The specific problem to be considered here concerns the boundary layer problem of a non-Newtonian fluid on a flat plate in length, whose surface has a constant velocity opposite in the direction to that of the mainstr...The specific problem to be considered here concerns the boundary layer problem of a non-Newtonian fluid on a flat plate in length, whose surface has a constant velocity opposite in the direction to that of the mainstream with Uw 〉〉 U∞, or alternatively when the plate surface velocity is kept fixed but the stream speed is reduced to zero. A theoretical analysis for a boundary layer flow is made and the self-similar equation is determined. Solutions are presented numerically for special power index and the associated transfer behavior is discussed.展开更多
Flow and heat transfer of a pseudo-plastic power-law fluid over a stretching permeable surface with the magnetic effect is investigated. In the boundary conditions,the nonlinear temperature jump and the velocity slip ...Flow and heat transfer of a pseudo-plastic power-law fluid over a stretching permeable surface with the magnetic effect is investigated. In the boundary conditions,the nonlinear temperature jump and the velocity slip are considered. Semi-similarity equations are obtained and solved by bvp4c with MATLAB. The problem can be considered as an extension of the previous work done by Mahmoud(Mahmoud, M. A. A. Slip velocity effect on a non-Newtonian power-law fluid over a moving permeable surface with heat generation. Mathematical and Computer Modelling, 54, 1228–1237(2011)). Efforts are made to discuss the effects of the power-law number, slip velocity, and temperature jump on the dimensionless velocity and temperature distribution.展开更多
Considering Brinkman⁃Forchheimer extended Darcy flow and local thermal non⁃equilibrium effect,a general model of forced convection with viscous dissipation in power⁃law fluid saturated porous media channel was establi...Considering Brinkman⁃Forchheimer extended Darcy flow and local thermal non⁃equilibrium effect,a general model of forced convection with viscous dissipation in power⁃law fluid saturated porous media channel was established.The dimensionless temperature profiles and Nusselt number were numerically solved using the classical fourth⁃order Runge Kutta method under a constant heat flux boundary condition.The conclusion showed that the fluid⁃solid temperature distributions were significantly affected by dimensionless Bi,k,Da,Br,and F,and the effects of power⁃law indexes on convection heat transfer characteristics were also non⁃negligible.展开更多
A modified power-law fluid of second grade is considered. The model is a combination of power-law and second grade fluid in which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. Th...A modified power-law fluid of second grade is considered. The model is a combination of power-law and second grade fluid in which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. The equations of motion are derived for two dimensional incompressible flows, and from which the boundary layer equations are derived. Symmetries of the boundary layer equations are found by using Lie group theory, and then group classification with respect to power-law index is performed. By using one of the symmetries, namely the scaling symmetry, the partial differential system is transformed into an ordinary differential system, which is numerically integrated under the classical boundary layer conditions. Effects of power-law index and second grade coefficient on the boundary layers are shown and solutions are contrasted with the usual second grade fluid solutions.展开更多
The long wave stability of core-annular flow of power-law fluids with an axial pressure gradient is investigated at low Reynolds number. The interface between the two fluids is populated with an insoluble surfactant. ...The long wave stability of core-annular flow of power-law fluids with an axial pressure gradient is investigated at low Reynolds number. The interface between the two fluids is populated with an insoluble surfactant. The analytic solution for the growth rate of perturbation is obtained with long wave approximation. We are mainly concerned with the effects of shear-thinning/thickening property and interfacial surfactant on the flow stability. The results show that the influence of shear-thinning/thickening property accounts to the change of the capillary number. For a clean interface, the shear-thinning property enhances the capillary instability when the interface is close to the pipe wall. The converse is true when the interface is close to the pipe centerline. For shear-thickening fluids, the situation is reversed. When the interface is close to the pipe centerline, the capillary instability can be restrained due to the influence of surfactant. A parameter set can be found under which the flow is linearly stable.展开更多
