In this work, an analytical study is carried out on double-diffusive natural convection through a horizontal anisotropic porous layer saturated with a non-Newtonian fluid by using the Darcy model with the Boussinesq a...In this work, an analytical study is carried out on double-diffusive natural convection through a horizontal anisotropic porous layer saturated with a non-Newtonian fluid by using the Darcy model with the Boussinesq approximations. The horizontal walls of the system are subject to vertical uniform fluxes of heat and mass, whereas the vertical walls are assumed to be adiabatic and impermeable. The Soret effect is taken into consideration. Based on parallel flow approximation theory, the problem is solved in the limit of a thin layer and documented the effects of the physical parameters describing this investigation.展开更多
Using k- model of turbulence and measured wall functions, turbulent flows of Newtonian (pure water) andasort of non-Newtonian fluid (dilute, drag-reduction solution of polymer) in a 180-degree curved bend were simulat...Using k- model of turbulence and measured wall functions, turbulent flows of Newtonian (pure water) andasort of non-Newtonian fluid (dilute, drag-reduction solution of polymer) in a 180-degree curved bend were simulated numerically. The calculated results agreed well with the measured velocity profiles. On the basis of calculation and measurement, appropriateness of turbulence model to complicated flow in which the large-scale vortex exists was analyzed and discussed.展开更多
This article proves that the random dynamical system generated by a twodimensional incompressible non-Newtonian fluid with multiplicative noise has a global random attractor, which is a random compact set absorbing an...This article proves that the random dynamical system generated by a twodimensional incompressible non-Newtonian fluid with multiplicative noise has a global random attractor, which is a random compact set absorbing any bounded nonrandom subset of the phase space.展开更多
This paper is joint with [27]. The authors prove in this article the existence and reveal its structure of uniform attractor for a two-dimensional nonautonomous incompressible non-Newtonian fluid with a new class of e...This paper is joint with [27]. The authors prove in this article the existence and reveal its structure of uniform attractor for a two-dimensional nonautonomous incompressible non-Newtonian fluid with a new class of external forces.展开更多
In this paper, the aim is to establish the local existence of classical solutions for a class of compressible non-Newtonian fluids with vacuum in one-dimensional bounded intervals, under the assumption that the data s...In this paper, the aim is to establish the local existence of classical solutions for a class of compressible non-Newtonian fluids with vacuum in one-dimensional bounded intervals, under the assumption that the data satisfies a natural compatibility condition. For the results, the initial density does not need to be bounded below away from zero.展开更多
The effect of chemical reaction on free convection heat and mass transfer for a non-Newtonian power law fluid over a vertical flat plate embedded in a fluid-saturated porous medium has been studied in the presence of ...The effect of chemical reaction on free convection heat and mass transfer for a non-Newtonian power law fluid over a vertical flat plate embedded in a fluid-saturated porous medium has been studied in the presence of the yield stress and the Soret effect. The governing boundary layer equations and boundary conditions are cast into a dimen- sionless form by similarity transformations, and the resulting system of equations is solved by a finite difference method. The results are preSented and discussed for concentration profiles, as well as the Nusselt number and the Sherwood number for various values of the parameters, which govern the problem. The results obtained show that the flow field is influenced appreciably by the presence of the chemical reaction parameter γ the order of.the chemical reaction parameter m, the Soret number St, the buoyancy ratio N, the Lewis number Le, and the dimensionless rheological parameter Ω.展开更多
This paper studies the trajectory asymptotic behavior of a non-autonomous in- compressible non-Newtonian fluid in 3D bounded domains. In appropriate topologies, the authors prove the existence of the uniform trajector...This paper studies the trajectory asymptotic behavior of a non-autonomous in- compressible non-Newtonian fluid in 3D bounded domains. In appropriate topologies, the authors prove the existence of the uniform trajectory attractor for the translation semigroup acting on the united trajectory space.展开更多
