cylindrical disk. The effects of the nanoparticle shape, the viscous dissipation, and the nonlinear radiation are considered. The governing equations are obtained by using similarity transformations, and the numerical outcomes for the flow and the temperature field are noted by bvp4c on MATLAB. The numerical solutions of the flow field are compared with the asymptotic behaviors of large shear-to-strain-rate ratio. The effects of variations of parameters involved are inspected for both nanofluid and hybrid nanofluid flows,temperature profiles, local Nusselt numbers, and skin frictions. It is concluded that the velocity and temperature fields in the hybrid nanophase function more rapidly than those in the nanofluid phase.



Nonlinear dynamical magnetosonic wave interactions and collisions in magnetized plasma

M. ISHAQ, Hang XU

2020, 41(8):  1139-1156.  doi:10.1007/s10483-020-2637-9

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The one-dimensional nonlinear dynamical wave interactions in a system of quasineutral two-fluid plasma in a constant magnetic field are investigated. The existence of the travelling wave solutions is discussed. The modulation stability of linear waves and the modulation instability of weakly nonlinear waves are presented. Both suggest that the Korteweg-de Vries (KdV) system is modulationally stable. Besides, the wave interactions including the periodic wave interaction and the solitary wave interaction are captured and presented. It is shown that these interacting waves alternately exchange their energy during propagation. The Fourier spectrum analysis is used to depict the energy transformation between the primary and harmonic waves. It is known that the wave interactions in magnetized plasma play an important role in various processes of heating and energy transportation in space and astrophysical plasma. However, few researchers have considered such magnetohydrodynamic (MHD) wave interactions in plasma. It is expected that this work can provide additional insight into understanding of behaviors of MHD wave interactions.

Transportation of heat through Cattaneo-Christov heat flux model in non-Newtonian fluid subject to internal resistance of particles

M. I. KHAN, F. ALZAHRANI

2020, 41(8):  1157-1166.  doi:10.1007/s10483-020-2641-9

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Thermal conduction which happens in all phases (liquid, solid, and gas) is the transportation of internal energy through minuscule collisions of particles and movement of electrons within a working body. The colliding particles comprise electrons, molecules, and atoms, and transfer disorganized microscopic potential and kinetic energy, mutually known as the internal energy. In engineering sciences, heat transfer comprises the processes of convection, thermal radiation, and sometimes mass transportation. Typically, more than one of these procedures may happen in a given circumstance. We use the Cattaneo-Christov (CC) heat flux model instead of the Fourier law of heat conduction to discuss the behavior of heat transportation. A mathematical model is presented for the Cattaneo-Christov double diffusion (CCDD) in the flow of a non-Newtonian nanofluid (the Jeffrey fluid) towards a stretched surface. The magnetohydrodynamic (MHD) fluid is considered. The behaviors of heat and mass transportation rates are discussed with the CCDD. These models are based on Fourier's and Fick's laws. The convective transportation in nanofluids is discussed, subject to thermophoresis and Brownian diffusions. The nonlinear governing flow expression is first altered into ordinary differential equations via appropriate transformations, and then numerical solutions are obtained through the built-in-shooting method. The impact of sundry flow parameters is discussed on the velocity, the skin friction coefficient, the temperature, and the concentration graphically. It is reported that the velocity of material particles decreases with higher values of the Deborah number and the ratio of the relaxation to retardation time parameter. The temperature distribution enhances when the Brownian motion and thermophoresis parameters increase. The concentration shows contrasting impact versus the Lewis number and the Brownian motion parameter. It is also noticed that the skin friction coefficient decreases when the ratio of the relaxation to retardation time parameter increases.

Heat transfer and Helmholtz-Smoluchowski velocity in Bingham fluid flow

A. SALEEM, M. N. KIANI, S. NADEEM, A. ISSAKHOV

2020, 41(8):  1167-1178.  doi:10.1007/s10483-020-2636-8

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A mathematical study is developed for the electro-osmotic flow of a nonNewtonian fluid in a wavy microchannel in which a Bingham viscoplastic fluid model is considered. For electric potential distributions, a Poisson-Boltzmann equation is employed in the presence of an electrical double layer (EDL). The analytical solutions of dimensionless boundary value problems are obtained with the Debye-Huckel theory, the lubrication theory, and the long wavelength approximations. The effects of the Debyelength parameter, the plug flow width, the Helmholtz-Smoluchowski velocity, and the Joule heating on the normalized temperature, the velocity, the pressure gradient, the volumetric flow rate, and the Nusselt number for heat transfer are evaluated in detail using graphs. The analysis provides important findings regarding heat transfer in electroosmotic flows through a wavy microchannel.

