Showing papers in "Applied Mathematics and Mechanics-english Edition in 2020"

MHD flow and heat transfer of a hybrid nanofluid past a permeable stretching/shrinking wedge

Abstract: The steady flow and heat transfer of a hybrid nanofluid past a permeable stretching/shrinking wedge with magnetic field and radiation effects are studied. The governing equations of the hybrid nanofluid are converted to the similarity equations by techniques of the similarity transformation. The bvp4c function that is available in MATLAB software is utilized for solving the similarity equations numerically. The numerical results are obtained for selected different values of parameters. The results discover that two solutions exist, up to a certain value of the stretching/shrinking and suction strengths. The critical value in which the solution is in existence decreases as nanoparticle volume fractions for copper and wedge angle parameter increase. It is also found that the hybrid nanofluid enhances the heat transfer rate compared with the regular nanofluid. The reduction of the heat transfer rate is observed with the increase in radiation parameter. The temporal stability analysis is performed to analyze the stability of the dual solutions, and it is revealed that only one of them is stable and physically reliable.

Effects of magnetic Reynolds number on swimming of gyrotactic microorganisms between rotating circular plates filled with nanofluids

Abstract: The three-dimensional (3D) nanofluid flow among the rotating circular plates filled with nanoparticles and gyrotactic microorganisms is studied. A generalized form of the magnetic Reynolds number is used for the mathematical modeling of the ferro-nanofluid flow. The torque effects on the lower and upper plates are calculated. A differential transform scheme with the Pade approximation is used to solve the coupled highly nonlinear ordinary differential equations. The results show that the squeeze Reynolds number significantly suppresses the temperature, microorganism, and nanoparticle concentration distribution, and agree well with those obtained by the numerical method.

Anomalous reactivity of thermo-bioconvective nanofluid towards oxytactic microorganisms

Abstract: The peristaltic flow of 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 en-doscopic 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.

Size-dependent shear buckling response of FGM skew nanoplates modeled via different homogenization schemes

Abstract: The size effects on the shear buckling behaviors of skew nanoplates made of functionally graded materials (FGMs) are presented. The material properties are supposed to be changed uniformly from the ceramic phase to the metal one along the plate thickness. To estimate the associated effective material properties, various homogeniza-tion schemes including the Reuss model, the Voigt model, the Mori-Tanaka model, and the Hashin-Shtrikman bound model are used. The nonlocal elasticity theory together with the oblique coordinate system is applied to the higher-order shear deformation plate theory to develop a size-dependent plate model for the shear buckling analysis of FGM skew nanoplates. The Ritz method using Gram-Schmidt shape functions is used to solve the size-dependent problem. It is found that the significance of the nonlocality in the reduction of the shear buckling load of an FGM skew nanoplate increases for a higher value of the material property gradient index. Also, by increasing the skew angle, the critical shear buckling load of an FGM skew nanoplate enhances. This pattern becomes a bit less significant for a higher value of the material property gradient index. Furthermore, among various homogenization models, the Voigt and Reuss models in order estimate the overestimated and underestimated shear buckling loads, and the difference between them reduces by increasing the aspect ratio of the skew nanoplate.

Vibration reduction evaluation of a linear system with a nonlinear energy sink under a harmonic and random excitation

Abstract: The nonlinear behaviors and vibration reduction of a linear system with nonlinear energy sink (NES) are investigated. The linear system is excited by a harmonic and random base excitation, consisting of a mass block, a linear spring, and a linear viscous damper. The NES is composed of a mass block, a linear viscous damper, and a spring with ideal cubic nonlinear stiffness. Based on the generalized harmonic function method, the steady-state Fokker-Planck-Kolmogorov equation is presented to reveal the response of the system. The path integral method based on the Gauss-Legendre polynomial is used to achieve the numerical solutions. The performance of vibration reduction is evaluated by the displacement and velocity transition probability densities, the transmissibility transition probability density, and the percentage of the energy absorption transition probability density of the linear oscillator. The sensitivity of the parameters is analyzed for varying the nonlinear stiffness coefficient and the damper ratio. The investigation illustrates that a linear system with NES can also realize great vibration reduction under harmonic and random base excitations and random bifurcation may appear under different parameters, which will affect the stability of the system.