This work deals with the modeling of the unsteady Newtonian fluid flow associated with an open cylindrical reservoir.This reservoir presents a hole on the right bottom wall.Fluid volume variation,heat and mass transfe...This work deals with the modeling of the unsteady Newtonian fluid flow associated with an open cylindrical reservoir.This reservoir presents a hole on the right bottom wall.Fluid volume variation,heat and mass transfers are neglected.The unsteady governing equations are based on the conservation of mass and momentum.A finite volume technique is used to solve the non-dimensional equations and related boundary conditions.The algebraic system of equations resulting from the discretization process are solved by means of the THOMAS algorithm.For pressure-velocity coupling,the SIMPLE algorithm(Semi Implicit Method for Pressure Linked Equations)is used.Results for laminar flow(Re<1000),including the pressure and velocities profiles as well as the streamlines in the reservoir are presented.Moreover,the effects of the D/d and H0/D ratios and Reynolds number Re on the fluid flow are discussed.It is shown that the velocities and pressure depend essentially on the reservoir size.To validate the model,the present results have been compared with Zhou et al.’s results,Poiseuille’s and Bernoulli’s exact solution.展开更多
A Jeffery-Hamel (J-H) flow model of the non-Newtonian fluid type inside a convergent wedge (inclined walls) with a wall friction is derived by a nonlinear ordinary differential equation with appropriate boundary c...A Jeffery-Hamel (J-H) flow model of the non-Newtonian fluid type inside a convergent wedge (inclined walls) with a wall friction is derived by a nonlinear ordinary differential equation with appropriate boundary conditions based on similarity relationships. Unlike the usual power law model, this paper develops nonlinear viscosity based only on a tangential coordinate function due to the radial geometry shape. Two kinds of solutions are developed, i.e., analytical and semi-analytical (numerical) solutions with suitable assumptions. As a result of the parametric examination, it has been found that the Newtonian normalized velocity gradually decreases with the tangential direction progress. Also, an increase in the friction coefficient leads to a decrease in the normalized Newtonian velocity profile values. However, an increase in the Reynolds number causes an increase in the normalized velocity function values. Additionally, for the small values of wedge semi-angle, the present solutions are in good agreement with the previous results in the literature.展开更多
The pressureless Navier-Stokes equations for non-Newtonian fluid are studied. The analytical solutions with arbitrary time blowup, in radial symmetry, are constructed in this paper. With the previous results for the a...The pressureless Navier-Stokes equations for non-Newtonian fluid are studied. The analytical solutions with arbitrary time blowup, in radial symmetry, are constructed in this paper. With the previous results for the analytical blowup solutions of the N-dimensional (N ≥ 2) Navier-Stokes equations, we extend the similar structure to construct an analytical family of solutions for the pressureless Navier-Stokes equations with a normal viscosity term (μ(ρ)| u|^α u).展开更多
A combination of the computational symbolic calculation, mathematical approach and physico-mechanical model lends to a computational intellectual analytical approach developed by the author. There is a principal diffe...A combination of the computational symbolic calculation, mathematical approach and physico-mechanical model lends to a computational intellectual analytical approach developed by the author. There is a principal difference between the computer proof and the computer derivation completed by the computer, also difference between the numerical and symbolic calculations. In this investigation the computational analytical approach is extended, and an unsteady flow of non-Newtonian fluid in the gap between two rotating coaxial cylinders is studied. The Oldroyd fluid B model is used by which the Weissenberg effects are explained in a good comparison with the experiments. The governing equations are reduced to a partial differential equation of 3 rd order for the dimensionless velocity. Using the computer software Macsyma and an improved variational approach the problem with the initial and boundary conditions is then reduced to a problem of an ordinary differential equation for different approximations. The analytical solutions are given for the 1 st, 2 nd and 3 rd approximations. The present investigation shows the ability of the computational symbolic manipulation in solving the problems of non-Newtonian fluid flows. There is a possibility of that to solve the problems in mathematics and mechanics. An important conclusion can be drawn from the results that the transition from a steady state to another steady state is non-unique.展开更多
In this paper, using Navier-Stokes equations and Reynolds time-averaged rules, the turbulent motional differential equations of variable density and variable viscosity Newtonian fluid have been presented, and the turb...In this paper, using Navier-Stokes equations and Reynolds time-averaged rules, the turbulent motional differential equations of variable density and variable viscosity Newtonian fluid have been presented, and the turbulent motional differential equations of variable density and variable viscosity Newtonian fluid in open channel have been further proposed. The concepts of the density turbulence stress and the viscosity turbulence stress have been firstly presented in the paper.展开更多
In this paper, the authors study the long time behavior of solutions to stochastic non-Newtonian fluids in a two-dimensional bounded domain, and prove the existence of H2-regularity random attractor.