Lattice Boltzmann study of the interaction between a single solid particle and a thin liquid film

Xiaojun QUAN, Xuewen LIU, Jinjing LI, Xunji GAO

2020, 41(8):  1179-1194.  doi:10.1007/s10483-020-2639-7

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The isothermal single-component multi-phase lattice Boltzmann method (LBM) combined with the particle motion model is used to simulate the detailed process of liquid film rupture induced by a single spherical particle. The entire process of the liquid film rupture can be divided into two stages. In Stage 1, the particle contacts with the liquid film and moves into it due to the interfacial force and finally penetrates the liquid film. Then in Stage 2, the upper and lower liquid surfaces of the thin film are driven by the capillary force and approach to each other along the surface of the particle, resulting in a complete rupture. It is found that a hydrophobic particle with a contact angle of 106.7° shows the shortest rupture duration when the liquid film thickness is less than the particle radius. When the thickness of the liquid film is greater than the immersed depth of the particle at equilibrium, the time of liquid film rupture caused by a hydrophobic particle will be increased. On the other hand, a moderately hydrophilic particle can form a bridge in the middle of the liquid film to enhance the stability of the thin liquid film.

Von Kármán rotating flow of Maxwell nanofluids featuring the Cattaneo-Christov theory with a Buongiorno model

A. AHMED, M. KHAN, J. AHMED, A. HAFEEZ

2020, 41(8):  1195-1208.  doi:10.1007/s10483-020-2632-8

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This research paper analyzes the transport of thermal and solutal energy in the Maxwell nanofluid flow induced above the disk which is rotating with a constant angular velocity. The significant features of thermal and solutal relaxation times of fluids are studied with a Cattaneo-Christov double diffusion theory rather than the classical Fourier's and Fick's laws. A novel idea of a Buongiorno nanofluid model together with the Cattaneo-Christov theory is introduced for the first time for the Maxwell fluid flow over a rotating disk. Additionally, the thermal and solutal distributions are controlled with the impacts of heat source and chemical reaction. The classical von Kármán similarities are used to acquire the non-linear system of ordinary differential equations (ODEs). The analytical series solution to the governing ODEs is obtained with the well-known homotopy analysis method (HAM). The validation of results is provided with the published results by the comparison tables. The graphically presented outcomes for the physical problem reveal that the higher values of the stretching strength parameter enhance the radial velocity and decline the circumferential velocity. The increasing trend is noted for the axial velocity profile in the downward direction with the higher values of the stretching strength parameter. The higher values of the relaxation time parameters in the Cattaneo-Christov theory decrease the thermal and solutal energy transport in the flow of Maxwell nanoliquids. The higher rate of the heat transport is observed in the case of a larger thermophoretic force.

Thermal vibration of functionally graded porous nanocomposite beams reinforced by graphene platelets

M. H. YAS, S. RAHIMI

2020, 41(8):  1209-1226.  doi:10.1007/s10483-020-2634-6

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The thermal vibration of functionally graded (FG) porous nanocomposite beams reinforced by graphene platelets (GPLs) is studied. The beams are exposed to the thermal gradient with a multilayer structure. The temperature varies linearly across the thickness direction. Three different types of dispersion patterns of GPLs as well as porosity distributions are presented. The material properties vary along the thickness direction. By using the mechanical parameters of closed-cell cellular solid, the variation of Poisson's ratio and the relation between the porosity coefficient and the mass density under the Gaussian random field (GRF) model are obtained. By using the Halpin-Tsai micromechanics model, the elastic modulus of the nanocomposite is achieved. The equations of motion based on the Timoshenko beam theory are obtained by using Hamilton's principle. These equations are discretized and solved by using the generalized differential quadrature method (GDQM) to obtain the fundamental frequencies. The effects of the weight fraction, the dispersion model, the geometry, and the size of GPLs, as well as the porosity distribution, the porosity coefficient, the boundary condition, the metal matrix, the slenderness ratio, and the thermal gradient are presented.

