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2020年 第41卷 第5期    刊出日期：2020-05-01

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论文

Homotopy Coiflets wavelet solution of electrohydrodynamic flows in a circular cylindrical conduit

Anyang WANG, Hang XU, Qiang YU

2020, 41(5):  681-698.  doi:10.1007/s10483-020-2607-8

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In previous studies, the nonlinear problem of electrohydrodynamic (EHD) ion drag flows in a circular cylindrical conduit has been studied by several authors. However, those studies seldom involve the computation for large physical parameters such as the electrical Hartmann number and the magnitude parameter for the strength of the nonlinearity due to the existence of strong nonlinearity in these extreme cases. To overcome this faultiness, the newly-developed homotopy Coiflets wavelet method is extended to solve this EHD flow problem with strong nonlinearity. The validity and reliability of the proposed technique are verified. Particularly, the highly accurate homotopy-wavelet solution is obtained for extreme large parameters, which seems to be overlooked before. Discussion about the effects of related physical parameters on the axial velocity field is presented.



Hybrid nanomaterial flow and heat transport in a stretchable convergent/divergent channel: a Darcy-Forchheimer model

G. K. RAMESH, S. A. SHEHZAD, I. TLILI

2020, 41(5):  699-710.  doi:10.1007/s10483-020-2605-7

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The flow behavior in non-parallel walls is an important factor of any physical model including cavity flow and canals, which is applicable for diverging/converging channel. The present communication explains that the flow of the hybrid nanomaterial subjected to the convergent/divergent channel has non-parallel walls. It is assumed that the hybrid nanomaterial movement is in the porous region. A Darcy-Forchheimer medium of porosity is considered to interpret the porosity features. A useful similarity function is adopted to get the strong ordinary coupled equations. Numerical solutions are achieved through the Runge-Kutta-Fehlberg (RKF) fourth-fifth order method, and they are validated with the existing results. Physical nature of the involving constraints is reported with the help of plots. It is explored that the velocity of divergent channel decreases, and convergent channel enhances for the higher solid volume faction. Further, the presence of inertia coefficient and porosity parameter amplifies the velocity at the wall.

Anomalous reactivity of thermo-bioconvective nanofluid towards oxytactic microorganisms

S. I. ABDELSALAM, M. M. BHATTI

2020, 41(5):  711-724.  doi:10.1007/s10483-020-2609-6

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The peristaltic flow of a non-Newtonian nanofluid with swimming oxytactic microorganisms through a space between two infinite coaxial conduits is investigated. A variable magnetic field is applied on the flow. The bioconvection flow and heat transfer in the porous annulus are formulated, and appropriate transformations are used, leading to the non-dimensionalized ruling partial differential equation model. The model is then solved by using the homotopy perturbation scheme. The effects of the germane parameters on the velocity profile, temperature distribution, concentration distribution, motile microorganism profile, oxytactic profile, pressure rise, and outer and inner tube friction forces for the blood clot and endoscopic effects are analyzed and presented graphically. It is noticed that the pressure rise and friction forces attain smaller values for the endoscopic model than for the blood clot model. The present analysis is believed to aid applications constituting hemodynamic structures playing indispensable roles inside the human body since some blood clotting disorders, e.g., haemophilia, occur when some blood constituents on the artery wall get confined away from the wall joining the circulation system.

Non-axisymmetric Homann stagnation-point flow of Walter's B nanofluid over a cylindrical disk

M. KHAN, M. SARFRAZ, J. AHMED, L. AHMAD, C. FETECAU

2020, 41(5):  725-740.  doi:10.1007/s10483-020-2611-5

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The study of non-axisymmetric Homann stagnation-point flow of Walter’s B nanofluid along with magnetohydrodynamic (MHD) and non-linear Rosseland thermal radiation over a cylindrical disk in the existence of the time-independent free stream is considered. Moreover, the notable impacts of thermophoresis and Brownian motion are analyzed by Buongiorno’s model. The momentum, energy, and concentration equations are converted into the dimensionless coupled ordinary differential equations via similarity transformations, which are later numerically solved by altering the values of the pertinent parameters. The numerical and asymptotic solutions for the large shear-to-strain rate ratio γ = a/b for the parameters of the displacement thicknesses and the wall-shear stress are computed by perturbative expansion and analyzed. Furthermore, the technique bvp4c in MATLAB is deployed as an efficient method to analyze the calculations for the non-dimensional velocities, temperature, displacement thickness, and concentration profiles. It is observed that the two-dimensional displacement thickness parameters α and β are reduced due to the viscoelasticity and magnetic field effects. Moreover, when the shear-to-strain rate ratio approaches infinity, α is closer to its asymptotic value, while β and the three-dimensional displacement thickness parameter δ₁ show the opposite trend. The outcomes of the viscoelasticity and the magnetic field on the skin friction are also determined. It is concluded that f″(0) reaches its asymptotic behavior when the shearto-strain rate ratio approaches infinity. Meanwhile, ge(0) shows different results.

Darcy-Forchheimer flow by rotating disk with partial slip

T. HAYAT, F. HAIDER, T. MUHAMMAD, A. ALSAEDI

2020, 41(5):  741-752.  doi:10.1007/s10483-020-2608-9

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The viscous dissipation and heat transfer in the Darcy-Forchheimer flow by a rotating disk are examined. The partial slip conditions are invoked. The optimal series solutions are computed via the optimal homotopic analysis method (OHAM). The thermophoresis and Brownian motions are studied. The Darcy-Forchheimer relation characterizes the porous space. The roles of influential variables on the physical quantities are graphically examined. A reduction in the local Nusselt number is observed through thermophoresis and thermal slip parameters. The local Sherwood number depicts an increasing trend for the higher Brownian motion and concentration slip parameters.