A revised Cattaneo-Christov micropolar viscoelastic nanofluid model with combined porosity and magnetic effects

Abstract: The dynamics of non-Newtonian fluids along with nanoparticles is quite interesting with numerous industrial applications. The current predominately predictive modeling deals with the flow of the viscoelastic micropolar fluid in the presence of nanoparticles. A progressive amendment in the heat and concentration equations is made by exploiting the Cattaneo-Christov (C-C) heat and mass flux expressions. Besides, the thermal radiation effects are contributed in the energy equation and aspect of the radiation parameter, and the Prandtl number is specified by the one-parameter approach. The formulated expressions are converted to the dimensionless forms by relevant similarity functions. The analytical solutions to these expressions have been erected by the homotopy analysis method. The variations in physical quantities, including the velocity, the temperature, the effective local Nusselt number, the concentration of nanoparticles, and the local Sherwood number, have been observed under the influence of emerging parameters. The results have shown good accuracy compared with those of the existing literature.

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

Abstract: 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 contrast 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

Numerical simulation of MHD natural convection flow in a wavy cavity filled by a hybrid Cu-Al2O3-water nanofluid with discrete heating

Abstract: We consider the combined effect of the magnetic field and heat transfer inside a square cavity containing a hybrid nanofluid (Cu-Al2O3-water). The upper and bottom walls of the cavity have a wavy shape. The temperature of the vertical walls is lower, the third part in the middle of the bottom wall is kept at a constant higher temperature, and the remaining parts of the bottom wall and the upper wall are thermally insulated. The magnetic field is applied under the angle γ, an opposite clockwise direction. For the numerical simulation, the finite element technique is employed. The ranges of the characteristics are as follows: the Rayleigh number (103 ⩽ Ra ⩽ 105), the Hartmann number (0 ⩽ Ha ⩽ 100), the nanoparticle hybrid concentration (ϕAl2o3, ϕCu = 0, 0.025, 0.05), the magnetic field orientation (0 ⩽ γ ⩽ 2π), and the Prandtl number Pr, the amplitude of wavy cavity A, and the number of waviness n are fixed at Pr = 7, A = 0.1, and n = 3, respectively. The comparison with a reported finding in the open literature is done, and the data are observed to be in very good agreement. The effects of the governing parameters on the energy transport and fluid flow parameters are studied. The results prove that the increment of the magnetic influence determines the decrease of the energy transference because the conduction motion dominates the fluid movement. When the Rayleigh number is raised, the Nusselt number is increased, too. For moderate Rayleigh numbers, the maximum ratio of the heat transfer takes place for the hybrid nanofluid and then the Cu-nanofluid, followed by the Al2O3-nanofluid. The nature of motion and energy transport parameters has been scrutinized.

Theoretical analysis on elastic buckling of nanobeams based on stress-driven nonlocal integral model

Abstract: Several studies indicate that Eringen’s nonlocal model may lead to some inconsistencies for both Euler-Bernoulli and Timoshenko beams, such as cantilever beams subjected to an end point force and fixed-fixed beams subjected a uniform distributed load. In this paper, the elastic buckling behavior of nanobeams, including both Euler-Bernoulli and Timoshenko beams, is investigated on the basis of a stress-driven nonlocal integral model. The constitutive equations are the Fredholm-type integral equations of the first kind, which can be transformed to the Volterra integral equations of the first kind. With the application of the Laplace transformation, the general solutions of the deflections and bending moments for the Euler-Bernoulli and Timoshenko beams as well as the rotation and shear force for the Timoshenko beams are obtained explicitly with several unknown constants. Considering the boundary conditions and extra constitutive constraints, the characteristic equations are obtained explicitly for the Euler-Bernoulli and Timoshenko beams under different boundary conditions, from which one can determine the critical buckling loads of nanobeams. The effects of the nonlocal parameters and buckling order on the buckling loads of nanobeams are studied numerically, and a consistent toughening effect is obtained.