Large deflection response-based geometrical nonlinearity of nanocomposite structures reinforced with carbon nanotubes

S. ZGHAL, A. FRIKHA, F. DAMMAK

2020, 41(8):  1227-1250.  doi:10.1007/s10483-020-2633-9

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This paper deals with the nonlinear large deflection analysis of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates and panels using a finite element method. Based on the first-order shear deformation theory (FSDT), the proposed model takes into account the transverse shear deformations and incorporates the geometrical nonlinearity type. A C⁰ isoparametric finite shell element is developed for the present nonlinear model with the description of large displacements and finite rotations. By adopting the extended rule of mixture, the effective material properties of FG-CNTRCs are approximated with the introduction of some efficiency parameters. Four carbon nanotube (CNT) distributions, labeled uniformly distributed (UD)-CNT, FG-VCNT, FG-O-CNT, and FG-X-CNT, are considered. The solution procedure is carried out via the Newton-Raphson incremental technique. Various numerical applications in both isotropic and CNTRC composite cases are performed to trace the potential of the present model. The effects of the CNT distributions, their volume fractions, and the geometrical characteristics on the nonlinear deflection responses of FG-CNTRC structures are highlighted via a detailed parametric study.

Effects of residual stress and viscous and hysteretic dampings on the stability of a spinning micro-shaft

A. A. MONAJEMI, M. MOHAMMADIMEHR

2020, 41(8):  1251-1268.  doi:10.1007/s10483-020-2640-8

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This study examines the effects of the residual stress and viscous and hysteretic dampings on the vibrational behavior and stability of a spinning Timoshenko micro-shaft. A modified couple stress theory (MCST) is used to elucidate the sizedependency of the micro-shaft spinning stability, and the equations of motion are derived by employing Hamilton's principle and a spatial beam for spinning micro-shafts. Moreover, a differential quadrature method (DQM) is presented, along with the exact solution for the forward and backward (FW-BW) complex frequencies and normal modes. The effects of the material length scale parameter (MLSP), the spinning speed, the viscous damping coefficient, the hysteretic damping, and the residual stress on the stability of the spinning micro-shafts are investigated. The results indicate that the MLSP, the internal dampings (viscous and hysteretic), and the residual stress have significant effects on the complex frequency and stability of the spinning micro-shafts. Therefore, it is crucial to take these factors into account while these systems are designed and analyzed. The results show that an increase in the MLSP leads to stiffening of the spinning micro-shaft, increases the FW-BW dimensionless complex frequencies of the system, and enhances the stability of the system. Additionally, a rise in the tensile residual stresses causes an increase in the FW-BW dimensionless complex frequencies and stability of the micro-shafts, while the opposite is true for the compressive residual stresses. The results of this research can be employed for designing spinning structures and controlling their vibrations, thus forestalling resonance.

Vibration suppression of magnetostrictive laminated beams resting on viscoelastic foundation

A. M. ZENKOUR, H. D. EL-SHAHRANY

2020, 41(8):  1269-1286.  doi:10.1007/s10483-020-2635-7

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The vibration suppression analysis of a simply-supported laminated composite beam with magnetostrictive layers resting on visco-Pasternak's foundation is presented. The constant gain distributed controller of the velocity feedback is utilized for the purpose of vibration damping. The formulation of displacement field is proposed according to Euler-Bernoulli's classical beam theory (ECBT), Timoshenko's first-order beam theory (TFBT), Reddy's third-order shear deformation beam theory, and the simple sinusoidal shear deformation beam theory. Hamilton's principle is utilized to give the equations of motion and then to describe the vibration of the current beam. Based on Navier's approach, the solution of the dynamic system is obtained. The effects of the material properties, the modes, the thickness ratios, the lamination schemes, the magnitudes of the feedback coefficient, the position of magnetostrictive layers at the structure, and the foundation modules are extensively studied and discussed.