This paper aims to investigate exact solutions for a second-grade fluid flow with the inverse method. By assuming the relation between the vorticity field and the streamfunction, the exact solutions of the motion of p...This paper aims to investigate exact solutions for a second-grade fluid flow with the inverse method. By assuming the relation between the vorticity field and the streamfunction, the exact solutions of the motion of plane second-grade fluids are investigated and obtained. The solutions obtained include simple Couette flows, slit jet flows and uniform flows over a series of distributed obstacles.展开更多
This paper is concerned with the steady flow of a second-grade fluid between two porous disks rotating eccentrically under the effect of a magnetic field. A perturbation solution for the velocity field is presented un...This paper is concerned with the steady flow of a second-grade fluid between two porous disks rotating eccentrically under the effect of a magnetic field. A perturbation solution for the velocity field is presented under the assumption that the second-grade fluid parameter β is small. It is also studied the effect of all the parameters on the horizontal force per unit area exerted by the fluid on the disks. It is found that the x- and y-components of the force increase and decrease, respectively, when the second-grade fluid parameter β and the Hartmann number M increase. It is seen that the forces in the x- and y-directions on the top disk increase with the increase of the suction/injection velocity parameter P but those on the bottom disk decrease. It is shown that the force acting on the top disk is greater than that acting on the bottom disk in view of the axial velocity in the positive z-direction. It is observed that the increase in the Reynolds number R leads to a rise in the horizontal force.展开更多
The second-grade fluid flow due to a rotating porous stretchable disk is modeled and analyzed. A porous medium is characterized by the Darcy relation. The heat and mass transport are characterized through Cattaneo-Chr...The second-grade fluid flow due to a rotating porous stretchable disk is modeled and analyzed. A porous medium is characterized by the Darcy relation. The heat and mass transport are characterized through Cattaneo-Christov double diffusions.The thermal and solutal stratifications at the surface are also accounted. The relevant nonlinear ordinary differential systems after using appropriate transformations are solved for the solutions with the homotopy analysis method(HAM). The effects of various involved variables on the temperature, velocity, concentration, skin friction, mass transfer rate, and heat transfer rate are discussed through graphs. From the obtained results,decreasing tendencies for the radial, axial, and tangential velocities are observed. Temperature is a decreasing function of the Reynolds number, thermal relaxation parameter,and Prandtl number. Moreover, the mass diffusivity decreases with the Schmidt number.展开更多
The aspiration of this research is to explore the impact of non-similar modeling for mixed convection in magnetized second-grade nanofluid flow.The flow is initiated by the stretching of a sheet at an exponential rate...The aspiration of this research is to explore the impact of non-similar modeling for mixed convection in magnetized second-grade nanofluid flow.The flow is initiated by the stretching of a sheet at an exponential rate in the upward vertical direction.The buoyancy effects in terms of temperature and concentration differences are inserted in the x-momentum equation.The aspects of heat and mass transfer are studied using dimensionless thermophoresis,Schmidt and Brownian motion parameters.The governing coupled partial differential system(PDEs)is remodeled into coupled non-similar nonlinear PDEs by introducing non-similar transformations.The numerical analysis for the dimensionless non-similar partial differential system is performed using a local non-similarity method via bvp4c.Finally,the quantitative effects of emerging dimensionless quantities on the nondimensional velocity,temperature and mass concentration in the boundary layer are conferred graphically,and inferences are drawn that important quantities of interest are substantially affected by these parameters.It is concluded that non-similar modeling,in contrast to similar models,is more general and more accurate in convection studies in the presence of buoyancy effects for second-grade non-Newtonian fluids.展开更多