An investigation is made of the magnetic Rayleigh problem where a semi_infinite plate is given an impulsive motion and thereafter moves with constant velocity in a non_Newtonian power law fluid of infinite extent. The...An investigation is made of the magnetic Rayleigh problem where a semi_infinite plate is given an impulsive motion and thereafter moves with constant velocity in a non_Newtonian power law fluid of infinite extent. The solution of this highly non_linear problem is obtained by means of the transformation group theoretic approach. The one_parameter group transformation reduces the number of independent variables by one and the governing partial differential equation with the boundary conditions reduce to an ordinary differential equation with the appropriate boundary conditions. Effect of the some parameters on the velocity u(y,t) has been studied and the results are plotted.展开更多
The problem of the boundary layer flow of power law non-Newtonian fluids with a novel boundary condition is studied. The existence and uniqueness of the solutions are examined, which are found to depend on the curvatu...The problem of the boundary layer flow of power law non-Newtonian fluids with a novel boundary condition is studied. The existence and uniqueness of the solutions are examined, which are found to depend on the curvature of the solutions for different values of the power law index n. It is established with the aid of the Picard-Lindelof theorem that the nonlinear boundary value problem has a unique solution in the global domain for all values of the power law index n but with certain conditions on the curva- ture of the solutions. This is done after a suitable transformation of the dependent and independent variables. For 0 〈 n ≤ 1, the solution has a positive curvature, while for n 〉 1, the solution has a negative or zero curvature on some part of the global domain. Some solutions are presented graphically to illustrate the results and the behaviors of the solutions.展开更多
A direct difference method has been developed for Non-Newtonian power law fluids to solve the simultaneous non-linear partial differential equations of melt spinning, and to determine the critical draw ratio for draw ...A direct difference method has been developed for Non-Newtonian power law fluids to solve the simultaneous non-linear partial differential equations of melt spinning, and to determine the critical draw ratio for draw resonance. The results show that for shear thin fluids, the logarithm of the critical draw ratio has a well defined linear relationship with the power index for isothermal and uniform tension melt spinning. When the power index approaches zero, the critical draw ratio points at unity, indicating no melt spinning can be processed stably for such fluids. For shear thick fluids, the critical draw ratio increases in a more rapid way with increasing the power index.展开更多
This paper presents a theoretical analysis for laminar boundary layer flow in a power law non-Newtonian fluids. The Adomian analytical decomposition technique is presented and an approximate analytical solution is obt...This paper presents a theoretical analysis for laminar boundary layer flow in a power law non-Newtonian fluids. The Adomian analytical decomposition technique is presented and an approximate analytical solution is obtained. The approximate analytical solution can be expressed in terms of a rapid convergent power series with easily computable terms. Reliability and efficiency of the approximate solution are verified by comparing with numerical solutions in the literature. Moreover, the approximate solution can be successfully applied to provide values for the skin friction coefficient of the laminar boundary layer flow in power law non-Newtonian fluids.展开更多
The hear transfer mechanism and the constitutive models for energy boundary layer in power law fluids were investigated.Two energy transfer constitutive equations models were proposed based on the assumption of simila...The hear transfer mechanism and the constitutive models for energy boundary layer in power law fluids were investigated.Two energy transfer constitutive equations models were proposed based on the assumption of similarity of velocity field momentum diffusion and temperature field heat transfer.The governing systems of partial different equations were transformed into ordinary differential equations respectively by using the similarity transformation group.One model was assumed that Prandtl number is a constant,and the other model was assumed that viscosity diffusion is analogous to thermal diffusion.The solutions were presented analytically and numerically by using the Runge-Kutta formulas and shooting technique and the associated transfer characteristics were discussed.展开更多
