Viscoelastic nanofluid flow has drawn substantial interest due to its industrial uses,including research and testing of medical devices,lubrication and tribology,drug delivery systems,and environmental remediation.Thi...Viscoelastic nanofluid flow has drawn substantial interest due to its industrial uses,including research and testing of medical devices,lubrication and tribology,drug delivery systems,and environmental remediation.This work studies nanofluid flow over a viscoelastic boundary layer,focusing on mass and heat transmission.An analysis is performed on the flow traversing a porous sheet undergoing nonlinear stretching.It assesses the consequences of viscous dissipation and thermal radiation.The scientific nanofluid framework laid out by Buongiorno has been exploited.The partial differential equations illustrating the phenomena can be transfigured into ordinary differential equations by utilizing appropriate similarity transformations.The simplified equations are unmasked using the Homotopy Analysis Method(HAM),a semi-analytical approach designed to solve nonlinear ordinary and partial differential equations commonly encountered in numerous scientific and engineering disciplines.Calculations are executed to ascertain the numerical solutions related to temperature,concentration,and velocity fields,accompanied by the skin friction coefficient,local Nusselt number,and local Sherwood number.Visualizations of the results are accompanied by pertinent explanations grounded in scientific principles.The temperature distribution and corresponding thermal layer have been enhanced due to radiative and viscous dissipation characteristics.Additionally,it has been noted that a delay in fluid movement results from an improvement in the porous medium parameter and magnetic field values.A falling trend in the Nusselt number is observed as the Eckert and thermophoresis parameters increase.The current numerical results have been effectively validated against previous difficulties.展开更多
This study presents a significant advancement in the vibration analysis of functionally graded sandwich plates with auxetic cores by introducing a general viscoelastic foundation model that more accurately reflects th...This study presents a significant advancement in the vibration analysis of functionally graded sandwich plates with auxetic cores by introducing a general viscoelastic foundation model that more accurately reflects the complex interactions between the plate and the foundation.The novelty of this study is that the proposed viscoelastic foundation model incorporates elastic and damping effects in both the Winkler and Pasternak layers.To develop the theoretical framework for this analysis,the higher-order shear deformation theory is employed,while Hamilton's principle is used to derive the governing equations of motion.The closed-form solution is used to determine the damped vibration behaviors of the sandwich plates.The precision and robustness of the proposed mathematical model are validated through several comparison studies with existing numerical results.A detailed parametric study is conducted to investigate the influence of various parameters,including the elastic and damping coefficients of the foundation,the material gradation,and the properties of the auxetic core on the vibration behavior of the plates.The numerical results provide new insights into the vibration characteristics of sandwich plates with auxetic cores resting on viscoelastic foundation,highlighting the significant role of the two damping coefficients and auxetic cores in the visco-vibration behavior of the plates.展开更多
Polymer flooding is an important means of improving oil recovery and is widely used in Daqing,Xinjiang,and Shengli oilfields,China.Different from conventional injection media such as water and gas,viscoelastic polymer...Polymer flooding is an important means of improving oil recovery and is widely used in Daqing,Xinjiang,and Shengli oilfields,China.Different from conventional injection media such as water and gas,viscoelastic polymer solutions exhibit non-Newtonian and nonlinear flow behavior including shear thinning and shear thickening,polymer convection,diffusion,adsorption,retention,inaccessible pore volume,and reduced effective permeability.However,available well test model of polymer flooding wells generally simplifies these characteristics on pressure transient response,which may lead to inaccurate results.This work proposes a novel two-phase numerical well test model to better describe the polymer viscoelasticity and nonlinear flow behavior.Different influence factors that related to near-well blockage during polymer flooding process,including the degree of blockage(inner zone permeability),the extent of blockage(composite radius),and polymer flooding front radius are explored to investigate these impacts on bottom hole pressure responses.Results show that polymer viscoelasticity has a significant impact on the transitional flow segment of type curves,and the effects of near-well formation blockage and polymer concentration distribution on well test curves are very similar.Thus,to accurately interpret the degree of near-well blockage in injection wells,it is essential to first eliminate the influence of polymer viscoelasticity.Finally,a field case is comprehensively analyzed and discussed to illustrate the applicability of the proposed model.展开更多
In this paper,we investigate the blow-up phenomenon for a class of logarithmic viscoelastic equations with delay and nonlocal terms under acoustic boundary conditions.Using the energy method,we prove that nontrivial s...In this paper,we investigate the blow-up phenomenon for a class of logarithmic viscoelastic equations with delay and nonlocal terms under acoustic boundary conditions.Using the energy method,we prove that nontrivial solutions with negative initial energy will blow up in finite time,and provide an upper bound estimate for the blow-up time.Additionally,we also derive a lower bound estimate for the blow-up time.展开更多
In industrial applications,plate-like structures such as steel strips in continuous hot-dip galvanizing and papers under fan action are ubiquitous.The vibration issues that arise when these structures are in axial mot...In industrial applications,plate-like structures such as steel strips in continuous hot-dip galvanizing and papers under fan action are ubiquitous.The vibration issues that arise when these structures are in axial motion,and are influenced by fluids and thermal fields,have attracted significant attention from the academic community.This study focuses on the nonlinear dynamic behavior of axially transporting immersed viscoelastic plates with particular emphasis on internal resonance and speed-dependent tension.The governing equation and the related boundary conditions for the axially transporting viscoelastic immersed plate are derived with Hamilton's principle,prioritizing the impact of time-varying tension induced by speed perturbations.Based on the second-order Galerkin truncation,the governing equation is discretized into a system of second-order ordinary differential equations.The multi-scale method is used to analyze the stable steady-state response of the immersed viscoelastic plate.The conditions for achieving a 3:1 frequency ratio between the first two orders of the system are analytically deduced.Notably,when the viscoelastic coefficient diminishes,the stability boundaries exhibit increased complexity,manifesting as the irregular W-shaped contours in the parameter space.Numerical examples comprehensively investigate the effects of viscoelasticity on both the stability region and the steady-state response under internal resonance conditions.Finally,the accuracy of the obtained results is validated through numerical computation.展开更多