This study derives the analytic solutions of boundary layer flows bounded by a shrinking sheet. With the similarity transformations, the partial differential equations are reduced into the ordinary differential equati...This study derives the analytic solutions of boundary layer flows bounded by a shrinking sheet. With the similarity transformations, the partial differential equations are reduced into the ordinary differential equations which are then solved by the homotopy analysis method （HAM）. Two-dimensional and axisymmetric shrinking flow cases are discussed.展开更多
In this paper, we consider the second-grade fluid equations in a 2D exterior domain satisfying the non-slip boundary conditions. The second-grade fluid model is a wellknown non-Newtonian fluid model, with two paramete...In this paper, we consider the second-grade fluid equations in a 2D exterior domain satisfying the non-slip boundary conditions. The second-grade fluid model is a wellknown non-Newtonian fluid model, with two parameters: α, which represents the length-scale,while ν > 0 corresponds to the viscosity. We prove that, as ν, α tend to zero, the solution of the second-grade fluid equations with suitable initial data converges to the one of Euler equations, provided that ν = o(α^(4/3)). Moreover, the convergent rate is obtained.展开更多
A differential constraint method is used to obtain analytical solutions of a second-grade fluid flow. By using the first-order differential constraint condition, exact solutions of Poiseuille flows, jet flows and Coue...A differential constraint method is used to obtain analytical solutions of a second-grade fluid flow. By using the first-order differential constraint condition, exact solutions of Poiseuille flows, jet flows and Couette flows subjected to suction or blowing forces, and planar elongational flows are derived. In addition, two new classes of exact solutions for a second-grade fluid flow are found. The obtained exact solutions show that the non-Newtonian second-grade flow behavior depends not only on the material viscosity but also on the material elasticity. Finally, some boundary value problems are discussed.展开更多
Studies on electro-osmotic flows of various types of fluids in microchannel are of great importance owing to their multifold applications in the transport of liquids, particularly when the ionized liquid flows with re...Studies on electro-osmotic flows of various types of fluids in microchannel are of great importance owing to their multifold applications in the transport of liquids, particularly when the ionized liquid flows with respect to a charged surface in the presence of an external electric field. In the case of viscoelastic fluids, the volumetric flow rate differs significantly from that of Newtonian fluids, even when the flow takes place under the same pressure gradient and the same electric field. With this end in view, this paper is devoted to a study concerning the flow pattern of an electro-osmotic flow in a porous microchannel, which is under the action of an alternating electric field. The influence of various rheological and electro-osmotic parameters, e.g., the Reynolds number, Debye-Huckel parameter, shape factor and fluid viscoelasticity on the kinematics of the fluid, has been investigated for a secondgrade viscoelastic fluid. The problem is first treated by using analytical methods, but the quantitative estimates are obtained numerically with the help of the software MATHEMATICA. The results presented here are applicable to the cases where the channel height is much greater than the thickness of the electrical double layer comprising the Stern and diffuse layers. The study reveals that a larger value of the Debye-Huckel parameter creates sharper profile near the wall and also that the velocity of electro-osmotic flow increases as the permeability of the porous microchannel is enhanced. The study further shows that the electro-osmotic flow dominates at lower values of Reynolds number. The results presented here will be quite useful to validate the observations of experimental investigations on the characteristics of electro-osmotic flows and also the results of complex numerical models that are necessary to deal with more realistic situations, where electro-osmotic flows come into the picture, as in blood flow in the micro-circulatory system subject to an electric field.展开更多