The erythrocyte and blood flowing in the blood vessel can be treated as the two-phase flow of the mixture of particles and a power-law fluid in a peristaltic tube.In the present work, the peristaltic transport of a po...The erythrocyte and blood flowing in the blood vessel can be treated as the two-phase flow of the mixture of particles and a power-law fluid in a peristaltic tube.In the present work, the peristaltic transport of a power-law fluid and the suspension of particles in a tube is investigated by a perturbation method using the long wavelength approximation. The influence of different parameters on the velocity profile and streamlines is explored. Results show that there is a deflection of the flow field when the power-law index n = 0.5 or 1.5 compared with the Newtonian fluid where the trapping zone is symmetric to a certain cross section. The flux rate and reflux of the material are identified,and the conditions under which the reflux appears are determined. Moreover, a reflux phenomenon occurs near the wall. The trapping zone is related to not only the tube geometry and the flow flux but also the fluid properties. Both the length and width of the trapping zone increase with an increase in θ or φ. The trapping zone is more difficult to produce in the shear-thinning fluid than the shear-thickening fluid.展开更多
The problem of magnetohydrodynamic （MHD） flow on a moving surface with the power-law velocity and special injection/blowing is investigated. A scaling group transformation is used to reduce the governing equations t...The problem of magnetohydrodynamic （MHD） flow on a moving surface with the power-law velocity and special injection/blowing is investigated. A scaling group transformation is used to reduce the governing equations to a system of ordinary differen- tial equations. The skin friction coefficients of the MHD boundary layer flow are derived, and the approximate solutions of the flow characteristics are obtained with the homotopy analysis method （HAM）. The approximate solutions are easily computed by use of a high order iterative procedure, and the effects of the power-law index, the magnetic parameter, and the special suction/blowing parameter on the dynamics are analyzed. The obtained results are compared with the numerical results published in the literature, verifying the reliability of the approximate solutions.展开更多
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
The steady oil production and pressure distribution formulae of vertically fractured well for power-law non-Newtonian fluid were derived on the basis of the elliptic flow model in fractal reservoirs. The corresponding...The steady oil production and pressure distribution formulae of vertically fractured well for power-law non-Newtonian fluid were derived on the basis of the elliptic flow model in fractal reservoirs. The corresponding transient flow in fractal reservoirs was studied by numerical differentiation method: the influence of fractal index to transient pressure of vertically fractured well was analyzed. Finally the approximate analytical solution of transient flow was given by average mass conservation law. The study shows that using elliptic flow method to analyze the flow of vertically fractured well is a simple method.展开更多
Effects of compliant wall properties on the peristaltic flow of a non-Newtonian fluid in an asymmetric channel are investigated.The rheological characteristics are characterized by the constitutive equations of a powe...Effects of compliant wall properties on the peristaltic flow of a non-Newtonian fluid in an asymmetric channel are investigated.The rheological characteristics are characterized by the constitutive equations of a power-law fluid.Long wavelength and low Reynolds number approximations are adopted in the presentation of mathematical developments.Exact solutions are established for the stream function and velocity.The streamlines pattern and trapping are given due attention.Salient features of the key parameters entering into the present flow are displayed and important conclusions are pointed out.展开更多
In this study,Large eddy simulation(LES)of the fully developed turbulence of power⁃law fluids in a circular pipe was performed using the dynamic subgrid⁃scale model.Under a specific Reynolds number,the flow informatio...In this study,Large eddy simulation(LES)of the fully developed turbulence of power⁃law fluids in a circular pipe was performed using the dynamic subgrid⁃scale model.Under a specific Reynolds number,the flow information of three fluids with a range of power⁃law indexes was obtained.The trends of the mean axial velocity and the normalized apparent viscosity were analyzed.Simulation results show that shearing⁃thinning fluid displayed more noticeable non⁃Newtonian characteristics than shear⁃thickening fluid.The predicted friction factors were approximately equal to the Dodge and Metzner correlation and Gomes correlation.The peak values of root mean squares(RMS)and Reynolds stress increased as the power⁃law index increased.The turbulence statistics(skewness and flatness)from the wall to the pipe center were calculated.From the calculated results,the velocity fluctuation near the wall had strong intermittent and asymmetry.As demonstrated by the contours of the normalized instantaneous axial velocity and viscosity,the turbulence was more developed as the power⁃law index increased.It is concluded that the LES is feasible to predict the turbulence of pipe flow under higher Reynolds numbers.展开更多