The two-dimensional non-Newtonian steady flow on a power-law stretched surface with suction or injection is studied. Thermal conductivity is assumed to vary as a linear function of temperature. The transformed governi...The two-dimensional non-Newtonian steady flow on a power-law stretched surface with suction or injection is studied. Thermal conductivity is assumed to vary as a linear function of temperature. The transformed governing equations in the present study are solved numerically using the Runge-Kutta method. Through a comparison, results for a special case of the problem show excellent agreement with those in a previous work. Two cases are considered, one corresponding to a cooled surface temperature and the other to a uniform surface temperature. Numerical results show that the thermal conductivity variation parameter, the injection parameter, and the power-law index have significant influences on the temperature profiles and the Nusselt number.展开更多
Using the perturbation method, the axial laminar flow of Non-Newtonian fluid through an eccentric annulus is studied in the present paper. The relative eccentricity e is taken as a perturbation parameter, and the firs...Using the perturbation method, the axial laminar flow of Non-Newtonian fluid through an eccentric annulus is studied in the present paper. The relative eccentricity e is taken as a perturbation parameter, and the first order perturbation solutions of the problem, such as velocity field, limit velocity and pressure gradient, are all obtained.展开更多
In this paper, the principle of maximum power losses for the incompressible viscous fluid proposed by professor Chien Weizang in reference [1] is further extended to the hydrodynamic problem of the non-Newtonian fluid...In this paper, the principle of maximum power losses for the incompressible viscous fluid proposed by professor Chien Weizang in reference [1] is further extended to the hydrodynamic problem of the non-Newtonian fluid with constitutive law expressed as epsilon(y) = partial derivative tau/partial derivative sigma'(y). The constraint conditions of variation are eliminated by the method of identified Lagrangian multiplier and a generalized variational principle is established.展开更多
Case histories have shown that the liquefaction-induced soil lateral spreading is one of the main causes of damage to pile foundations subjected to seismic loading. Post-liquefaction soil behaves similarly to a viscou...Case histories have shown that the liquefaction-induced soil lateral spreading is one of the main causes of damage to pile foundations subjected to seismic loading. Post-liquefaction soil behaves similarly to a viscous fluid. This study investigated the effect of soil lateral spreading on a single pile based on fluid mechanics in which the liquefied soils were treated as Newtonian fluids. A numerical simulation on a single pile embedded in a fully saturated sandy foundation was conducted and compared with shake table tests. The lateral flow effect and the effect of shear strain rate were discussed. After liquefaction, the acceleration of the foundation shows that there are no obvious spikes and finally reaches a stable state. The presented method can predict the pile response better than p-y curve method. A parametric study was performed to explore the effect of several influence factors on pile behaviors. The results show that the pile head displacement decreases and the maximum bending moment at pile bottom increases with the increase of bending stiffness. With the same pile bending stiffness, the displacement and bending moment of pile increase with the increase of soil viscosity and acceleration amplitude.展开更多
Fluid-structure-interaction (FSI) phenomenon is common in science and engineering. The fluidinvolved in an FSI problem may be non-Newtonian such as blood. A popular framework for FSIproblems is Peskin’s imm...Fluid-structure-interaction (FSI) phenomenon is common in science and engineering. The fluidinvolved in an FSI problem may be non-Newtonian such as blood. A popular framework for FSIproblems is Peskin’s immersed boundary (IB) method. However, most of the IB formulations arebased on Newtonian fluids. In this letter, we report an extension of the IB framework to FSIinvolving Oldroyd-B and FENE-P fluids in three dimensions using the lattice Boltzmann approach.The new method is tested on two FSI model problems. Numerical experiments show that themethod is conditionally stable and convergent with the first order of accuracy.展开更多
In this paper. the principle of maximum power losses for the incompressibleviscous fluid proposed by professor Chien Wei-zang is extended to the hydrodynamicproblems of a special class of non-Newtonian fluid-generaliz...In this paper. the principle of maximum power losses for the incompressibleviscous fluid proposed by professor Chien Wei-zang is extended to the hydrodynamicproblems of a special class of non-Newtonian fluid-generalized Newtonian fluid.The constraint condition of variation are eliminated by the method of idetifiedLagrangian multipliers and a generalized variational principle is established.展开更多