As oil and gas development increasingly targets unconventional reservoirs,the limitations of conventional hydraulic fracturing,namely high water consumption and significant reservoir damage,have become more pronounced...As oil and gas development increasingly targets unconventional reservoirs,the limitations of conventional hydraulic fracturing,namely high water consumption and significant reservoir damage,have become more pronounced.This has driven growing interest in the development of clean fracturing fluids that minimize both water usage and formation impairment.In this study,a low-liquid-content viscoelastic surfactant(VES)foam fracturing fluid system was formulated and evaluated through laboratory experiments.The optimized formulation comprises 0.2%foaming agent CTAB(cetyltrimethylammonium bromide)and 2%foam stabilizer EAPB(erucamidopropyl betaine).Laboratory tests demonstrated that the VES foam system achieved a composite foam value of 56,700 mL・s,reflecting excellent foaming performance.Proppant transport experiments revealed minimal variation in suspended sand volume over 120 min across different sand ratios,indicating robust sand-carrying capacity even at high proppant concentrations.Rheological measurements showed that the fluid maintained a viscosity above 120 mPa・s after 120 min of shearing at 70℃ and a shear rate of 170 s−1,with the elastic modulus exceeding the viscous modulus,confirming the system’s exceptional stability and resilience.Furthermore,core damage tests indicated that the VES foam caused only 4.42%formation damage,highlighting its potential for efficient and low-damage stimulation of tight reservoirs.Overall,the findings demonstrate that this low-liquid-content VES foam provides a highly effective,environmentally considerate alternative for hydraulic fracturing in unconventional formations,combining superior proppant transport,rheological stability,and minimal reservoir impairment.展开更多
Earthquakes contribute to the failure of anti-dip bedding rock slopes(ABRSs)in seismically active regions.The pseudo-static method is commonly employed to assess the ABRSs stability.However,simplifying seismic effects...Earthquakes contribute to the failure of anti-dip bedding rock slopes(ABRSs)in seismically active regions.The pseudo-static method is commonly employed to assess the ABRSs stability.However,simplifying seismic effects as static loads often underestimates rock slope stability.The development of a practical stability analysis approach for ABRSs,particularly in slope engineering design,is imperative.This study proposes a stability evaluation model for ABRSs,incorporating the viscoelastic properties of rock,to quantitatively assess the safety factor and failure surface under seismic conditions.The mathematical description of the pseudo-dynamic method,derived in this study,accounts for the viscoelastic properties of ABRSs and integrates the HoekeBrown failure criterion with the Kelvin-Voigt stress-strain relationship of rocks.Furthermore,to address concurrent translation-rotation failure in ABRSs,upper bound limit analysis is utilized to quantify the safety factor.Through a comparison with existing literature,the proposed method considers the effect of harmonic vibration on the stability of ABRSs.The obtained safety factor is lower than that of the quasi-static method,with the resulting percentage change exceeding 5%.The critical failure surface demonstrates superior positional accuracy compared to the Aydan and Adhikary basal planes,with minimal error observed between the physical model test and the numerical simulation test.The parameter sensitivity analysis reveals that the inclination of ABRSs exhibits the highest sensitivity(Sk)value across the three levels of horizontal seismic coefficient(kh).The study aims to devise an expeditious calculation approach for assessing the stability of ABRSs during seismic events,intending to offer theoretical guidance for their stability analysis.展开更多
In this study,the free vibration of a piezoelectric semiconductor(PS)composite structure composed of a PS layer,a fractional viscoelastic layer,and an elastic substrate with simply-supported boundary conditions is inv...In this study,the free vibration of a piezoelectric semiconductor(PS)composite structure composed of a PS layer,a fractional viscoelastic layer,and an elastic substrate with simply-supported boundary conditions is investigated.The fractional derivative Zener model is used to establish the constitutive relation of the viscoelastic layer.The first-order shear deformation theory and Hamilton's principle are used to derive the motion equations of the present problem.The frequency parameter is numerically resolved with the Newton-Raphson method through the eigenvalue equation.The effects of either geometric parameters,carrier density,and electric voltage applied on the surface of the composite structure or the fractional order of the Zener model on both the natural frequency and loss factor are discussed,and some interesting conclusions are drawn.This work will be helpful for designing and manufacturing PS materials and structures.展开更多
F-actin microstructures dominate cellular viscoelasticity and have been used to identify the migration and malignance of living cancer cells.Diabetic cancer patients suffer from increased metastasis and tumor recurren...F-actin microstructures dominate cellular viscoelasticity and have been used to identify the migration and malignance of living cancer cells.Diabetic cancer patients suffer from increased metastasis and tumor recurrence.However,the long-term evolution and correlation of F-actin microstructures and viscoelasticity distribution are still poorly understood in living cancer cells under varying glucose environment.Herein,by using atomic force microscopy with amplitude modulation-frequency modulation and nanoindentation mode,we characterized the hierarchical F-actin microstructures and the multi-passage viscoelasticity evolution in living Huh-7 cancer cells transferred from high to low glucose level.The highly oriented stress fibers connected by thinner fiber networks were observed in high glucose environment.The circumferential actin networks composed by straight segment-like fibers and the randomly distributed actin fragments connected by ultrathin crosslinking fibers were observed in low glucose environment.The viscoelasticity within the nucleus and the cytoplasm of living Huh-7 cancer cells showed longterm fluctuations over tens of passages after switching glucose environments.The viscoelasticity of cytoplasm was more responsive to the change of glucose environments than nucleus,which was due to the reorganization of F-actin microstructures.Our work provides the microstructural and nanomechanical understanding on the migration and proliferation of living cancer cells under varying glucose environment.展开更多
Natural biomaterials with staggered structures exhibit remarkable mechanical properties owing to their unique microstructure.The microstructural arrangement can induce size-dependent and viscoelastic responses within ...Natural biomaterials with staggered structures exhibit remarkable mechanical properties owing to their unique microstructure.The microstructural arrangement can induce size-dependent and viscoelastic responses within the material.This study proposes a strain gradient viscoelastic shear-lag model to elucidate the intricate interplay between the strain gradient and viscoelastic effect in staggered shells.Our model clarifies the role of both effects,as experimentally observed,in governing the mechanical properties of these biomaterials.A detailed characterization of the size-dependent responses is conducted through the utilization of a microstructural characterization parameter alongside viscoelastic constitutive models.Then,the effective modulus of the staggered shell is defined and its formula is derived through the Laplace transform.Compared to classical models and even the strain gradient elastic model,the strain gradient viscoelastic model offers calculated moduli that are more consistent with experimental data.Moreover,the strengthening-softening effect of staggered structures is predicted using the strain gradient viscoelastic model and critical energy principle.This study contributes significantly to our understanding of the mechanical behavior of structural materials.Additionally,it provides insights for the design of advanced bionic materials with tailored properties.展开更多