Nonlinear primary resonance analysis of nanoshells including vibrational mode interactions based on the surface elasticity theory

Abstract: The deviation from the classical elastic characteristics induced by the free surface energy can be considerable for nanostructures due to the high surface to volume ratio. Consequently, this type of size dependency should be accounted for in the mechanical behaviors of nanoscale structures. In the current investigation, the influence of free surface energy on the nonlinear primary resonance of silicon nanoshells under soft harmonic external excitation is studied. In order to obtain more accurate results, the interaction between the first, third, and fifth symmetric vibration modes with the main oscillation mode is taken into consideration. Through the implementation of the Gurtin-Murdoch theory of elasticity into the classical shell theory, a size-dependent shell model is developed incorporating the effect of surface free energy. With the aid of the variational approach, the governing differential equations of motion including both of the cubic and quadratic nonlinearities are derived. Thereafter, the multi-time-scale method is used to achieve an analytical solution for the nonlinear size-dependent problem. The frequency-response and amplitude-response of the soft harmonic excited nanoshells are presented corresponding to different values of shell thickness and surface elastic constants as well as various vibration mode interactions. It is depicted that through consideration of the interaction between the higher symmetric vibration modes and the main oscillation mode, the hardening response of nanoshell changes to the softening one. This pattern is observed corresponding to both of the positive and negative values of the surface elastic constants and the surface residual stress.

A review of computational modeling and deep brain stimulation: applications to Parkinson’s disease

Abstract: Biophysical computational models are complementary to experiments and theories, providing powerful tools for the study of neurological diseases. The focus of this review is the dynamic modeling and control strategies of Parkinson's disease (PD). In previous studies, the development of parkinsonian network dynamics modeling has made great progress. Modeling mainly focuses on the cortex-thalamus-basal ganglia (CTBG) circuit and its sub-circuits, which helps to explore the dynamic behavior of the parkinsonian network, such as synchronization. Deep brain stimulation (DBS) is an effective strategy for the treatment of PD. At present, many studies are based on the side effects of the DBS. However, the translation from modeling results to clinical disease mitigation therapy still faces huge challenges. Here, we introduce the progress of DBS improvement. Its specific purpose is to develop novel DBS treatment methods, optimize the treatment effect of DBS for each patient, and focus on the study in closed-loop DBS. Our goal is to review the inspiration and insights gained by combining the system theory with these computational models to analyze neurodynamics and optimize DBS treatment.

Suppression of multiple modal resonances of a cantilever beam by an impact damper

Abstract: Impact dampers are usually used to suppress single mode resonance. The goal of this paper is to clarify the difference when the impact damper suppresses the resonances of different modes. A cantilever beam equipped with the impact damper is modeled. The elastic contact of the ball and the cantilever beam is described by using the Hertz contact model. The viscous damper between the ball and the cantilever beam is modeled to consume the vibrational energy of the cantilever beam. A piecewise ordinary differential-partial differential equation of the cantilever beam is established, including equations with and without the impact damper. The vibration responses of the cantilever beam with and without the impact damper are numerically calculated. The effects of the impact absorber parameters on the vibration reduction are examined. The results show that multiple resonance peaks of the cantilever beam can be effectively suppressed by the impact damper. Specifically, all resonance amplitudes can be reduced by a larger weight ball. Moreover, the impacting gap is very effective in suppressing the vibration of the cantilever beam. More importantly, there is an optimal impacting gap for each resonance mode of the cantilever beam, but the optimal gap for each mode is different.

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

Abstract: 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-V-CNT, 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.

Rotational flow of Oldroyd-B nanofluid subject to Cattaneo-Christov double diffusion theory

Abstract: A nanofluid is composed of a base fluid component and nanoparticles, in which the nanoparticles are dispersed in the base fluid. The addition of nanoparticles into a base fluid can remarkably improve the thermal conductivity of the nanofluid, and such an increment of thermal conductivity can play an important role in improving the heat transfer rate of the base fluid. Further, the dynamics of non-Newtonian fluids along with nanoparticles is quite interesting with numerous industrial applications. The present predominately predictive modeling studies the flow of the viscoelastic Oldroyd-B fluid over a rotating disk in the presence of nanoparticles. A progressive amendment in the heat and concentration equations is made by exploiting the Cattaneo-Christov heat and mass flux expressions. The characteristic of the Lorentz force due to the magnetic field applied normal to the disk is studied. The Buongiorno model together with the Cattaneo-Christov theory is implemented in the Oldroyd-B nanofluid flow to investigate the heat and mass transport mechanism. This theory predicts the characteristics of the fluid thermal and solutal relaxation time on the boundary layer flow. The von Karman similarity functions are utilized to convert the partial differential equations (PDEs) into ordinary differential equations (ODEs). A homotopic approach for obtaining the analytical solutions to the governing nonlinear problem is carried out. The graphical results are obtained for the velocity field, temperature, and concentration distributions. Comparisons are made for a limiting case between the numerical and analytical solutions, and the results are found in good agreement. The results reveal that the thermal and solutal relaxation time parameters diminish the temperature and concentration distributions, respectively. The axial flow decreases in the downward direction for higher values of the retardation time parameter. The impact of the thermophoresis parameter boosts the temperature distribution.