This paper presents a hybrid finite volume/finite element method for the incompressible generalized Newtonian fluid flow (Power-Law model). The collocated (i.e. non-staggered) arrangement of variables is used on t...This paper presents a hybrid finite volume/finite element method for the incompressible generalized Newtonian fluid flow (Power-Law model). The collocated (i.e. non-staggered) arrangement of variables is used on the unstructured triangular grids, and a fractional step projection method is applied for the velocity-pressure coupling. The cell-centered finite volume method is employed to discretize the momentum equation and the vertex-based finite element for the pressure Poisson equation. The momentum interpolation method is used to suppress unphysical pressure wiggles. Numerical experiments demonstrate that the current hybrid scheme has second order accuracy in both space and time. Results on flows in the lid-driven cavity and between parallel walls for Newtonian and Power-Law models are also in good agreement with the published solutions.展开更多
文摘In this work, an analytical study is carried out on double-diffusive natural convection through a horizontal anisotropic porous layer saturated with a non-Newtonian fluid by using the Darcy model with the Boussinesq approximations. The horizontal walls of the system are subject to vertical uniform fluxes of heat and mass, whereas the vertical walls are assumed to be adiabatic and impermeable. The Soret effect is taken into consideration. Based on parallel flow approximation theory, the problem is solved in the limit of a thin layer and documented the effects of the physical parameters describing this investigation.
文摘Using k- model of turbulence and measured wall functions, turbulent flows of Newtonian (pure water) andasort of non-Newtonian fluid (dilute, drag-reduction solution of polymer) in a 180-degree curved bend were simulated numerically. The calculated results agreed well with the measured velocity profiles. On the basis of calculation and measurement, appropriateness of turbulence model to complicated flow in which the large-scale vortex exists was analyzed and discussed.
基金Sponsored by the National NSF (10901121, 10826091,10771074, and 10771139)NSF for Postdoctors in China (20090460952)+3 种基金NSF of Zhejiang Province (Y6080077)NSF of Guangdong Province (004020077)NSF of Wenzhou University (2008YYLQ01)Zhejiang youthteacher training project and Wenzhou 551 project
文摘This article proves that the random dynamical system generated by a twodimensional incompressible non-Newtonian fluid with multiplicative noise has a global random attractor, which is a random compact set absorbing any bounded nonrandom subset of the phase space.
基金Sponsored by the NSFC (10901121,10826091 and 10771139)NSF for Postdoctors of China (20090460952)+2 种基金NSF of Zhejiang Province (Y6080077)NSF of Wenzhou University (2008YYLQ01)by the Zhejiang Youth Teacher Training Project and Wenzhou 551 Project
文摘This paper is joint with [27]. The authors prove in this article the existence and reveal its structure of uniform attractor for a two-dimensional nonautonomous incompressible non-Newtonian fluid with a new class of external forces.
基金Supported by NSFC(11201371,1331005)Natural Science Foundation of Shaanxi Province(2012JQ020)
文摘In this paper, the aim is to establish the local existence of classical solutions for a class of compressible non-Newtonian fluids with vacuum in one-dimensional bounded intervals, under the assumption that the data satisfies a natural compatibility condition. For the results, the initial density does not need to be bounded below away from zero.
文摘The effect of chemical reaction on free convection heat and mass transfer for a non-Newtonian power law fluid over a vertical flat plate embedded in a fluid-saturated porous medium has been studied in the presence of the yield stress and the Soret effect. The governing boundary layer equations and boundary conditions are cast into a dimen- sionless form by similarity transformations, and the resulting system of equations is solved by a finite difference method. The results are preSented and discussed for concentration profiles, as well as the Nusselt number and the Sherwood number for various values of the parameters, which govern the problem. The results obtained show that the flow field is influenced appreciably by the presence of the chemical reaction parameter γ the order of.the chemical reaction parameter m, the Soret number St, the buoyancy ratio N, the Lewis number Le, and the dimensionless rheological parameter Ω.