Taking into account three important porous media mechanisms during wave propagation （the Biot-flow, squirt-flow, and solid-skeleton viscoelastic mechanisms）, we introduce water saturation into the dynamic governing ...Taking into account three important porous media mechanisms during wave propagation （the Biot-flow, squirt-flow, and solid-skeleton viscoelastic mechanisms）, we introduce water saturation into the dynamic governing equations of wave propagation by analyzing the effective medium theory and then providing a viscoelastic Biot/squirt （BISQ） model which can analyze the wave propagation problems in a partially viscous pore fluid saturated porous media. In this model, the effects of pore fluid distribution patterns on the effective bulk modulus at different frequencies are considered. Then we derive the wave dynamic equations in the time-space domain. The phase velocity and the attenuation coefficient equations of the viscoelatic BISQ model in the frequency-wavenumber domain are deduced through a set of plane harmonic solution assumptions. Finally, by means of numerical simulations, we investigate the effects of water saturation, permeability, and frequency on compressional wave velocity and attenuation. Based on tight sandstone and carbonate experimental observed data, the compressional wave velocities of partially saturated reservoir rocks are calculated. The compressional wave velocity in carbonate reservoirs is more sensitive to gas saturation than in sandstone reservoirs.展开更多
We propose a method for mOdeling azimuthal AVO responses from a fractured i reflector. The method calculates the integrated reflected wavetrains, and the wavetrains contain elastodynamic information including the con...We propose a method for mOdeling azimuthal AVO responses from a fractured i reflector. The method calculates the integrated reflected wavetrains, and the wavetrains contain elastodynamic information including the contrast in impedance and anelasticity i across interfaces, the intemal anisotropic propagation, the dispersion and attenuation along i the wave path, and tuning and interference. The results suggest that for large angles of incidence, the velocity dispersion and attenuation increase the amplitudes of PP waves from the top and decrease those from the bottom. For azimuthal responses at specific angles of incidence, the reflected wavetrains of PP waves tend to have longer duration with increasing azimuth. In contrast, model-converted PSV and PSH reflections show stable azimuthal features and are less affected by the reflector thickness. The amplitudes of PSV reflections increase with increasing azimuth; moreover, the waves have no reflection energy at 0° and 90° azimuth and maximum amplitude at 45° azimuth.展开更多
To simultaneously take into account the Biot-flow mechanism, the squirt-flow mechanism, and the frame-viscoelasticity mechanism, a generalized viscoelastic BISQ （Biot/squirt） model is developed for wave propagation ...To simultaneously take into account the Biot-flow mechanism, the squirt-flow mechanism, and the frame-viscoelasticity mechanism, a generalized viscoelastic BISQ （Biot/squirt） model is developed for wave propagation in clay-bearing sandstones based on Dvorkin＇s elastic BISQ model. The present model is extended to a wide range of permeabilities （k 〉 0.05 mD） by introducing a dimensionless correction factor for viscoelastic parameters, defined as a function of the permeability and the clay content. We describe the frame＇s stress-strain relationship of the clay-bearing sandstones by the differential constitutive equations of generalized viscoelasticity and then derive the viscoelastic-wave dynamic equations. With the assumption of a plane-wave solution, we finally yield the phase velocities and the attenuation coefficients by solving the dynamic wave equations in the frequency and wave number domain. The comparison of numerical results and experimental data shows that the generalized viscoelastic BISQ model is applicable for modeling the wave propagation in most of the sandstones mainly bearing kaolinite clay.展开更多
In the characterization of elastic properties of tissue using dynarmic optical coherence elasto-graphy,shear/surface waves are propagated and tracked in order to estimate speed and Y oung's modulus.However,for dis...In the characterization of elastic properties of tissue using dynarmic optical coherence elasto-graphy,shear/surface waves are propagated and tracked in order to estimate speed and Y oung's modulus.However,for dispersive tssues,the displacement pulse is highly damped and distorted during propagation,diminishing the ffectiveness of peak tracking approaches,and leading to biased cstimates of wave speed.Further,plane wave propagation is sometimes assumed,which contributes to estimation erors.Therefore,we invert a wave propagation model that incorpo-rates propagation,decay,and distortion of pulses in a dispersive media in order to accurately estimate its elastic and viscous components.The model uses a general first-order approximation of dispersion,avoiding the use of any particular rheological model of tisue.Experiments are conducted in elastic and viscoelastic tissue mimicking phantoms by producing a Gaussian push using acoustic radiation force excitation and measuring the wave propagation using a Fourier domain optical coherence tomography system.Results confirmed the ffectiveness of the inversion method in est imat ing viscoelastic parameters in both the viscoelastic and elastic phantoms when compared to mechanical measurements.Finally,the viscoelastic characterization of a fresh porcine comea was conducted.Preliminary results validate this approach when compared to other methods.展开更多
Based on the Church-Hoff model, the nonlinear oscillations of a single encapsulated microbubble with a finite thickness shell are theoretically studied. The effects of viscoelasticity on radial oscillations and the fu...Based on the Church-Hoff model, the nonlinear oscillations of a single encapsulated microbubble with a finite thickness shell are theoretically studied. The effects of viscoelasticity on radial oscillations and the fundamental and harmonic components are researched. The peaks of radial oscillations and magnitudes of power spectra of the fundamental and harmonic components all increase gradually with the shear modulus of shell varying from 0 to 10 MPa by an interval of 0. 1 MPa at the same shear viscosity, while they decrease as the shear viscosity increases from 0 to 1 Pa · s by an interval of 0. 01 Pa · s at the same shear modulus. The fluctuation ranges of subharmonic and ultraharmonic signals are much larger than both the fundamental and second harmonic components. It means that the effect of viscoelasticity on the subharmonic and ultraharmonic signals is greater than that on the fundamental and second harmonic components. So adjusting the viscoelasticity of the shell is a potential method to obtain a perfect microbubble contrast agent used for the subharmonic and ultraharmonic imaging. Four points with significant fundamental and harmonic components are chosen as an example： a shear viscosity of 0. 39 Pa · s with shear modulus of 3.9, 6. 6, and 8.6 MPa, respectively; a shear modulus of 6.6 MPa with a shear viscosity of 0.42 Pa · s.展开更多