In this paper,we first establish a new fractional magnetohydrodynamic(MHD)coupled flow and heat transfer model for a generalized second-grade fluid.This coupled model consists of a fractional momentum equation and a h...In this paper,we first establish a new fractional magnetohydrodynamic(MHD)coupled flow and heat transfer model for a generalized second-grade fluid.This coupled model consists of a fractional momentum equation and a heat conduction equation with a generalized form of Fourier law.The second-order fractional backward difference formula is applied to the temporal discretization and the Legendre spectral method is used for the spatial discretization.The fully discrete scheme is proved to be stable and convergent with an accuracy of O(τ^(2)+N-r),whereτis the time step-size and N is the polynomial degree.To reduce the memory requirements and computational cost,a fast method is developed,which is based on a globally uniform approximation of the trapezoidal rule for integrals on the real line.The strict convergence of the numerical scheme with this fast method is proved.We present the results of several numerical experiments to verify the effectiveness of the proposed method.Finally,we simulate the unsteady fractional MHD flow and heat transfer of the generalized second-grade fluid through a porous medium.The effects of the relevant parameters on the velocity and temperature are presented and analyzed in detail.展开更多
In this paper,we establish a moderate deviation principle for stochastic models of two-dimensional second-grade fluids driven by Lévy noise.We will adopt the weak convergence approach.Because of the appearance of...In this paper,we establish a moderate deviation principle for stochastic models of two-dimensional second-grade fluids driven by Lévy noise.We will adopt the weak convergence approach.Because of the appearance of jumps,this result is significantly different from that in Gaussian case.展开更多
The present study is concerned with unsteady natural convective boundary layer flow and heat transfer of fractional second-grade nanofuids for different particle shapes.Nonlinear boundary layer governing equations are...The present study is concerned with unsteady natural convective boundary layer flow and heat transfer of fractional second-grade nanofuids for different particle shapes.Nonlinear boundary layer governing equations are formulated with time fractional derivatives in the momentum equation.The governing boundary layer equations of continuity,momentum and energy are reduced by dimensionless variable.Numerical solutions of the momentum and energy equations are obtained by the finite difference method combined with L1-algorithm.The quantites of physical interest are graphically presented and discussed in details.It is found that particle shape,fractional derivative parameter and the Grashof number have profound influences on the the flow and heat transfer.展开更多
相同灌溉条件下,作物生长及水分利用效率(Water use efficiency,WUE)会因灌溉水质的不同而存在差异。本研究采用盆栽实验方法,以清水灌溉为对照,比较了北京市高碑店污水处理厂的2级再生水、3级再生水对玉米(Zea maysL.)和大豆(Glycine m...相同灌溉条件下,作物生长及水分利用效率(Water use efficiency,WUE)会因灌溉水质的不同而存在差异。本研究采用盆栽实验方法,以清水灌溉为对照,比较了北京市高碑店污水处理厂的2级再生水、3级再生水对玉米(Zea maysL.)和大豆(Glycine maxesL.)生长及WUE的影响。结果表明:2级再生水对玉米苗期生长有一定影响,3级再生水对玉米苗期生长有一定促进作用;2级和3级再生水对玉米拔节期和收获期生长影响不显著或有所促进;再生水灌溉对玉米苗期WUE有一定影响,自拔节期开始影响降低并表现出一定的促进作用。2级和3级再生水可促进大豆苗期和花荚期的生长,对收获期的生长影响不显著;再生水灌溉对大豆苗期WUE有一定促进作用,花荚期开始促进作用减弱。总体而言,玉米苗期灌溉2级再生水对其生长和WUE有一定影响,拔节期后灌溉则促进玉米生长和提高WUE;3级再生水灌溉有利于玉米生长,提高WUE;大豆各个生育期灌溉2级或3级再生水都可促进生长,对WUE影响不大。展开更多
基金supported by the National Natural Science Foundation of China (Grant No.10472063)
文摘This paper aims to investigate exact solutions for a second-grade fluid flow with the inverse method. By assuming the relation between the vorticity field and the streamfunction, the exact solutions of the motion of plane second-grade fluids are investigated and obtained. The solutions obtained include simple Couette flows, slit jet flows and uniform flows over a series of distributed obstacles.
文摘This paper is concerned with the steady flow of a second-grade fluid between two porous disks rotating eccentrically under the effect of a magnetic field. A perturbation solution for the velocity field is presented under the assumption that the second-grade fluid parameter β is small. It is also studied the effect of all the parameters on the horizontal force per unit area exerted by the fluid on the disks. It is found that the x- and y-components of the force increase and decrease, respectively, when the second-grade fluid parameter β and the Hartmann number M increase. It is seen that the forces in the x- and y-directions on the top disk increase with the increase of the suction/injection velocity parameter P but those on the bottom disk decrease. It is shown that the force acting on the top disk is greater than that acting on the bottom disk in view of the axial velocity in the positive z-direction. It is observed that the increase in the Reynolds number R leads to a rise in the horizontal force.
