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
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
This paper investigates flow and heat transfer of power law fluids on a continuous moving surface. The temperature distribution is obtained numerically by considering the effect of the power law viscosity on thermal d...This paper investigates flow and heat transfer of power law fluids on a continuous moving surface. The temperature distribution is obtained numerically by considering the effect of the power law viscosity on thermal diffusivity and the characteristics of the flow and heat transfer are analyzed. The results show that the distribution of the thermal boundary layer depends not only on the velocity ratio parameter of the plate, but also on the power law index and Prandtl number of fluids.展开更多
An analysis is carried out to study the steady flow characteristics from a continuous flat surface moving in a parallel free stream of non-Newtonian power law fluid. The constitutive equations of the fluid are transfo...An analysis is carried out to study the steady flow characteristics from a continuous flat surface moving in a parallel free stream of non-Newtonian power law fluid. The constitutive equations of the fluid are transformed into dimensionless ones. The velocity field is measured by Particle Image Velocimetry. Experimental results are obtained for the distribution of velocity. The influence of wall velocity ratio parameter on boundary layer flow field is observed in the experiment. Dimensionless velocity distribution and shearing stress distribution are obtained by post-processing experimental results. The effects of various physical parameters like velocity ratio parameter and similarity variable on various momentum transfer characteristics are discussed in detail and shown graphically. It is indicated that dimensionless velocity increases with velocity ratio parameter and similarity variable, and that dimensionless shearing stress decreases with velocity ratio parameter and similarity variable.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
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
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
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
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
On account of limited knowledge of the breakup of power law liquid film, the process of its disintegration and atomization was studied by using a planar liquid film. A linear stability analysis was adopted to predict ...On account of limited knowledge of the breakup of power law liquid film, the process of its disintegration and atomization was studied by using a planar liquid film. A linear stability analysis was adopted to predict the breakup characteristics of the power law film. The predicting formulas of stripping breakup length and diameter of ligament were put forward presently. Through high-speed photography and laser light sheet illumination,different breakup characteristics of flat power law film under different conditions were derived. The characteristic dimension of breakup regimes were defined and extracted. The effects of several parameters(injection pressure,ambient pressure, nozzle structure and fluid property) on the stripping breakup length and spray angle were investigated. The results revealed that increasing both the velocity of liquid film and the ambient pressure facilitated the breakup of film, reduced the stripping breakup length and enlarged the spray angle in different extents. The comparison between theoretical and experimental results was conducted to validate the feasibility of the linear stability theory.展开更多
Analytical and numerical solutions are presented for the momentum and energy laminar boundary layer equations in power law fluids utilizing a similarity transformation and the shooting technique. The results indica...Analytical and numerical solutions are presented for the momentum and energy laminar boundary layer equations in power law fluids utilizing a similarity transformation and the shooting technique. The results indicated that for power law exponents 0< n ≤1, the skin friction σ decreases with increasing n , and the dimensionless shear force decreases with increasing dimensionless velocity t . When Pr =1, the velocity distribution in the viscous boundary layer is the same as the temperature distribution in the thermal boundary layer and δ=δ T. For Pr >1, the increase of the viscous diffusion exceeds that of thermal diffusion with increasing Pr , i.e. , δ T (t)<δ(t) . The thermal diffusion ratio increases with increasing n(0<n≤1) .展开更多
This paper presents a theoretical analysis of the heat transfer for the boundary layer flow on a continuous moving surface in power law fluid. The expressions of the thermal boundary layer thickness with the different...This paper presents a theoretical analysis of the heat transfer for the boundary layer flow on a continuous moving surface in power law fluid. The expressions of the thermal boundary layer thickness with the different heat conductivity coefficients are obtained according to the theory of the dimensional analysis of fluid dynamics and heat transfer. And the numerical results of CFD agree well with the proposed expressions. The estimate formulas can be successfully applied to giving the thermal boundary layer thickness.展开更多
The USM-θ model of power law fluid for dense two-phase turbulent flow was developed, which combines the unified second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-parti...The USM-θ model of power law fluid for dense two-phase turbulent flow was developed, which combines the unified second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. This model was used to simulate the turbulent flow of power law fluid single-phase in pipe. It is shown that the USM- θ model has better prediction result than the κf -κf - κ- εp -θ model. The USM-O model was then used to simulate the dense two-phase turbulent up flow of power law fluid with particles. With the increase of the flow exponent, the velocities of power law fluid and particles increase near the pipe centre. Comparison between the two-phase flow of power law fluid-particle and of liquid-particle indicates that the axial fluctuation velocity of fluid phase and particle phase in liquid-particle two-phase flow is smaller than that in the power law fluid two-phase flow, but the two-phase velocities of power law fluid-particle and liquid-particle are close to each other.展开更多