In order to investigate the mechanical response of reflective cracking in asphalt concrete pavement under dynamic vehicle loading, a finite element model is established in ABAQUS. The viscoelastic behavior is describe...In order to investigate the mechanical response of reflective cracking in asphalt concrete pavement under dynamic vehicle loading, a finite element model is established in ABAQUS. The viscoelastic behavior is described by a prony series which is calculated through nonlinear fitting to the creep test data obtained in the laboratory. Based on the viscoelastic theory, the time-temperature equivalence principle, fracture mechanics and the dynamic finite element method, both the Jintegral and the mix-mode stress intensity factor are utilized as fracture evaluation parameters, and a half-sine dynamic loading is used to simulate the vehicle loading. Finally, the mechanical response of the pavement reflective cracking is analyzed under different vehicle speeds, different environmental conditions and various damping factors. The results indicate that increasing either the vehicle speed or the structure damping factor decreases the maximum values of fracture parameters, while the structure temperature has little effect on the fracture parameters. Due to the fact that the vehicle speed can be enhanced by improving the road traffic conditions, and the pavement damping factor can become greater by modifying the components of materials, the development of reflective cracking can be delayed and the asphalt pavement service life can be effectively extended through both of these ways.展开更多
A recent review publication presented an extensive and comprehensive assessment of the phenomenological relations of Poisson’s ratios (PRs) to the behavior and responses of contemporary materials under specific loadi...A recent review publication presented an extensive and comprehensive assessment of the phenomenological relations of Poisson’s ratios (PRs) to the behavior and responses of contemporary materials under specific loading conditions. The present review and analysis paper is intended as a theoretical mechanics complement covering mathematical and physical modeling of a single original elastic and of six time and process (i.e. path and stress) dependent viscoelastic PR definitions as well as a seventh special path independent one. The implications and consequences of such models on material characterization are analyzed and summarized. Indeed, PRs based on experimentally obtained 2-D strains under distinct creep and/or relaxation processes exhibit radically different time responses for identical material specimen. These results confirm the PR’s implicit path dependence in addition to their separate intrinsic time reliance. Such non-uniqueness of viscoelastic PRs renders them unsuitable as universal material descriptors. Analytical formulations and experimental measurements also examine the physical impossibility of instantaneously achieving time independent loads or strains or their rates thus making certain PR definitions based on constant state variables, while mathematically valid, physically unrealistic and unachievable. A newly developed theoretical/experimental protocol for the determination of the time when loading patterns reach stead-state conditions based on strain accelerations demonstrates the capability to measure this time from experimental data. Due to the process dependent PRs, i.e. stress and stress history paths, the non-existence of a unique viscoelastic PR and of a universal elastic-viscoelastic correspondence principle or analogy (EVCP) in terms of PRs is demonstrated. Additionally and independently, the required double convolution integral construction of linear viscoelastic constitutive relations with the inclusion of PRs is cumbersome analytically and computationally needlessly highly CPU intensive. Furthermore, there is no theoretical fundamental hint as to what loading path is required to produce a unique universal viscoelastic PR definition necessary for formulating a PR based constitutive relation or an EVCP protocol. The analysis associated with an additional Class VII viscoelastic PR establishes it as a universal representation which is loading path and strain independent while still remaining time dependent. This Class PR can be the one used if it is desired to express constitutive relations in terms of PRs, subject to the caveat applying to all PR Classes regarding the CPU intensiveness in the time space due to triple product and double convolution integral constitutive relations. However, the use PRs is unnecessary since any set of material behavior can be uniquely and completely defined in terms of only moduli and/or compliances. The mathematical model of instantaneous initial loading paths, based on Heavi-side functions, is examined in detail and shown to lead to infinite velocities and accelerations. Additionally, even if non-instantaneous gradual loading functions are employed the resulting PRs are still load and load history dependent. Consequently, they represent specialized PR responses applicable and limited to those particular load and history combinations. Although the analyses contained herein are generalized to non-homogeneous linear viscoelastic materials, the main focus is on PR time and process dependence. The non-homogeneous material results and conclusions presented herein apply equally to homogeneous viscoelasticity and per se do not influence the results or conclusions of the analytical development regarding viscoelastic PRs. In short, these PR analyses apply to all linear viscoelastic material characterization.展开更多
The present research focuses on the analysis of wave propagation on a rotating viscoelastic nanobeam supported on the viscoelastic foundation which is subject to thermal gradient effects.A comprehensive and accurate m...The present research focuses on the analysis of wave propagation on a rotating viscoelastic nanobeam supported on the viscoelastic foundation which is subject to thermal gradient effects.A comprehensive and accurate model of a viscoelastic nanobeam is constructed by using a novel nonclassical mechanical model.Based on the general nonlocal theory(GNT),Kelvin-Voigt model,and Timoshenko beam theory,the motion equations for the nanobeam are obtained.Through the GNT,material hardening and softening behaviors are simultaneously taken into account during wave propagation.An analytical solution is utilized to generate the results for torsional(TO),longitudinal(LA),and transverse(TA)types of wave dispersion.Moreover,the effects of nonlocal parameters,Kelvin-Voigt damping,foundation damping,Winkler-Pasternak coefficients,rotating speed,and thermal gradient are illustrated and discussed in detail.展开更多
In this paper,the non-harmonic resonance of Bernoulli viscoelastic beams,Kirchhoff viscoelastic plates,Timoshenko viscoelastic beams,and Mindlin viscoelastic plates subjected to time-dependent exponentially decreasing...In this paper,the non-harmonic resonance of Bernoulli viscoelastic beams,Kirchhoff viscoelastic plates,Timoshenko viscoelastic beams,and Mindlin viscoelastic plates subjected to time-dependent exponentially decreasing transverse distributed load is investigated for the first time.The constitutive equations are expressed utilizing Boltzmann integral law with a constant bulk modulus.The displacement vector is approximated by employing the separation of variables method.The Laplace transformation is used to transfer equations from the time domain to the Laplace domain and vice versa.The novel point of the proposed method is to express,prove and calculate the critical time in which the displacement will be several times the displacement at time zero.In addition,this new method calculates the maximum deflection at the critical time,explicitly and exactly,without any need to follow the time-displacement curve with a low computational cost.Additionally,the proposed method introduces the critical range of time so that the responses are greater than the responses at time zero.展开更多