Darcy-Forchheimer flow with nonlinear mixed convection

Abstract: An analysis of the mixed convective flow of viscous fluids induced by a nonlinear inclined stretching surface is addressed. Heat and mass transfer phenomena are analyzed with additional effects of heat generation/absorption and activation energy, respectively. The nonlinear Darcy-Forchheimer relation is deliberated. The dimensionless problem is obtained through appropriate transformations. Convergent series solutions are obtained by utilizing an optimal homotopic analysis method (OHAM). Graphs depicting the consequence of influential variables on physical quantities are presented. Enhancement in the velocity is observed through the local mixed convection parameter while an opposite trend of the concentration field is noted for the chemical reaction rate parameter.

Vibration suppression of magnetostrictive laminated beams resting on viscoelastic foundation

Abstract: 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.

Merging phononic crystals and acoustic black holes

Abstract: Phononic crystals (PCs) have recently been developed as effective components for vibration suppression and sound absorption. As a typical design of PCs, wave attenuation occurs in the so-called stop-band. However, the structural response is still significantly large in the pass-band. In this paper, we combine PCs and acoustic black holes (ABHs) in a unique device, achieving a versatile device that can attenuate vibration in the stop-band, while suppress vibration in the pass-band. This approach provides a versatile platform for controlling vibration in a multiband with a simple design.

Improving control effects of absence seizures using single-pulse alternately resetting stimulation (SARS) of corticothalamic circuit

Abstract: Presently, we develop a simplified corticothalamic (SCT) model and propose a single-pulse alternately resetting stimulation (SARS) with sequentially applying anodic (A, “+”) or cathodic (C, “−”) phase pulses to the thalamic reticular (RE) nuclei, thalamus-cortex (TC) relay nuclei, and cortical excitatory (EX) neurons, respectively. Abatement effects of ACC-SARS of RE, TC, and EX for the 2Hz–4Hz spike and wave discharges (SWD) of absence seizures are then concerned. The m:n on-off ACC-SARS protocol is shown to effectively reduce the SWD with the least current consumption. In particular, when its frequency is out of the 2 Hz–4Hz SWD dominant rhythm, the desired seizure abatements can be obtained, which can be further improved by our proposed directional steering (DS) stimulation. The dynamical explanations for the SARS induced seizure abatements are lastly given by calculating the averaged mean firing rate (AMFR) of neurons and triggering averaged mean firing rates (TAMFRs) of 2Hz–4Hz SWD.

Interaction effects of DNA, RNA-polymerase, and cellular fluid on the local dynamic behaviors of DNA

Abstract: In view of the complex structure and environment, the dynamic analysis on deoxyribonucleic acid (DNA) is a challenge in the biophysics field. Considering the local interaction with ribonucleic acid (RNA)-polymerase as well as the dissipative effect of cellular fluid, a coupling sine-Gordon-type dynamic model is used to describe the rotational motions of the bases in DNA. First, the approximate symmetric form is constructed. Then, the wave form and the wave velocity of the kink solution to the proposed dynamic model are investigated by a Runge-Kutta structure-preserving scheme based on the generalized multi-symplectic idea. The numerical results indicate that, the strengthening of the local interaction between DNA and RNA-polymerase described by the coupling potential makes the form of the kink solution steep, while the appearance of the friction between DNA and cellular fluid makes the form of the kink solution flat. In addition, the appearance of the friction decreases the velocities of both the symplectic configuration and the anti-symplectic configuration with different degrees. The above findings are beneficial to comprehend the DNA transcription mechanism.

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

Abstract: 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 $$\gamma = {b \over a}$$ 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 $${\widetilde{f}^"}\left( 0 \right)$$ (0) reaches its asymptotic behavior when the shear-to-strain rate ratio approaches infinity. Meanwhile, $${\widetilde{g}^"}\left( 0 \right)$$ (0) shows different results.