While studying the flow of oil and gas in the reservoir, it is not realistic that capillary with circular section is only used to express the pores. It is more representative to simulate porous media pore with kinds o...While studying the flow of oil and gas in the reservoir, it is not realistic that capillary with circular section is only used to express the pores. It is more representative to simulate porous media pore with kinds of capillary with triangle or rectangle section etc. In the condition of the same diameter, when polymer for oil displacement flows in the porous medium, there only exists shear flow which can be expressed with power law model. Based on fluid flow-pressure drop equation in single capillary, this paper gives a calculation method of equivalent permeability of power law fluid of single capillary and capillary bundles with different sections.展开更多
This paper investigates the flow, heat andmass transfer of a power law fluid from a vertical plate in presence of a magnetic field. The resulting non-linear partial differential equations governing the flow together w...This paper investigates the flow, heat andmass transfer of a power law fluid from a vertical plate in presence of a magnetic field. The resulting non-linear partial differential equations governing the flow together with the boundary conditions are reduced to non-dimensional form. The governing equations are discretized using implicit finite difference scheme and solved numerically. The velocity, temperature and concentration profile are presented graphically while the skin friction, local Nusselt number and the Sherwood number are presented in tabular form for different values of parameters of the problem.展开更多
In this paper, analysis of post-treatment of wire coating is presented. Coating material satisfies power law fluid model. Exact solutions for the velocity field, volume flow rate and average velocity are obtained. Mor...In this paper, analysis of post-treatment of wire coating is presented. Coating material satisfies power law fluid model. Exact solutions for the velocity field, volume flow rate and average velocity are obtained. Moreover, the heat transfer results are presented for different cases of linearly varying on the boundaries. The variations of velocity, volume flow rate, radius of coated wire, shear rate and the force on the total wire are presented graphically and discussed.展开更多
Based on the governing equations of the inner cyinder of the unsteady flow of the power law fluid in eccentric annuli with the inner cylinder reciprocating axially in bipolar coordinate system, the calculation formula...Based on the governing equations of the inner cyinder of the unsteady flow of the power law fluid in eccentric annuli with the inner cylinder reciprocating axially in bipolar coordinate system, the calculation formulae of tangential force were established, and the relevant numerical calculation method was given. Taking the aqueous solution of partially hydrolyzed polyacrylamides (HPAM) for examples, the tangential forces were calculated by using the formulae and numerical calculation method mentioned above;the curves of the tangential force on the wall of the inner cylinder of HPAM aqueous solution were plotted;and the effects on the tangential force of the flow behavior index of the power law fluid, the stroke and the stroke frequency of the inner cylinder were analyzed.展开更多
基金This work is supported by the National Natural Science Foundation of China (No.50476083) and the Cross-Century Talents Projectsby the Ministry Education of China.
文摘The specific problem to be considered here concerns the boundary layer problem of a non-Newtonian fluid on a flat plate in length, whose surface has a constant velocity opposite in the direction to that of the mainstream with Uw 〉〉 U∞, or alternatively when the plate surface velocity is kept fixed but the stream speed is reduced to zero. A theoretical analysis for a boundary layer flow is made and the self-similar equation is determined. Solutions are presented numerically for special power index and the associated transfer behavior is discussed.