The paper explores the gravity-driven flow of the thin film of a viscoelastic-fluid-based nanofluids(VFBN)along an inclined plane under non-isothermal conditions and subjected to convective cooling at the free-surface...The paper explores the gravity-driven flow of the thin film of a viscoelastic-fluid-based nanofluids(VFBN)along an inclined plane under non-isothermal conditions and subjected to convective cooling at the free-surface.The Newton’s law of cooling is used to model the convective heat-exchange with the ambient at the free-surface.The Giesekus viscoelastic constitutive model,with appropriate modifications to account for non-isothermal effects,is employed to describe the polymeric effects.The unsteady and coupled non-linear partial differential equations(PDEs)describing the model problem are obtained and solved via efficient semi-implicit numerical schemes based on finite difference methods(FDM)implemented in Matlab.The response of the VFBN velocity,temperature,thermal-conductivity and polymeric-stresses to variations in the volume-fraction of embedded nanoparticles is investigated.It is shown that these quantities all increase as the nanoparticle volume-fraction becomes higher.展开更多
文摘Viscoelastic nanofluid flow has drawn substantial interest due to its industrial uses,including research and testing of medical devices,lubrication and tribology,drug delivery systems,and environmental remediation.This work studies nanofluid flow over a viscoelastic boundary layer,focusing on mass and heat transmission.An analysis is performed on the flow traversing a porous sheet undergoing nonlinear stretching.It assesses the consequences of viscous dissipation and thermal radiation.The scientific nanofluid framework laid out by Buongiorno has been exploited.The partial differential equations illustrating the phenomena can be transfigured into ordinary differential equations by utilizing appropriate similarity transformations.The simplified equations are unmasked using the Homotopy Analysis Method(HAM),a semi-analytical approach designed to solve nonlinear ordinary and partial differential equations commonly encountered in numerous scientific and engineering disciplines.Calculations are executed to ascertain the numerical solutions related to temperature,concentration,and velocity fields,accompanied by the skin friction coefficient,local Nusselt number,and local Sherwood number.Visualizations of the results are accompanied by pertinent explanations grounded in scientific principles.The temperature distribution and corresponding thermal layer have been enhanced due to radiative and viscous dissipation characteristics.Additionally,it has been noted that a delay in fluid movement results from an improvement in the porous medium parameter and magnetic field values.A falling trend in the Nusselt number is observed as the Eckert and thermophoresis parameters increase.The current numerical results have been effectively validated against previous difficulties.
基金the funding of the Deanship of Graduate Studies and Scientific Research,Jazan University,Saudi Arabia,through project number:RG24-M027.
文摘This study presents a significant advancement in the vibration analysis of functionally graded sandwich plates with auxetic cores by introducing a general viscoelastic foundation model that more accurately reflects the complex interactions between the plate and the foundation.The novelty of this study is that the proposed viscoelastic foundation model incorporates elastic and damping effects in both the Winkler and Pasternak layers.To develop the theoretical framework for this analysis,the higher-order shear deformation theory is employed,while Hamilton's principle is used to derive the governing equations of motion.The closed-form solution is used to determine the damped vibration behaviors of the sandwich plates.The precision and robustness of the proposed mathematical model are validated through several comparison studies with existing numerical results.A detailed parametric study is conducted to investigate the influence of various parameters,including the elastic and damping coefficients of the foundation,the material gradation,and the properties of the auxetic core on the vibration behavior of the plates.The numerical results provide new insights into the vibration characteristics of sandwich plates with auxetic cores resting on viscoelastic foundation,highlighting the significant role of the two damping coefficients and auxetic cores in the visco-vibration behavior of the plates.
基金supported by the National Natural Science Foundation of China(52104049)the Young Elite Scientist Sponsorship Program by Beijing Association for Science and Technology(BYESS2023262)。
文摘Polymer flooding is an important means of improving oil recovery and is widely used in Daqing,Xinjiang,and Shengli oilfields,China.Different from conventional injection media such as water and gas,viscoelastic polymer solutions exhibit non-Newtonian and nonlinear flow behavior including shear thinning and shear thickening,polymer convection,diffusion,adsorption,retention,inaccessible pore volume,and reduced effective permeability.However,available well test model of polymer flooding wells generally simplifies these characteristics on pressure transient response,which may lead to inaccurate results.This work proposes a novel two-phase numerical well test model to better describe the polymer viscoelasticity and nonlinear flow behavior.Different influence factors that related to near-well blockage during polymer flooding process,including the degree of blockage(inner zone permeability),the extent of blockage(composite radius),and polymer flooding front radius are explored to investigate these impacts on bottom hole pressure responses.Results show that polymer viscoelasticity has a significant impact on the transitional flow segment of type curves,and the effects of near-well formation blockage and polymer concentration distribution on well test curves are very similar.Thus,to accurately interpret the degree of near-well blockage in injection wells,it is essential to first eliminate the influence of polymer viscoelasticity.Finally,a field case is comprehensively analyzed and discussed to illustrate the applicability of the proposed model.
基金supported by the National Natural Sciences Foundation of China(No.62363005)。
文摘In this paper,we investigate the blow-up phenomenon for a class of logarithmic viscoelastic equations with delay and nonlocal terms under acoustic boundary conditions.Using the energy method,we prove that nontrivial solutions with negative initial energy will blow up in finite time,and provide an upper bound estimate for the blow-up time.Additionally,we also derive a lower bound estimate for the blow-up time.
基金Project supported by the Science and Technology Support Plan for Youth Innovation of Colleges and Universities of Shandong Province of China(No.2023KJ215)the National Natural Science Foundation of China(Nos.12002142 and 52405274)the National Natural Science Foundation of Shanghai of China(No.ZR2023QE100)。
文摘In industrial applications,plate-like structures such as steel strips in continuous hot-dip galvanizing and papers under fan action are ubiquitous.The vibration issues that arise when these structures are in axial motion,and are influenced by fluids and thermal fields,have attracted significant attention from the academic community.This study focuses on the nonlinear dynamic behavior of axially transporting immersed viscoelastic plates with particular emphasis on internal resonance and speed-dependent tension.The governing equation and the related boundary conditions for the axially transporting viscoelastic immersed plate are derived with Hamilton's principle,prioritizing the impact of time-varying tension induced by speed perturbations.Based on the second-order Galerkin truncation,the governing equation is discretized into a system of second-order ordinary differential equations.The multi-scale method is used to analyze the stable steady-state response of the immersed viscoelastic plate.The conditions for achieving a 3:1 frequency ratio between the first two orders of the system are analytically deduced.Notably,when the viscoelastic coefficient diminishes,the stability boundaries exhibit increased complexity,manifesting as the irregular W-shaped contours in the parameter space.Numerical examples comprehensively investigate the effects of viscoelasticity on both the stability region and the steady-state response under internal resonance conditions.Finally,the accuracy of the obtained results is validated through numerical computation.