基金Project supported by the Natural Science and Engineering Research Council(NSERC)of Canada(No.NSERC-RGPIN204992)
文摘The second-grade fluid flow due to a rotating porous stretchable disk is modeled and analyzed. A porous medium is characterized by the Darcy relation. The heat and mass transport are characterized through Cattaneo-Christov double diffusions.The thermal and solutal stratifications at the surface are also accounted. The relevant nonlinear ordinary differential systems after using appropriate transformations are solved for the solutions with the homotopy analysis method(HAM). The effects of various involved variables on the temperature, velocity, concentration, skin friction, mass transfer rate, and heat transfer rate are discussed through graphs. From the obtained results,decreasing tendencies for the radial, axial, and tangential velocities are observed. Temperature is a decreasing function of the Reynolds number, thermal relaxation parameter,and Prandtl number. Moreover, the mass diffusivity decreases with the Schmidt number.
文摘The aspiration of this research is to explore the impact of non-similar modeling for mixed convection in magnetized second-grade nanofluid flow.The flow is initiated by the stretching of a sheet at an exponential rate in the upward vertical direction.The buoyancy effects in terms of temperature and concentration differences are inserted in the x-momentum equation.The aspects of heat and mass transfer are studied using dimensionless thermophoresis,Schmidt and Brownian motion parameters.The governing coupled partial differential system(PDEs)is remodeled into coupled non-similar nonlinear PDEs by introducing non-similar transformations.The numerical analysis for the dimensionless non-similar partial differential system is performed using a local non-similarity method via bvp4c.Finally,the quantitative effects of emerging dimensionless quantities on the nondimensional velocity,temperature and mass concentration in the boundary layer are conferred graphically,and inferences are drawn that important quantities of interest are substantially affected by these parameters.It is concluded that non-similar modeling,in contrast to similar models,is more general and more accurate in convection studies in the presence of buoyancy effects for second-grade non-Newtonian fluids.
文摘This study derives the analytic solutions of boundary layer flows bounded by a shrinking sheet. With the similarity transformations, the partial differential equations are reduced into the ordinary differential equations which are then solved by the homotopy analysis method （HAM）. Two-dimensional and axisymmetric shrinking flow cases are discussed.
基金Aibin Zang was supported partially by the National Natural Science Foundation of China (11771382, 12061080, 12261093)the Jiangxi Provincial Natural Science Foundation (20224ACB201004)。
文摘In this paper, we consider the second-grade fluid equations in a 2D exterior domain satisfying the non-slip boundary conditions. The second-grade fluid model is a wellknown non-Newtonian fluid model, with two parameters: α, which represents the length-scale,while ν > 0 corresponds to the viscosity. We prove that, as ν, α tend to zero, the solution of the second-grade fluid equations with suitable initial data converges to the one of Euler equations, provided that ν = o(α^(4/3)). Moreover, the convergent rate is obtained.
基金supported by the National Natural Science Foundation of China (No. 10772110)
文摘A differential constraint method is used to obtain analytical solutions of a second-grade fluid flow. By using the first-order differential constraint condition, exact solutions of Poiseuille flows, jet flows and Couette flows subjected to suction or blowing forces, and planar elongational flows are derived. In addition, two new classes of exact solutions for a second-grade fluid flow are found. The obtained exact solutions show that the non-Newtonian second-grade flow behavior depends not only on the material viscosity but also on the material elasticity. Finally, some boundary value problems are discussed.
文摘Studies on electro-osmotic flows of various types of fluids in microchannel are of great importance owing to their multifold applications in the transport of liquids, particularly when the ionized liquid flows with respect to a charged surface in the presence of an external electric field. In the case of viscoelastic fluids, the volumetric flow rate differs significantly from that of Newtonian fluids, even when the flow takes place under the same pressure gradient and the same electric field. With this end in view, this paper is devoted to a study concerning the flow pattern of an electro-osmotic flow in a porous microchannel, which is under the action of an alternating electric field. The influence of various rheological and electro-osmotic parameters, e.g., the Reynolds number, Debye-Huckel parameter, shape factor and fluid viscoelasticity on the kinematics of the fluid, has been investigated for a secondgrade viscoelastic fluid. The problem is first treated by using analytical methods, but the quantitative estimates are obtained numerically with the help of the software MATHEMATICA. The results presented here are applicable to the cases where the channel height is much greater than the thickness of the electrical double layer comprising the Stern and diffuse layers. The study reveals that a larger value of the Debye-Huckel parameter creates sharper profile near the wall and also that the velocity of electro-osmotic flow increases as the permeability of the porous microchannel is enhanced. The study further shows that the electro-osmotic flow dominates at lower values of Reynolds number. The results presented here will be quite useful to validate the observations of experimental investigations on the characteristics of electro-osmotic flows and also the results of complex numerical models that are necessary to deal with more realistic situations, where electro-osmotic flows come into the picture, as in blood flow in the micro-circulatory system subject to an electric field.