基金Project supported by the National Natural Science Foundation of China(No.11302024)the Fundamental Research Funds for the Central Universities(No.FRF-TP-12-108A)the Foundation of the China Scholarship Council in 2014(No.154201406465041)
文摘Flow and heat transfer of a pseudo-plastic power-law fluid over a stretching permeable surface with the magnetic effect is investigated. In the boundary conditions,the nonlinear temperature jump and the velocity slip are considered. Semi-similarity equations are obtained and solved by bvp4c with MATLAB. The problem can be considered as an extension of the previous work done by Mahmoud(Mahmoud, M. A. A. Slip velocity effect on a non-Newtonian power-law fluid over a moving permeable surface with heat generation. Mathematical and Computer Modelling, 54, 1228–1237(2011)). Efforts are made to discuss the effects of the power-law number, slip velocity, and temperature jump on the dimensionless velocity and temperature distribution.
基金Sponsored by the Liaoning Provincial Doctoral Initiation Fund Project(Grant No.2019-BS-030).
文摘Considering Brinkman⁃Forchheimer extended Darcy flow and local thermal non⁃equilibrium effect,a general model of forced convection with viscous dissipation in power⁃law fluid saturated porous media channel was established.The dimensionless temperature profiles and Nusselt number were numerically solved using the classical fourth⁃order Runge Kutta method under a constant heat flux boundary condition.The conclusion showed that the fluid⁃solid temperature distributions were significantly affected by dimensionless Bi,k,Da,Br,and F,and the effects of power⁃law indexes on convection heat transfer characteristics were also non⁃negligible.
文摘A modified power-law fluid of second grade is considered. The model is a combination of power-law and second grade fluid in which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. The equations of motion are derived for two dimensional incompressible flows, and from which the boundary layer equations are derived. Symmetries of the boundary layer equations are found by using Lie group theory, and then group classification with respect to power-law index is performed. By using one of the symmetries, namely the scaling symmetry, the partial differential system is transformed into an ordinary differential system, which is numerically integrated under the classical boundary layer conditions. Effects of power-law index and second grade coefficient on the boundary layers are shown and solutions are contrasted with the usual second grade fluid solutions.
基金supported by the National Natural Science Foundation of China (10972115)
文摘The long wave stability of core-annular flow of power-law fluids with an axial pressure gradient is investigated at low Reynolds number. The interface between the two fluids is populated with an insoluble surfactant. The analytic solution for the growth rate of perturbation is obtained with long wave approximation. We are mainly concerned with the effects of shear-thinning/thickening property and interfacial surfactant on the flow stability. The results show that the influence of shear-thinning/thickening property accounts to the change of the capillary number. For a clean interface, the shear-thinning property enhances the capillary instability when the interface is close to the pipe wall. The converse is true when the interface is close to the pipe centerline. For shear-thickening fluids, the situation is reversed. When the interface is close to the pipe centerline, the capillary instability can be restrained due to the influence of surfactant. A parameter set can be found under which the flow is linearly stable.
文摘An investigation is made of the magnetic Rayleigh problem where a semi_infinite plate is given an impulsive motion and thereafter moves with constant velocity in a non_Newtonian power law fluid of infinite extent. The solution of this highly non_linear problem is obtained by means of the transformation group theoretic approach. The one_parameter group transformation reduces the number of independent variables by one and the governing partial differential equation with the boundary conditions reduce to an ordinary differential equation with the appropriate boundary conditions. Effect of the some parameters on the velocity u(y,t) has been studied and the results are plotted.
文摘The problem of the boundary layer flow of power law non-Newtonian fluids with a novel boundary condition is studied. The existence and uniqueness of the solutions are examined, which are found to depend on the curvature of the solutions for different values of the power law index n. It is established with the aid of the Picard-Lindelof theorem that the nonlinear boundary value problem has a unique solution in the global domain for all values of the power law index n but with certain conditions on the curva- ture of the solutions. This is done after a suitable transformation of the dependent and independent variables. For 0 〈 n ≤ 1, the solution has a positive curvature, while for n 〉 1, the solution has a negative or zero curvature on some part of the global domain. Some solutions are presented graphically to illustrate the results and the behaviors of the solutions.