文摘As oil and gas development increasingly targets unconventional reservoirs,the limitations of conventional hydraulic fracturing,namely high water consumption and significant reservoir damage,have become more pronounced.This has driven growing interest in the development of clean fracturing fluids that minimize both water usage and formation impairment.In this study,a low-liquid-content viscoelastic surfactant(VES)foam fracturing fluid system was formulated and evaluated through laboratory experiments.The optimized formulation comprises 0.2%foaming agent CTAB(cetyltrimethylammonium bromide)and 2%foam stabilizer EAPB(erucamidopropyl betaine).Laboratory tests demonstrated that the VES foam system achieved a composite foam value of 56,700 mL・s,reflecting excellent foaming performance.Proppant transport experiments revealed minimal variation in suspended sand volume over 120 min across different sand ratios,indicating robust sand-carrying capacity even at high proppant concentrations.Rheological measurements showed that the fluid maintained a viscosity above 120 mPa・s after 120 min of shearing at 70℃ and a shear rate of 170 s−1,with the elastic modulus exceeding the viscous modulus,confirming the system’s exceptional stability and resilience.Furthermore,core damage tests indicated that the VES foam caused only 4.42%formation damage,highlighting its potential for efficient and low-damage stimulation of tight reservoirs.Overall,the findings demonstrate that this low-liquid-content VES foam provides a highly effective,environmentally considerate alternative for hydraulic fracturing in unconventional formations,combining superior proppant transport,rheological stability,and minimal reservoir impairment.
基金funding support from the National Natural Science Foundation of China(Grant No.42072303)the State Key Laboratory of Geohazard Prevention and Geoenvironment Protection Independent Research Project(Grant No.SKLGP2021Z004).
文摘Earthquakes contribute to the failure of anti-dip bedding rock slopes(ABRSs)in seismically active regions.The pseudo-static method is commonly employed to assess the ABRSs stability.However,simplifying seismic effects as static loads often underestimates rock slope stability.The development of a practical stability analysis approach for ABRSs,particularly in slope engineering design,is imperative.This study proposes a stability evaluation model for ABRSs,incorporating the viscoelastic properties of rock,to quantitatively assess the safety factor and failure surface under seismic conditions.The mathematical description of the pseudo-dynamic method,derived in this study,accounts for the viscoelastic properties of ABRSs and integrates the HoekeBrown failure criterion with the Kelvin-Voigt stress-strain relationship of rocks.Furthermore,to address concurrent translation-rotation failure in ABRSs,upper bound limit analysis is utilized to quantify the safety factor.Through a comparison with existing literature,the proposed method considers the effect of harmonic vibration on the stability of ABRSs.The obtained safety factor is lower than that of the quasi-static method,with the resulting percentage change exceeding 5%.The critical failure surface demonstrates superior positional accuracy compared to the Aydan and Adhikary basal planes,with minimal error observed between the physical model test and the numerical simulation test.The parameter sensitivity analysis reveals that the inclination of ABRSs exhibits the highest sensitivity(Sk)value across the three levels of horizontal seismic coefficient(kh).The study aims to devise an expeditious calculation approach for assessing the stability of ABRSs during seismic events,intending to offer theoretical guidance for their stability analysis.
基金supported by the National Natural Science Foundation of China(No.12372153)the Funding by Guangdong Basic and Applied Basic Research Foundation(No.2023A1515012366)。
文摘In this study,the free vibration of a piezoelectric semiconductor(PS)composite structure composed of a PS layer,a fractional viscoelastic layer,and an elastic substrate with simply-supported boundary conditions is investigated.The fractional derivative Zener model is used to establish the constitutive relation of the viscoelastic layer.The first-order shear deformation theory and Hamilton's principle are used to derive the motion equations of the present problem.The frequency parameter is numerically resolved with the Newton-Raphson method through the eigenvalue equation.The effects of either geometric parameters,carrier density,and electric voltage applied on the surface of the composite structure or the fractional order of the Zener model on both the natural frequency and loss factor are discussed,and some interesting conclusions are drawn.This work will be helpful for designing and manufacturing PS materials and structures.
基金supported by the National Natural Science Foundation of China(Grant No.11972383)to Wenpeng Zhuby the National Natural Science Foundation of China(Grant No.12132020)to Yue Zhengby the Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices(Grant No.2022B1212010008).
文摘F-actin microstructures dominate cellular viscoelasticity and have been used to identify the migration and malignance of living cancer cells.Diabetic cancer patients suffer from increased metastasis and tumor recurrence.However,the long-term evolution and correlation of F-actin microstructures and viscoelasticity distribution are still poorly understood in living cancer cells under varying glucose environment.Herein,by using atomic force microscopy with amplitude modulation-frequency modulation and nanoindentation mode,we characterized the hierarchical F-actin microstructures and the multi-passage viscoelasticity evolution in living Huh-7 cancer cells transferred from high to low glucose level.The highly oriented stress fibers connected by thinner fiber networks were observed in high glucose environment.The circumferential actin networks composed by straight segment-like fibers and the randomly distributed actin fragments connected by ultrathin crosslinking fibers were observed in low glucose environment.The viscoelasticity within the nucleus and the cytoplasm of living Huh-7 cancer cells showed longterm fluctuations over tens of passages after switching glucose environments.The viscoelasticity of cytoplasm was more responsive to the change of glucose environments than nucleus,which was due to the reorganization of F-actin microstructures.Our work provides the microstructural and nanomechanical understanding on the migration and proliferation of living cancer cells under varying glucose environment.
基金supported by the National Natural Science Foundation of China(with Grant Nos.12432003 and 12032001)the National Science and Technology Major Project(Grant No.J2022-V-0003-0029).
文摘Natural biomaterials with staggered structures exhibit remarkable mechanical properties owing to their unique microstructure.The microstructural arrangement can induce size-dependent and viscoelastic responses within the material.This study proposes a strain gradient viscoelastic shear-lag model to elucidate the intricate interplay between the strain gradient and viscoelastic effect in staggered shells.Our model clarifies the role of both effects,as experimentally observed,in governing the mechanical properties of these biomaterials.A detailed characterization of the size-dependent responses is conducted through the utilization of a microstructural characterization parameter alongside viscoelastic constitutive models.Then,the effective modulus of the staggered shell is defined and its formula is derived through the Laplace transform.Compared to classical models and even the strain gradient elastic model,the strain gradient viscoelastic model offers calculated moduli that are more consistent with experimental data.Moreover,the strengthening-softening effect of staggered structures is predicted using the strain gradient viscoelastic model and critical energy principle.This study contributes significantly to our understanding of the mechanical behavior of structural materials.Additionally,it provides insights for the design of advanced bionic materials with tailored properties.