Chebyshev spectral variational integrator and applications

Zhonggui YI, Baozeng YUE, Mingle DENG

2020, 41(5):  753-768.  doi:10.1007/s10483-020-2602-8

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The Chebyshev spectral variational integrator (CSVI) is presented in this paper. Spectral methods have aroused great interest in approximating numerically a smooth problem for their attractive geometric convergence rates. The geometric numerical methods are praised for their excellent long-time geometric structure-preserving properties. According to the generalized Galerkin framework, we combine two methods together to construct a variational integrator, which captures the merits of both methods. Since the interpolating points of the variational integrator are chosen as the Chebyshev points, the integration of Lagrangian can be approximated by the Clenshaw-Curtis quadrature rule, and the barycentric Lagrange interpolation is presented to substitute for the classic Lagrange interpolation in the approximation of configuration variables and the corresponding derivatives. The numerical float errors of the first-order spectral differentiation matrix can be alleviated by using a trigonometric identity especially when the number of Chebyshev points is large. Furthermore, the spectral variational integrator (SVI) constructed by the Gauss-Legendre quadrature rule and the multi-interval spectral method are carried out to compare with the CSVI, and the interesting kink phenomena for the Clenshaw-Curtis quadrature rule are discovered. The numerical results reveal that the CSVI has an advantage on the computing time over the whole progress and a higher accuracy than the SVI before the kink position. The effectiveness of the proposed method is demonstrated and verified perfectly through the numerical simulations for several classical mechanics examples and the orbital propagation for the planet systems and the Solar system.

A subspace expanding technique for global zero finding of multi-degree-of-freedom nonlinear systems

Zigang LI, Jun JIANG, Ling HONG, J. Q. SUN

2020, 41(5):  769-784.  doi:10.1007/s10483-020-2604-6

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A subspace expanding technique (SET) is proposed to efficiently discover and find all zeros of nonlinear functions in multi-degree-of-freedom (MDOF) engineering systems by discretizing the space into smaller subdomains, which are called cells. The covering set of the cells is identified by parallel calculations with the root bracketing method. The covering set can be found first in a low-dimensional subspace, and then gradually extended to higher dimensional spaces with the introduction of more equations and variables into the calculations. The results show that the proposed SET is highlyefficient for finding zeros in high-dimensional spaces. The subdivision technique of the cell mapping method is further used to refine the covering set, and the obtained numerical results of zeros are accurate. Three examples are further carried out to verify the applicability of the proposed method, and very good results are achieved. It is believed that the proposed method will significantly enhance the ability to study the stability, bifurcation, and optimization problems in complex MDOF nonlinear dynamic systems.

Dynamic and buckling analysis of polymer hybrid composite beam with variable thickness

S. AFSHIN, M. H. YAS

2020, 41(5):  785-804.  doi:10.1007/s10483-020-2610-7

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This work deals with a study of the dynamic and buckling analysis of polymer hybrid composite (PHC) beam. The beam has variable thickness and is reinforced by carbon nanotubes (CNTs) and nanoclay (NC) simultaneously. The governing equations are derived based on the first shear deformation theory (FSDT). A three-phase HalpinTsai approach is used to predict the mechanical properties of the PHC. We focus our attention on the effect of the simultaneous addition of NC and CNT on the vibration and buckling analysis of the PHC beam with variable thickness. Also a comparison study is done on the sensation of three impressive parameters including CNT, NC weight fractions, and the shape factor of fillers on the mechanical properties of PHC beams, as well as fundamental frequencies of free vibrations and critical buckling load. The results show that the increase of shape factor value, NC, and CNT weight fractions leads to considerable reinforcement in mechanical properties as well as increase of the dimensionless fundamental frequency and buckling load. The variation of CNT weight fraction on elastic modulus is more sensitive rather than shear modulus but the effect of NC weight fraction on elastic and shear moduli is fairly the same. The shape factor values more than the medium level do not affect the mechanical properties.

A hybrid multi-degree-of-freedom vibration isolation platform for spacecrafts by the linear active disturbance rejection control

Weichao CHI, S. J. MA, J. Q. SUN

2020, 41(5):  805-818.  doi:10.1007/s10483-020-2606-5

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The hybrid vibration isolation, which takes advantages of both the passive and active approaches, has been an important solution for space missions. The objective of this paper is to design a vibration isolation platform for payloads on spacecrafts with the robust, wide bandwidth, and multi-degree-of-freedom (MDOF). The proposed solution is based on a parallel mechanism with six voice-coil motors (VCMs) as the actuators. The linear active disturbance resistance control (LADRC) algorithm is used for the active control. Numerical simulation results show that the vibration isolation platform performs effectively over a wide bandwidth, and the resonance introduced by the passive isolation is eliminated. The system robustness to the uncertainties of the structure is also verified by simulation.

Novel model of thermo-magneto-viscoelastic medium with variable thermal conductivity under effect of gravity

S. M. SAID

2020, 41(5):  819-832.  doi:10.1007/s10483-020-2603-9

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The basic equations for a homogeneous and isotropic thermo-magnetoviscoelastic medium are formulated based on three different theories, i.e., the GreenLindsay (G-L) theory, the coupled (CD) theory, and the Lord-Shulman (L-S) theory. The variable thermal conductivity is considered as a linear function of the temperature. Using suitable non-dimensional variables, these basic equations are solved via the eigenvalue approach. The medium is initially assumed to be stress-free and subject to a thermal shock. The numerical results reveal that the viscosity, the two-temperature parameter, the gravity term, and the magnetic field significantly influence the distribution of the physical quantities of the thermoelastic medium.