文摘A direct difference method has been developed for Non-Newtonian power law fluids to solve the simultaneous non-linear partial differential equations of melt spinning, and to determine the critical draw ratio for draw resonance. The results show that for shear thin fluids, the logarithm of the critical draw ratio has a well defined linear relationship with the power index for isothermal and uniform tension melt spinning. When the power index approaches zero, the critical draw ratio points at unity, indicating no melt spinning can be processed stably for such fluids. For shear thick fluids, the critical draw ratio increases in a more rapid way with increasing the power index.
基金the Science Foundation of North China Electric Power University(No.93210706)
文摘This paper presents a theoretical analysis for laminar boundary layer flow in a power law non-Newtonian fluids. The Adomian analytical decomposition technique is presented and an approximate analytical solution is obtained. The approximate analytical solution can be expressed in terms of a rapid convergent power series with easily computable terms. Reliability and efficiency of the approximate solution are verified by comparing with numerical solutions in the literature. Moreover, the approximate solution can be successfully applied to provide values for the skin friction coefficient of the laminar boundary layer flow in power law non-Newtonian fluids.
基金Project(50476083) supported by the National Natural Science Foundation of China
文摘The hear transfer mechanism and the constitutive models for energy boundary layer in power law fluids were investigated.Two energy transfer constitutive equations models were proposed based on the assumption of similarity of velocity field momentum diffusion and temperature field heat transfer.The governing systems of partial different equations were transformed into ordinary differential equations respectively by using the similarity transformation group.One model was assumed that Prandtl number is a constant,and the other model was assumed that viscosity diffusion is analogous to thermal diffusion.The solutions were presented analytically and numerically by using the Runge-Kutta formulas and shooting technique and the associated transfer characteristics were discussed.
基金supported by the Major Program of National Natural Science Foundation of China(Nos.11632016 and 91634103)
文摘The erythrocyte and blood flowing in the blood vessel can be treated as the two-phase flow of the mixture of particles and a power-law fluid in a peristaltic tube.In the present work, the peristaltic transport of a power-law fluid and the suspension of particles in a tube is investigated by a perturbation method using the long wavelength approximation. The influence of different parameters on the velocity profile and streamlines is explored. Results show that there is a deflection of the flow field when the power-law index n = 0.5 or 1.5 compared with the Newtonian fluid where the trapping zone is symmetric to a certain cross section. The flux rate and reflux of the material are identified,and the conditions under which the reflux appears are determined. Moreover, a reflux phenomenon occurs near the wall. The trapping zone is related to not only the tube geometry and the flow flux but also the fluid properties. Both the length and width of the trapping zone increase with an increase in θ or φ. The trapping zone is more difficult to produce in the shear-thinning fluid than the shear-thickening fluid.
基金Project supported by the National Natural Science Foundation of China(Nos.51276014 and 51406008)
文摘The problem of magnetohydrodynamic （MHD） flow on a moving surface with the power-law velocity and special injection/blowing is investigated. A scaling group transformation is used to reduce the governing equations to a system of ordinary differen- tial equations. The skin friction coefficients of the MHD boundary layer flow are derived, and the approximate solutions of the flow characteristics are obtained with the homotopy analysis method （HAM）. The approximate solutions are easily computed by use of a high order iterative procedure, and the effects of the power-law index, the magnetic parameter, and the special suction/blowing parameter on the dynamics are analyzed. The obtained results are compared with the numerical results published in the literature, verifying the reliability of the approximate solutions.
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The steady oil production and pressure distribution formulae of vertically fractured well for power-law non-Newtonian fluid were derived on the basis of the elliptic flow model in fractal reservoirs. The corresponding transient flow in fractal reservoirs was studied by numerical differentiation method: the influence of fractal index to transient pressure of vertically fractured well was analyzed. Finally the approximate analytical solution of transient flow was given by average mass conservation law. The study shows that using elliptic flow method to analyze the flow of vertically fractured well is a simple method.