基金Supported by NSFC(51209242,2011BAB09B01,11271290)NSF of Zhejiang Province(LY17A010011)
文摘This paper studies the trajectory asymptotic behavior of a non-autonomous in- compressible non-Newtonian fluid in 3D bounded domains. In appropriate topologies, the authors prove the existence of the uniform trajectory attractor for the translation semigroup acting on the united trajectory space.
文摘This work deals with the modeling of the unsteady Newtonian fluid flow associated with an open cylindrical reservoir.This reservoir presents a hole on the right bottom wall.Fluid volume variation,heat and mass transfers are neglected.The unsteady governing equations are based on the conservation of mass and momentum.A finite volume technique is used to solve the non-dimensional equations and related boundary conditions.The algebraic system of equations resulting from the discretization process are solved by means of the THOMAS algorithm.For pressure-velocity coupling,the SIMPLE algorithm(Semi Implicit Method for Pressure Linked Equations)is used.Results for laminar flow(Re<1000),including the pressure and velocities profiles as well as the streamlines in the reservoir are presented.Moreover,the effects of the D/d and H0/D ratios and Reynolds number Re on the fluid flow are discussed.It is shown that the velocities and pressure depend essentially on the reservoir size.To validate the model,the present results have been compared with Zhou et al.’s results,Poiseuille’s and Bernoulli’s exact solution.
文摘A Jeffery-Hamel (J-H) flow model of the non-Newtonian fluid type inside a convergent wedge (inclined walls) with a wall friction is derived by a nonlinear ordinary differential equation with appropriate boundary conditions based on similarity relationships. Unlike the usual power law model, this paper develops nonlinear viscosity based only on a tangential coordinate function due to the radial geometry shape. Two kinds of solutions are developed, i.e., analytical and semi-analytical (numerical) solutions with suitable assumptions. As a result of the parametric examination, it has been found that the Newtonian normalized velocity gradually decreases with the tangential direction progress. Also, an increase in the friction coefficient leads to a decrease in the normalized Newtonian velocity profile values. However, an increase in the Reynolds number causes an increase in the normalized velocity function values. Additionally, for the small values of wedge semi-angle, the present solutions are in good agreement with the previous results in the literature.
基金Supported by the NSFC of China (1087117510931007+1 种基金10901137)supported by the Scientific Research Fund of Education Department of Zhejiang Province (Y200803203)
文摘The pressureless Navier-Stokes equations for non-Newtonian fluid are studied. The analytical solutions with arbitrary time blowup, in radial symmetry, are constructed in this paper. With the previous results for the analytical blowup solutions of the N-dimensional (N ≥ 2) Navier-Stokes equations, we extend the similar structure to construct an analytical family of solutions for the pressureless Navier-Stokes equations with a normal viscosity term (μ(ρ)| u|^α u).
文摘A combination of the computational symbolic calculation, mathematical approach and physico-mechanical model lends to a computational intellectual analytical approach developed by the author. There is a principal difference between the computer proof and the computer derivation completed by the computer, also difference between the numerical and symbolic calculations. In this investigation the computational analytical approach is extended, and an unsteady flow of non-Newtonian fluid in the gap between two rotating coaxial cylinders is studied. The Oldroyd fluid B model is used by which the Weissenberg effects are explained in a good comparison with the experiments. The governing equations are reduced to a partial differential equation of 3 rd order for the dimensionless velocity. Using the computer software Macsyma and an improved variational approach the problem with the initial and boundary conditions is then reduced to a problem of an ordinary differential equation for different approximations. The analytical solutions are given for the 1 st, 2 nd and 3 rd approximations. The present investigation shows the ability of the computational symbolic manipulation in solving the problems of non-Newtonian fluid flows. There is a possibility of that to solve the problems in mathematics and mechanics. An important conclusion can be drawn from the results that the transition from a steady state to another steady state is non-unique.
文摘In this paper, using Navier-Stokes equations and Reynolds time-averaged rules, the turbulent motional differential equations of variable density and variable viscosity Newtonian fluid have been presented, and the turbulent motional differential equations of variable density and variable viscosity Newtonian fluid in open channel have been further proposed. The concepts of the density turbulence stress and the viscosity turbulence stress have been firstly presented in the paper.