Extremely large-amplitude oscillation of soft pipes conveying fluid under gravity

Abstract: In this work, the nonlinear behaviors of soft cantilevered pipes containing internal fluid flow are studied based on a geometrically exact model, with particular focus on the mechanism of large-amplitude oscillations of the pipe under gravity Four key parameters, including the flow velocity, the mass ratio, the gravity parameter, and the inclination angle between the pipe length and the gravity direction, are considered to affect the static and dynamic behaviors of the soft pipe The stability analyses show that, provided that the inclination angle is not equal to π, the soft pipe is stable at a low flow velocity and becomes unstable via flutter once the flow velocity is beyond a critical value As the inclination angle is equal to π, the pipe experiences, in turn, buckling instability, regaining stability, and flutter instability with the increase in the flow velocity Interestingly, the stability of the pipe can be either enhanced or weakened by varying the gravity parameter, mainly dependent on the value of the inclination angle In the nonlinear dynamic analysis, it is demonstrated that the post-flutter amplitude of the soft pipe can be extremely large in the form of limit-cycle oscillations Besides, the oscillating shapes for various inclination angles are provided to display interesting dynamical behaviors of the inclined soft pipe conveying fluid

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

Abstract: 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.

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

Abstract: 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.

Modelling two-layer nanofluid flow in a micro-channel with electro-osmotic effects by means of Buongiorno's model

Abstract: A fully developed steady immiscible flow of nanofluid in a two-layer microchannel is studied in the presence of electro-kinetic effects. Buongiorno’s model is employed for describing the behavior of nanofluids. Different from the previous studies on two-layer channel flow of a nanofluid, the present paper introduces the flux conservation conditions for the nanoparticle volume fraction field, which makes this work new and unique, and it is in coincidence with practical observations. The governing equations are reduced into a group of ordinary differential equations via appropriate similarity transformations. The highly accurate analytical approximations are obtained. Important physical quantities and total entropy generation are analyzed and discussed. A comparison is made to determine the significance of electrical double layer (EDL) effects in the presence of an external electric field. It is found that the Brownian diffusion, the thermophoresis diffusion, and the viscosity have significant effect on altering the flow behaviors.

Boundary layer flow of Maxwell fluid due to torsional motion of cylinder: modeling and simulation

Abstract: This paper investigates the boundary layer flow of the Maxwell fluid around a stretchable horizontal rotating cylinder under the influence of a transverse magnetic field. The constitutive flow equations for the current physical problem are modeled and analyzed for the first time in the literature. The torsional motion of the cylinder is considered with the constant azimuthal velocity E. The partial differential equations (PDEs) governing the torsional motion of the Maxwell fluid together with energy transport are simplified with the boundary layer concept. The current analysis is valid only for a certain range of the positive Reynolds numbers. However, for very large Reynolds numbers, the flow becomes turbulent. Thus, the governing similarity equations are simplified through suitable transformations for the analysis of the large Reynolds numbers. The numerical simulations for the flow, heat, and mass transport phenomena are carried out in view of the bvp4c scheme in MATLAB. The outcomes reveal that the velocity decays exponentially faster and reduces for higher values of the Reynolds numbers and the flow penetrates shallower into the free stream fluid. It is also noted that the phenomenon of stress relaxation, described by the Deborah number, causes to decline the flow fields and enhance the thermal and solutal energy transport during the fluid motion. The penetration depth decreases for the transport of heat and mass in the fluid with the higher Reynolds numbers. An excellent validation of the numerical results is assured through tabular data with the existing literature.

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

Abstract: 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.

Size-dependent thermoelastic initially stressed micro-beam due to a varying temperature in the light of the modified couple stress theory

Abstract: The bending of the Euler-Bernoulli micro-beam has been extensively modeled based on the modified couple stress (MCS) theory. Although many models have been incorporated into the literature, there is still room for introducing an improved model in this context. In this work, we investigate the thermoelastic vibration of a micro-beam exposed to a varying temperature due to the application of the initial stress employing the MCS theory and generalized thermoelasticity. The MCS theory is used to investigate the material length scale effects. Using the Laplace transform, the temperature, deflection, displacement, flexure moment, and stress field variables of the micro-beam are derived. The effects of the temperature pulse and couple stress on the field distributions of the micro-beam are obtained numerically and graphically introduced. The numerical results indicate that the temperature pulse and couple stress have a significant effect on all field variables.