基金supported by the Higher Education Commission(HEC)of Pakistan
文摘Effects of compliant wall properties on the peristaltic flow of a non-Newtonian fluid in an asymmetric channel are investigated.The rheological characteristics are characterized by the constitutive equations of a power-law fluid.Long wavelength and low Reynolds number approximations are adopted in the presentation of mathematical developments.Exact solutions are established for the stream function and velocity.The streamlines pattern and trapping are given due attention.Salient features of the key parameters entering into the present flow are displayed and important conclusions are pointed out.
基金Sponsored by the National Natural Science Foundation of China(Grant Nos.51876032,21676051)the Natural Science Foundation of Heilongjiang Province(Grant No.ZD2019E002).
文摘In this study,Large eddy simulation(LES)of the fully developed turbulence of power⁃law fluids in a circular pipe was performed using the dynamic subgrid⁃scale model.Under a specific Reynolds number,the flow information of three fluids with a range of power⁃law indexes was obtained.The trends of the mean axial velocity and the normalized apparent viscosity were analyzed.Simulation results show that shearing⁃thinning fluid displayed more noticeable non⁃Newtonian characteristics than shear⁃thickening fluid.The predicted friction factors were approximately equal to the Dodge and Metzner correlation and Gomes correlation.The peak values of root mean squares(RMS)and Reynolds stress increased as the power⁃law index increased.The turbulence statistics(skewness and flatness)from the wall to the pipe center were calculated.From the calculated results,the velocity fluctuation near the wall had strong intermittent and asymmetry.As demonstrated by the contours of the normalized instantaneous axial velocity and viscosity,the turbulence was more developed as the power⁃law index increased.It is concluded that the LES is feasible to predict the turbulence of pipe flow under higher Reynolds numbers.
基金Supported by the National Natural Science Foundation of China Youth Science Fund （51104030） Supported by the Science and Technology Research Project of Heilongjiang Province Department of Education（12521059） Supported by the China Postdoctoral Science Foundation（2014M561325）
文摘While studying the flow of oil and gas in the reservoir, it is not realistic that capillary with circular section is only used to express the pores. It is more representative to simulate porous media pore with kinds of capillary with triangle or rectangle section etc. In the condition of the same diameter, when polymer for oil displacement flows in the porous medium, there only exists shear flow which can be expressed with power law model. Based on fluid flow-pressure drop equation in single capillary, this paper gives a calculation method of equivalent permeability of power law fluid of single capillary and capillary bundles with different sections.
文摘This paper investigates the flow, heat andmass transfer of a power law fluid from a vertical plate in presence of a magnetic field. The resulting non-linear partial differential equations governing the flow together with the boundary conditions are reduced to non-dimensional form. The governing equations are discretized using implicit finite difference scheme and solved numerically. The velocity, temperature and concentration profile are presented graphically while the skin friction, local Nusselt number and the Sherwood number are presented in tabular form for different values of parameters of the problem.
文摘In this paper, analysis of post-treatment of wire coating is presented. Coating material satisfies power law fluid model. Exact solutions for the velocity field, volume flow rate and average velocity are obtained. Moreover, the heat transfer results are presented for different cases of linearly varying on the boundaries. The variations of velocity, volume flow rate, radius of coated wire, shear rate and the force on the total wire are presented graphically and discussed.
文摘Based on the governing equations of the inner cyinder of the unsteady flow of the power law fluid in eccentric annuli with the inner cylinder reciprocating axially in bipolar coordinate system, the calculation formulae of tangential force were established, and the relevant numerical calculation method was given. Taking the aqueous solution of partially hydrolyzed polyacrylamides (HPAM) for examples, the tangential forces were calculated by using the formulae and numerical calculation method mentioned above;the curves of the tangential force on the wall of the inner cylinder of HPAM aqueous solution were plotted;and the effects on the tangential force of the flow behavior index of the power law fluid, the stroke and the stroke frequency of the inner cylinder were analyzed.