基金supported by the Project of the National Key R&D Program(Grant No.2021YFA1000202)National Natural Science Foundation of China(Grant Nos.12120101001,12001326 and 12171283)+2 种基金Natural Science Foundation of Shandong Province(Grant Nos.ZR2021ZD03,ZR2020QA032 and ZR2019ZD42)China Postdoctoral Science Foundation(Grant Nos.BX20190191 and 2020M672038)the Startup Fund from Shandong University(Grant No.11140082063130)。
文摘In this paper,we first establish a new fractional magnetohydrodynamic(MHD)coupled flow and heat transfer model for a generalized second-grade fluid.This coupled model consists of a fractional momentum equation and a heat conduction equation with a generalized form of Fourier law.The second-order fractional backward difference formula is applied to the temporal discretization and the Legendre spectral method is used for the spatial discretization.The fully discrete scheme is proved to be stable and convergent with an accuracy of O(τ^(2)+N-r),whereτis the time step-size and N is the polynomial degree.To reduce the memory requirements and computational cost,a fast method is developed,which is based on a globally uniform approximation of the trapezoidal rule for integrals on the real line.The strict convergence of the numerical scheme with this fast method is proved.We present the results of several numerical experiments to verify the effectiveness of the proposed method.Finally,we simulate the unsteady fractional MHD flow and heat transfer of the generalized second-grade fluid through a porous medium.The effects of the relevant parameters on the velocity and temperature are presented and analyzed in detail.
基金supported by National Natural Science Foundation of China(NSFC)(No.11431014,No.11671372,No.11721101)the Fundamental Research Funds for the Central Universities(No.WK0010450002).
文摘In this paper,we establish a moderate deviation principle for stochastic models of two-dimensional second-grade fluids driven by Lévy noise.We will adopt the weak convergence approach.Because of the appearance of jumps,this result is significantly different from that in Gaussian case.
基金the Natural Science Foundation of Fujian Province(Grant No.2019J01646).
文摘The present study is concerned with unsteady natural convective boundary layer flow and heat transfer of fractional second-grade nanofuids for different particle shapes.Nonlinear boundary layer governing equations are formulated with time fractional derivatives in the momentum equation.The governing boundary layer equations of continuity,momentum and energy are reduced by dimensionless variable.Numerical solutions of the momentum and energy equations are obtained by the finite difference method combined with L1-algorithm.The quantites of physical interest are graphically presented and discussed in details.It is found that particle shape,fractional derivative parameter and the Grashof number have profound influences on the the flow and heat transfer.
文摘相同灌溉条件下,作物生长及水分利用效率(Water use efficiency,WUE)会因灌溉水质的不同而存在差异。本研究采用盆栽实验方法,以清水灌溉为对照,比较了北京市高碑店污水处理厂的2级再生水、3级再生水对玉米(Zea maysL.)和大豆(Glycine maxesL.)生长及WUE的影响。结果表明:2级再生水对玉米苗期生长有一定影响,3级再生水对玉米苗期生长有一定促进作用;2级和3级再生水对玉米拔节期和收获期生长影响不显著或有所促进;再生水灌溉对玉米苗期WUE有一定影响,自拔节期开始影响降低并表现出一定的促进作用。2级和3级再生水可促进大豆苗期和花荚期的生长,对收获期的生长影响不显著;再生水灌溉对大豆苗期WUE有一定促进作用,花荚期开始促进作用减弱。总体而言,玉米苗期灌溉2级再生水对其生长和WUE有一定影响,拔节期后灌溉则促进玉米生长和提高WUE;3级再生水灌溉有利于玉米生长,提高WUE;大豆各个生育期灌溉2级或3级再生水都可促进生长,对WUE影响不大。