基金supported by the National Natural Science Foundation of China (No. 11002025, 40114066)the National Basic Research Program of China (973 Program) (No.2007CB209505)the RIPED Youth Innovation Foundation (No. 2010-A-26-01)
文摘Taking into account three important porous media mechanisms during wave propagation （the Biot-flow, squirt-flow, and solid-skeleton viscoelastic mechanisms）, we introduce water saturation into the dynamic governing equations of wave propagation by analyzing the effective medium theory and then providing a viscoelastic Biot/squirt （BISQ） model which can analyze the wave propagation problems in a partially viscous pore fluid saturated porous media. In this model, the effects of pore fluid distribution patterns on the effective bulk modulus at different frequencies are considered. Then we derive the wave dynamic equations in the time-space domain. The phase velocity and the attenuation coefficient equations of the viscoelatic BISQ model in the frequency-wavenumber domain are deduced through a set of plane harmonic solution assumptions. Finally, by means of numerical simulations, we investigate the effects of water saturation, permeability, and frequency on compressional wave velocity and attenuation. Based on tight sandstone and carbonate experimental observed data, the compressional wave velocities of partially saturated reservoir rocks are calculated. The compressional wave velocity in carbonate reservoirs is more sensitive to gas saturation than in sandstone reservoirs.
基金sponsored by the National Natural Science Foundation of China(under Grant Nos.41404090 and U1262208
文摘We propose a method for mOdeling azimuthal AVO responses from a fractured i reflector. The method calculates the integrated reflected wavetrains, and the wavetrains contain elastodynamic information including the contrast in impedance and anelasticity i across interfaces, the intemal anisotropic propagation, the dispersion and attenuation along i the wave path, and tuning and interference. The results suggest that for large angles of incidence, the velocity dispersion and attenuation increase the amplitudes of PP waves from the top and decrease those from the bottom. For azimuthal responses at specific angles of incidence, the reflected wavetrains of PP waves tend to have longer duration with increasing azimuth. In contrast, model-converted PSV and PSH reflections show stable azimuthal features and are less affected by the reflector thickness. The amplitudes of PSV reflections increase with increasing azimuth; moreover, the waves have no reflection energy at 0° and 90° azimuth and maximum amplitude at 45° azimuth.
基金supported by the National Science Fund for Distinguished Young Scholars of China (Grant No. 40725012)the National Hi-tech Research and Development Program of China(863 Program) (Grant No. 2006AA06Z240)the National Basic Research Program of China (973 program)(Grant No. 2007CB209505).
文摘To simultaneously take into account the Biot-flow mechanism, the squirt-flow mechanism, and the frame-viscoelasticity mechanism, a generalized viscoelastic BISQ （Biot/squirt） model is developed for wave propagation in clay-bearing sandstones based on Dvorkin＇s elastic BISQ model. The present model is extended to a wide range of permeabilities （k 〉 0.05 mD） by introducing a dimensionless correction factor for viscoelastic parameters, defined as a function of the permeability and the clay content. We describe the frame＇s stress-strain relationship of the clay-bearing sandstones by the differential constitutive equations of generalized viscoelasticity and then derive the viscoelastic-wave dynamic equations. With the assumption of a plane-wave solution, we finally yield the phase velocities and the attenuation coefficients by solving the dynamic wave equations in the frequency and wave number domain. The comparison of numerical results and experimental data shows that the generalized viscoelastic BISQ model is applicable for modeling the wave propagation in most of the sandstones mainly bearing kaolinite clay.
文摘In the characterization of elastic properties of tissue using dynarmic optical coherence elasto-graphy,shear/surface waves are propagated and tracked in order to estimate speed and Y oung's modulus.However,for dispersive tssues,the displacement pulse is highly damped and distorted during propagation,diminishing the ffectiveness of peak tracking approaches,and leading to biased cstimates of wave speed.Further,plane wave propagation is sometimes assumed,which contributes to estimation erors.Therefore,we invert a wave propagation model that incorpo-rates propagation,decay,and distortion of pulses in a dispersive media in order to accurately estimate its elastic and viscous components.The model uses a general first-order approximation of dispersion,avoiding the use of any particular rheological model of tisue.Experiments are conducted in elastic and viscoelastic tissue mimicking phantoms by producing a Gaussian push using acoustic radiation force excitation and measuring the wave propagation using a Fourier domain optical coherence tomography system.Results confirmed the ffectiveness of the inversion method in est imat ing viscoelastic parameters in both the viscoelastic and elastic phantoms when compared to mechanical measurements.Finally,the viscoelastic characterization of a fresh porcine comea was conducted.Preliminary results validate this approach when compared to other methods.
基金The National Basic Research Program of China ( 973Program) ( No. 2011CB933503)the National Natural Science Foundation of China ( No. 50872021, 60725101, 31000453)
文摘Based on the Church-Hoff model, the nonlinear oscillations of a single encapsulated microbubble with a finite thickness shell are theoretically studied. The effects of viscoelasticity on radial oscillations and the fundamental and harmonic components are researched. The peaks of radial oscillations and magnitudes of power spectra of the fundamental and harmonic components all increase gradually with the shear modulus of shell varying from 0 to 10 MPa by an interval of 0. 1 MPa at the same shear viscosity, while they decrease as the shear viscosity increases from 0 to 1 Pa · s by an interval of 0. 01 Pa · s at the same shear modulus. The fluctuation ranges of subharmonic and ultraharmonic signals are much larger than both the fundamental and second harmonic components. It means that the effect of viscoelasticity on the subharmonic and ultraharmonic signals is greater than that on the fundamental and second harmonic components. So adjusting the viscoelasticity of the shell is a potential method to obtain a perfect microbubble contrast agent used for the subharmonic and ultraharmonic imaging. Four points with significant fundamental and harmonic components are chosen as an example： a shear viscosity of 0. 39 Pa · s with shear modulus of 3.9, 6. 6, and 8.6 MPa, respectively; a shear modulus of 6.6 MPa with a shear viscosity of 0.42 Pa · s.