In the present paper an unsteady thermal flow of non-Newtonian fluid is investigated which is of the flow into axisymmetric mould cavity. In the second part an unsteady thermal flow of upper-convected Maxwell fluid is...In the present paper an unsteady thermal flow of non-Newtonian fluid is investigated which is of the flow into axisymmetric mould cavity. In the second part an unsteady thermal flow of upper-convected Maxwell fluid is studied. For the flow into mould cavity the constitutive equation of power-law fluid is used as a Theological model of polymer fluid. The apparent viscosity is considered as a function of shear rate and temperature. A characteristic viscosity is introduced in order to avoid the nonlinearity due to the temperature dependence of the apparent viscosity. As the viscosity of the fluid is relatively high the flow of the thermal fluid can be considered as a flow of fully developed velocity field. However, the temperature field of the fluid flow is considered as an unsteady one. The governing equations are constitutive equation, momentum equation of steady flow and energy conservation equation of non-steady form. The present system of equations has been solved numerically by the splitting difference method. The numerical results show that the splitting difference method is suitable for the 2D problem of non-Newtonian fluid. The present application of the splitting diffference method is at first developed by us for non-Newtonian case. For the unsteady flow in the tube the finite difference scheme is given which leads to a tridiagonal system of equations.展开更多
Flow and heat transfer analysis of an electrically conducting MHD power law nano fluid is carried out through annular sector duct,under the influence of constant pressure gradient.Two types of nano particles(i.e.Cu an...Flow and heat transfer analysis of an electrically conducting MHD power law nano fluid is carried out through annular sector duct,under the influence of constant pressure gradient.Two types of nano particles(i.e.Cu and TiO2)are used in power law nano fluid.Strongly implicit procedure,(SIP)is used to simulate the discretized coupled algebraic equations.It has been observed that volume fraction of nano particles,ϕand magnetic field parameter,Ha are favourable for the heat transfer rate,however,both resist the fluid flow.Impact of applied uniform transverse magnetic field exceeds in the case of shear thickening fluids(i.e.n>1)by increasing the value of Ha as compared to that in shear thinning fluids(i.e.n<1).Therefore,enhancement in heat transfer rate is comparably more in shear thickening fluid.Furthermore,comparable limiting case study with published result is also carried out in this research paper.展开更多
This paper .Studies power law no-Newtonian fluid rotative flow. in an annularpipe. The governing equation is nonlinear one, we linearized the governing equationby assuming that partial factor is at state. With Lapla...This paper .Studies power law no-Newtonian fluid rotative flow. in an annularpipe. The governing equation is nonlinear one, we linearized the governing equationby assuming that partial factor is at state. With Laplace transform we obtain ananalytical solution of the problem In the paper several groups of curves are given.these curves reflect the temporal change law and. spatial distribution of fluid velocity.In addition.we study the effection of power law index on the flow field the resultindicates that when the power law index n < l. the flow velocity is highly sensitive tothe index. and this fact is importanl in related engineering decisions.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The work is supported by the National Natural Science Foundation of China （No. 50476083）.
文摘This paper investigates flow and heat transfer of power law fluids on a continuous moving surface. The temperature distribution is obtained numerically by considering the effect of the power law viscosity on thermal diffusivity and the characteristics of the flow and heat transfer are analyzed. The results show that the distribution of the thermal boundary layer depends not only on the velocity ratio parameter of the plate, but also on the power law index and Prandtl number of fluids.
基金supported by the National Natural Science Foundation of China (No. 50476083)
文摘An analysis is carried out to study the steady flow characteristics from a continuous flat surface moving in a parallel free stream of non-Newtonian power law fluid. The constitutive equations of the fluid are transformed into dimensionless ones. The velocity field is measured by Particle Image Velocimetry. Experimental results are obtained for the distribution of velocity. The influence of wall velocity ratio parameter on boundary layer flow field is observed in the experiment. Dimensionless velocity distribution and shearing stress distribution are obtained by post-processing experimental results. The effects of various physical parameters like velocity ratio parameter and similarity variable on various momentum transfer characteristics are discussed in detail and shown graphically. It is indicated that dimensionless velocity increases with velocity ratio parameter and similarity variable, and that dimensionless shearing stress decreases with velocity ratio parameter and similarity variable.
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.
基金Supported by the National Natural Science Foundation of China(11172205,11372219,51176137)
文摘On account of limited knowledge of the breakup of power law liquid film, the process of its disintegration and atomization was studied by using a planar liquid film. A linear stability analysis was adopted to predict the breakup characteristics of the power law film. The predicting formulas of stripping breakup length and diameter of ligament were put forward presently. Through high-speed photography and laser light sheet illumination,different breakup characteristics of flat power law film under different conditions were derived. The characteristic dimension of breakup regimes were defined and extracted. The effects of several parameters(injection pressure,ambient pressure, nozzle structure and fluid property) on the stripping breakup length and spray angle were investigated. The results revealed that increasing both the velocity of liquid film and the ambient pressure facilitated the breakup of film, reduced the stripping breakup length and enlarged the spray angle in different extents. The comparison between theoretical and experimental results was conducted to validate the feasibility of the linear stability theory.