基金Project supported by the National Natural Science Foundation of China(Nos.11126160,11201475,11371183,and 11101356)
文摘In this paper, the authors study the long time behavior of solutions to stochastic non-Newtonian fluids in a two-dimensional bounded domain, and prove the existence of H2-regularity random attractor.
文摘The two-dimensional non-Newtonian steady flow on a power-law stretched surface with suction or injection is studied. Thermal conductivity is assumed to vary as a linear function of temperature. The transformed governing equations in the present study are solved numerically using the Runge-Kutta method. Through a comparison, results for a special case of the problem show excellent agreement with those in a previous work. Two cases are considered, one corresponding to a cooled surface temperature and the other to a uniform surface temperature. Numerical results show that the thermal conductivity variation parameter, the injection parameter, and the power-law index have significant influences on the temperature profiles and the Nusselt number.
文摘Using the perturbation method, the axial laminar flow of Non-Newtonian fluid through an eccentric annulus is studied in the present paper. The relative eccentricity e is taken as a perturbation parameter, and the first order perturbation solutions of the problem, such as velocity field, limit velocity and pressure gradient, are all obtained.
文摘In this paper, the principle of maximum power losses for the incompressible viscous fluid proposed by professor Chien Weizang in reference [1] is further extended to the hydrodynamic problem of the non-Newtonian fluid with constitutive law expressed as epsilon(y) = partial derivative tau/partial derivative sigma'(y). The constraint conditions of variation are eliminated by the method of identified Lagrangian multiplier and a generalized variational principle is established.
文摘Case histories have shown that the liquefaction-induced soil lateral spreading is one of the main causes of damage to pile foundations subjected to seismic loading. Post-liquefaction soil behaves similarly to a viscous fluid. This study investigated the effect of soil lateral spreading on a single pile based on fluid mechanics in which the liquefied soils were treated as Newtonian fluids. A numerical simulation on a single pile embedded in a fully saturated sandy foundation was conducted and compared with shake table tests. The lateral flow effect and the effect of shear strain rate were discussed. After liquefaction, the acceleration of the foundation shows that there are no obvious spikes and finally reaches a stable state. The presented method can predict the pile response better than p-y curve method. A parametric study was performed to explore the effect of several influence factors on pile behaviors. The results show that the pile head displacement decreases and the maximum bending moment at pile bottom increases with the increase of bending stiffness. With the same pile bending stiffness, the displacement and bending moment of pile increase with the increase of soil viscosity and acceleration amplitude.
基金the US National Science Foundation (DMS-1522554) for the support
文摘Fluid-structure-interaction (FSI) phenomenon is common in science and engineering. The fluidinvolved in an FSI problem may be non-Newtonian such as blood. A popular framework for FSIproblems is Peskin’s immersed boundary (IB) method. However, most of the IB formulations arebased on Newtonian fluids. In this letter, we report an extension of the IB framework to FSIinvolving Oldroyd-B and FENE-P fluids in three dimensions using the lattice Boltzmann approach.The new method is tested on two FSI model problems. Numerical experiments show that themethod is conditionally stable and convergent with the first order of accuracy.
文摘In this paper. the principle of maximum power losses for the incompressibleviscous fluid proposed by professor Chien Wei-zang is extended to the hydrodynamicproblems of a special class of non-Newtonian fluid-generalized Newtonian fluid.The constraint condition of variation are eliminated by the method of idetifiedLagrangian multipliers and a generalized variational principle is established.
基金supported by the National Natural Science Foundation of China (10771134).
文摘This paper presents a hybrid finite volume/finite element method for the incompressible generalized Newtonian fluid flow (Power-Law model). The collocated (i.e. non-staggered) arrangement of variables is used on the unstructured triangular grids, and a fractional step projection method is applied for the velocity-pressure coupling. The cell-centered finite volume method is employed to discretize the momentum equation and the vertex-based finite element for the pressure Poisson equation. The momentum interpolation method is used to suppress unphysical pressure wiggles. Numerical experiments demonstrate that the current hybrid scheme has second order accuracy in both space and time. Results on flows in the lid-driven cavity and between parallel walls for Newtonian and Power-Law models are also in good agreement with the published solutions.