Vibration analysis of piezoelectric sandwich nanobeam with flexoelectricity based on nonlocal strain gradient theory

Abstract: A nonlocal strain gradient theory (NSGT) accounts for not only the nongradient nonlocal elastic stress but also the nonlocality of higher-order strain gradients, which makes it benefit from both hardening and softening effects in small-scale structures. In this study, based on the NSGT, an analytical model for the vibration behavior of a piezoelectric sandwich nanobeam is developed with consideration of flexoelectricity. The sandwich nanobeam consists of two piezoelectric sheets and a non-piezoelectric core. The governing equation of vibration of the sandwich beam is obtained by the Hamiltonian principle. The natural vibration frequency of the nanobeam is calculated for the simply supported (SS) boundary, the clamped-clamped (CC) boundary, the clamped-free (CF) boundary, and the clamped-simply supported (CS) boundary. Effects of geometric dimensions, length scale parameters, nonlocal parameters, piezoelectric constants, as well as the flexoelectric constants are discussed. Results demonstrate that both the flexoelectric and piezoelectric constants enhance the vibration frequency of the nanobeam. The nonlocal stress decreases the natural vibration frequency, while the strain gradient increases the natural vibration frequency. The natural vibration frequency based on the NSGT can be increased or decreased, depending on the value of the nonlocal parameter to length scale parameter ratio.

Transient flow of magnetized Maxwell nanofluid: Buongiorno model perspective of Cattaneo-Christov theory

Abstract: The present research article is devoted to studying the characteristics of Cattaneo-Christov heat and mass fluxes in the Maxwell nanofluid flow caused by a stretching sheet with the magnetic field properties. The Maxwell nanofluid is investigated with the impact of the Lorentz force to examine the consequence of a magnetic field on the flow characteristics and the transport of energy. The heat and mass transport mechanisms in the current physical model are analyzed with the modified versions of Fourier’s and Fick’s laws, respectively. Additionally, the well-known Buongiorno model for the nanofluids is first introduced together with the Cattaneo-Christov heat and mass fluxes during the transient motion of the Maxwell fluid. The governing partial differential equations (PDEs) for the flow and energy transport phenomena are obtained by using the Maxwell model and the Cattaneo-Christov theory in addition to the laws of conservation. Appropriate transformations are used to convert the PDEs into a system of nonlinear ordinary differential equations (ODEs). The homotopic solution methodology is applied to the nonlinear differential system for an analytic solution. The results for the time relaxation parameter in the flow, thermal energy, and mass transport equations are discussed graphically. It is noted that higher values of the thermal and solutal relaxation time parameters in the Cattaneo-Christov heat and mass fluxes decline the thermal and concentration fields of the nanofluid. Further, larger values of the thermophoretic force enhance the heat and mass transport in the nanoliquid. Moreover, the Brownian motion of the nanoparticles declines the concentration field and increases the temperature field. The validation of the results is assured with the help of numerical tabular data for the surface velocity gradient.

Nonlocal and strain gradient effects on nonlinear forced vibration of axially moving nanobeams under internal resonance conditions

Abstract: Based on the nonlocal strain gradient theory (NSGT), a model is proposed for an axially moving nanobeam with two kinds of scale effects. The internal resonance-accompanied fundamental harmonic response of the external excitation frequency in the vicinities of the first and second natural frequencies is studied by adopting the multivariate Lindstedt-Poincare (L-P) method. Based on the root discriminant of the frequency-amplitude equation under internal resonance conditions, theoretical analyses are performed to investigate the scale effects of the resonance region and the critical external excitation amplitude. Numerical results show that the region of internal resonance is related to the amplitude of the external excitation. Particularly, the internal resonance disappears after a certain critical value of the external excitation amplitude is reached. It is also shown that the scale parameters, i.e., the nonlocal parameters and the material characteristic length parameters, respectively, reduce and increase the critical amplitude, leading to a promotion or suppression of the occurrence of internal resonance. In addition, the scale parameters affect the size of the enclosed loop of the bifurcated solution curves as well by changing their intersection, divergence, or tangency.