文摘Analytical and numerical solutions are presented for the momentum and energy laminar boundary layer equations in power law fluids utilizing a similarity transformation and the shooting technique. The results indicated that for power law exponents 0< n ≤1, the skin friction σ decreases with increasing n , and the dimensionless shear force decreases with increasing dimensionless velocity t . When Pr =1, the velocity distribution in the viscous boundary layer is the same as the temperature distribution in the thermal boundary layer and δ=δ T. For Pr >1, the increase of the viscous diffusion exceeds that of thermal diffusion with increasing Pr , i.e. , δ T (t)<δ(t) . The thermal diffusion ratio increases with increasing n(0<n≤1) .
基金the National Natural Science Foundation of China (No.50476083)
文摘This paper presents a theoretical analysis of the heat transfer for the boundary layer flow on a continuous moving surface in power law fluid. The expressions of the thermal boundary layer thickness with the different heat conductivity coefficients are obtained according to the theory of the dimensional analysis of fluid dynamics and heat transfer. And the numerical results of CFD agree well with the proposed expressions. The estimate formulas can be successfully applied to giving the thermal boundary layer thickness.
基金Supported by China Postdoctoral Science Foundation (Grant No.2004036239).
文摘The USM-θ model of power law fluid for dense two-phase turbulent flow was developed, which combines the unified second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. This model was used to simulate the turbulent flow of power law fluid single-phase in pipe. It is shown that the USM- θ model has better prediction result than the κf -κf - κ- εp -θ model. The USM-O model was then used to simulate the dense two-phase turbulent up flow of power law fluid with particles. With the increase of the flow exponent, the velocities of power law fluid and particles increase near the pipe centre. Comparison between the two-phase flow of power law fluid-particle and of liquid-particle indicates that the axial fluctuation velocity of fluid phase and particle phase in liquid-particle two-phase flow is smaller than that in the power law fluid two-phase flow, but the two-phase velocities of power law fluid-particle and liquid-particle are close to each other.
基金The project supported by the National Natural Science foundation of China
文摘In the present paper an unsteady thermal flow of non-Newtonian fluid is investigated which is of the flow into axisymmetric mould cavity. In the second part an unsteady thermal flow of upper-convected Maxwell fluid is studied. For the flow into mould cavity the constitutive equation of power-law fluid is used as a Theological model of polymer fluid. The apparent viscosity is considered as a function of shear rate and temperature. A characteristic viscosity is introduced in order to avoid the nonlinearity due to the temperature dependence of the apparent viscosity. As the viscosity of the fluid is relatively high the flow of the thermal fluid can be considered as a flow of fully developed velocity field. However, the temperature field of the fluid flow is considered as an unsteady one. The governing equations are constitutive equation, momentum equation of steady flow and energy conservation equation of non-steady form. The present system of equations has been solved numerically by the splitting difference method. The numerical results show that the splitting difference method is suitable for the 2D problem of non-Newtonian fluid. The present application of the splitting diffference method is at first developed by us for non-Newtonian case. For the unsteady flow in the tube the finite difference scheme is given which leads to a tridiagonal system of equations.
文摘Flow and heat transfer analysis of an electrically conducting MHD power law nano fluid is carried out through annular sector duct,under the influence of constant pressure gradient.Two types of nano particles(i.e.Cu and TiO2)are used in power law nano fluid.Strongly implicit procedure,(SIP)is used to simulate the discretized coupled algebraic equations.It has been observed that volume fraction of nano particles,ϕand magnetic field parameter,Ha are favourable for the heat transfer rate,however,both resist the fluid flow.Impact of applied uniform transverse magnetic field exceeds in the case of shear thickening fluids(i.e.n>1)by increasing the value of Ha as compared to that in shear thinning fluids(i.e.n<1).Therefore,enhancement in heat transfer rate is comparably more in shear thickening fluid.Furthermore,comparable limiting case study with published result is also carried out in this research paper.
文摘This paper .Studies power law no-Newtonian fluid rotative flow. in an annularpipe. The governing equation is nonlinear one, we linearized the governing equationby assuming that partial factor is at state. With Laplace transform we obtain ananalytical solution of the problem In the paper several groups of curves are given.these curves reflect the temporal change law and. spatial distribution of fluid velocity.In addition.we study the effection of power law index on the flow field the resultindicates that when the power law index n < l. the flow velocity is highly sensitive tothe index. and this fact is importanl in related engineering decisions.