文摘In order to investigate the mechanical response of reflective cracking in asphalt concrete pavement under dynamic vehicle loading, a finite element model is established in ABAQUS. The viscoelastic behavior is described by a prony series which is calculated through nonlinear fitting to the creep test data obtained in the laboratory. Based on the viscoelastic theory, the time-temperature equivalence principle, fracture mechanics and the dynamic finite element method, both the Jintegral and the mix-mode stress intensity factor are utilized as fracture evaluation parameters, and a half-sine dynamic loading is used to simulate the vehicle loading. Finally, the mechanical response of the pavement reflective cracking is analyzed under different vehicle speeds, different environmental conditions and various damping factors. The results indicate that increasing either the vehicle speed or the structure damping factor decreases the maximum values of fracture parameters, while the structure temperature has little effect on the fracture parameters. Due to the fact that the vehicle speed can be enhanced by improving the road traffic conditions, and the pavement damping factor can become greater by modifying the components of materials, the development of reflective cracking can be delayed and the asphalt pavement service life can be effectively extended through both of these ways.
文摘A recent review publication presented an extensive and comprehensive assessment of the phenomenological relations of Poisson’s ratios (PRs) to the behavior and responses of contemporary materials under specific loading conditions. The present review and analysis paper is intended as a theoretical mechanics complement covering mathematical and physical modeling of a single original elastic and of six time and process (i.e. path and stress) dependent viscoelastic PR definitions as well as a seventh special path independent one. The implications and consequences of such models on material characterization are analyzed and summarized. Indeed, PRs based on experimentally obtained 2-D strains under distinct creep and/or relaxation processes exhibit radically different time responses for identical material specimen. These results confirm the PR’s implicit path dependence in addition to their separate intrinsic time reliance. Such non-uniqueness of viscoelastic PRs renders them unsuitable as universal material descriptors. Analytical formulations and experimental measurements also examine the physical impossibility of instantaneously achieving time independent loads or strains or their rates thus making certain PR definitions based on constant state variables, while mathematically valid, physically unrealistic and unachievable. A newly developed theoretical/experimental protocol for the determination of the time when loading patterns reach stead-state conditions based on strain accelerations demonstrates the capability to measure this time from experimental data. Due to the process dependent PRs, i.e. stress and stress history paths, the non-existence of a unique viscoelastic PR and of a universal elastic-viscoelastic correspondence principle or analogy (EVCP) in terms of PRs is demonstrated. Additionally and independently, the required double convolution integral construction of linear viscoelastic constitutive relations with the inclusion of PRs is cumbersome analytically and computationally needlessly highly CPU intensive. Furthermore, there is no theoretical fundamental hint as to what loading path is required to produce a unique universal viscoelastic PR definition necessary for formulating a PR based constitutive relation or an EVCP protocol. The analysis associated with an additional Class VII viscoelastic PR establishes it as a universal representation which is loading path and strain independent while still remaining time dependent. This Class PR can be the one used if it is desired to express constitutive relations in terms of PRs, subject to the caveat applying to all PR Classes regarding the CPU intensiveness in the time space due to triple product and double convolution integral constitutive relations. However, the use PRs is unnecessary since any set of material behavior can be uniquely and completely defined in terms of only moduli and/or compliances. The mathematical model of instantaneous initial loading paths, based on Heavi-side functions, is examined in detail and shown to lead to infinite velocities and accelerations. Additionally, even if non-instantaneous gradual loading functions are employed the resulting PRs are still load and load history dependent. Consequently, they represent specialized PR responses applicable and limited to those particular load and history combinations. Although the analyses contained herein are generalized to non-homogeneous linear viscoelastic materials, the main focus is on PR time and process dependence. The non-homogeneous material results and conclusions presented herein apply equally to homogeneous viscoelasticity and per se do not influence the results or conclusions of the analytical development regarding viscoelastic PRs. In short, these PR analyses apply to all linear viscoelastic material characterization.
文摘The present research focuses on the analysis of wave propagation on a rotating viscoelastic nanobeam supported on the viscoelastic foundation which is subject to thermal gradient effects.A comprehensive and accurate model of a viscoelastic nanobeam is constructed by using a novel nonclassical mechanical model.Based on the general nonlocal theory(GNT),Kelvin-Voigt model,and Timoshenko beam theory,the motion equations for the nanobeam are obtained.Through the GNT,material hardening and softening behaviors are simultaneously taken into account during wave propagation.An analytical solution is utilized to generate the results for torsional(TO),longitudinal(LA),and transverse(TA)types of wave dispersion.Moreover,the effects of nonlocal parameters,Kelvin-Voigt damping,foundation damping,Winkler-Pasternak coefficients,rotating speed,and thermal gradient are illustrated and discussed in detail.
文摘In this paper,the non-harmonic resonance of Bernoulli viscoelastic beams,Kirchhoff viscoelastic plates,Timoshenko viscoelastic beams,and Mindlin viscoelastic plates subjected to time-dependent exponentially decreasing transverse distributed load is investigated for the first time.The constitutive equations are expressed utilizing Boltzmann integral law with a constant bulk modulus.The displacement vector is approximated by employing the separation of variables method.The Laplace transformation is used to transfer equations from the time domain to the Laplace domain and vice versa.The novel point of the proposed method is to express,prove and calculate the critical time in which the displacement will be several times the displacement at time zero.In addition,this new method calculates the maximum deflection at the critical time,explicitly and exactly,without any need to follow the time-displacement curve with a low computational cost.Additionally,the proposed method introduces the critical range of time so that the responses are greater than the responses at time zero.
文摘The paper explores the gravity-driven flow of the thin film of a viscoelastic-fluid-based nanofluids(VFBN)along an inclined plane under non-isothermal conditions and subjected to convective cooling at the free-surface.The Newton’s law of cooling is used to model the convective heat-exchange with the ambient at the free-surface.The Giesekus viscoelastic constitutive model,with appropriate modifications to account for non-isothermal effects,is employed to describe the polymeric effects.The unsteady and coupled non-linear partial differential equations(PDEs)describing the model problem are obtained and solved via efficient semi-implicit numerical schemes based on finite difference methods(FDM)implemented in Matlab.The response of the VFBN velocity,temperature,thermal-conductivity and polymeric-stresses to variations in the volume-fraction of embedded nanoparticles is investigated.It is shown that these quantities all increase as the nanoparticle volume-fraction becomes higher.
