The boundary-layer flow and heat transfer in a viscous fluid containing metallic nanoparticles over a nonlinear stretching sheet are analyzed. The stretching velocity is assumed to vary as a power function of the dist...The boundary-layer flow and heat transfer in a viscous fluid containing metallic nanoparticles over a nonlinear stretching sheet are analyzed. The stretching velocity is assumed to vary as a power function of the distance from the origin. The governing partial differential equation and auxiliary conditions are reduced to coupled nonlinear ordinary differential equations with the appropriate corresponding auxiliary conditions. The resulting nonlinear ordinary differential equations (ODEs) are solved numerically. The effects of various relevant parameters, namely, the Eckert number Ec, the solid volume fraction of the nanoparticles ~, and the nonlinear stretching parameter n are discussed. The comparison with published results is also presented. Different types of nanoparticles are studied. It is shown that the behavior of the fluid flow changes with the change of the nanoparticles type.展开更多
This paper considers the problem of hydrodynamics and thermal boundary layers of Darcy flow over horizontal surface embedded in a porous medium. The solutions of such problems for the cases of uniform surface temperat...This paper considers the problem of hydrodynamics and thermal boundary layers of Darcy flow over horizontal surface embedded in a porous medium. The solutions of such problems for the cases of uniform surface temperature and variable surface temperature have been studied and analysed in many papers. This paper, however, attempts to find similarity solutions for the Darcy flow problem with a convective boundary condition at the plate surface. It is found that the solution is possible when the heat transfer coefficient is proportional to x<sup>–2/3</sup>. The numerical solutions thus obtained are analyzed for a range of values of the parameter characterizing the hot fluid convection process. Analytical expressions are provided for local surface heat flux and total surface heat transfer rate while the flow variables are discussed graphically.展开更多
Unsteady mixed convective boundary layer flow of viscous incompressible fluid along isothermal horizontal plate is analyzed through Similarity Solutions. The governing partial differential equations are transformed in...Unsteady mixed convective boundary layer flow of viscous incompressible fluid along isothermal horizontal plate is analyzed through Similarity Solutions. The governing partial differential equations are transformed into ordinary differential equations using the similarity transformation and solved numerically along with shooting technique. The flow field for the fluid velocity, temperature and concentration at the plate surface are significantly influenced by the governing parameters such as unsteadiness parameter, permeability parameter, Prandtl number, Schmidt number and the other driving parameters. The results show that both fluid velocity and temperature decrease but no significant effect on concentration for the increasing values of Prandtl number. It is also exposed that velocity and concentration is higher at lower Schmidt number for low Prandtl fluid. Finally, the dependency of the Skin-friction co-efficient, Nusselt number and Sherwood number, which are of physical interest, are also illustrated in tabular form for the governing parameters.展开更多
The equation used to model the unidirectional flow of methane gas in coal seams is usually formulated as a nonlinear partial differential equation, which needs to be solved numerically with a computer program.Neverthe...The equation used to model the unidirectional flow of methane gas in coal seams is usually formulated as a nonlinear partial differential equation, which needs to be solved numerically with a computer program.Nevertheless, for people without access to the computer program, the conventional numerical method may be inconvenient. Thus, the objective here is to seek some method simpler than the conventional one for solving the flow problem. A commonly used model of the unidirectional methane gas flow is considered, where the methane adsorption is described by the Langmuir isotherm and the free gas is treated as real gas. By introducing the similarity solution, a simple method for solving the flow model is proposed, which can be done on a hand calculator. It is shown by two examples that the gas pressure profile obtained by the proposed method agrees well with the direct numerical solution of the flow model.展开更多
Similarity solution of unsteady convective boundary layer flow along isothermal vertical plate with porous medium is analyzed. The plate surface is reactive with the fluid and generates inert specie which diffuses ins...Similarity solution of unsteady convective boundary layer flow along isothermal vertical plate with porous medium is analyzed. The plate surface is reactive with the fluid and generates inert specie which diffuses inside the boundary. The flux of the specie at the plate is proportional to specie concentration at the plate. The governing equations of continuity, momentum, energy and specie diffusion are transformed into ordinary differential equation by using the similarity transformation and solved numerically by using free parameter method along with shooting technique. The dimensionless velocity, temperature and concentration profiles are obtained and presented through figures for different parameters entering into the problem. The local Skin-friction co-efficient, Nusselt number and Sherwood number at the plate for physical interest are also discussed through tables.展开更多
The unsteady flow of viscoelastic fluid in a cylindrical pipe was investigated using the fractional Maxwell model. Two special cases of unsteady pipe flow were expressed. The first is start-up flow, and the second is ...The unsteady flow of viscoelastic fluid in a cylindrical pipe was investigated using the fractional Maxwell model. Two special cases of unsteady pipe flow were expressed. The first is start-up flow, and the second is oscillating flow. The exact solution of start-up flow under a constant pressure gradient was obtained by using the theories of Laplace transform and Fourier-Bessel series for fractional derivatives. The exact solution of oscillating flow was obtained by utilizing the separation of variables.展开更多
The laminar analytic solutions of velocities and pressure in the central zone of the inlet region of pipe flow are given under the condition of uniform inflow, based on the Navier-Stokes equations of incompressible vi...The laminar analytic solutions of velocities and pressure in the central zone of the inlet region of pipe flow are given under the condition of uniform inflow, based on the Navier-Stokes equations of incompressible viscous flow.展开更多
According to a mathematical model for dense two-phase flows presented in the previous pape[1],a dense two-phase flow in a vertical pipeline is analytically solved, and the analytic expressions of velocity of each cont...According to a mathematical model for dense two-phase flows presented in the previous pape[1],a dense two-phase flow in a vertical pipeline is analytically solved, and the analytic expressions of velocity of each continuous phase and dispersed phase are respectively derived. The results show that when the drag force between twophasesdepends linearly on their relative velocity, the relative velocity profile in the pipeline coincides with Darcy's law except for the thin layer region near the pipeline wall, and that the theoretical assumptions in the dense two-phase flow theory mentioned are reasonable.展开更多
This paper aims to present complete series solution of non-similarity boundary-layer flow of an incompressible viscous fluid over a porous wedge. The corresponding nonlinear partial differential equations are solved a...This paper aims to present complete series solution of non-similarity boundary-layer flow of an incompressible viscous fluid over a porous wedge. The corresponding nonlinear partial differential equations are solved analytically by means of the homotopy analysis method (HAM). An auxiliary parameter is introduced to ensure the convergence of solution series. As a result, series solutions valid for all physical parameters in the whole domain are given. Then, the effects of physical parameters γ and Prandtl number Pr on the local Nusselt number and momentum thickness are investigated. To the best of our knowledge, it is the first time that the series solutions of this kind of non-similarity boundary-layer flows are reported.展开更多
In this article,we employ a fully-resolved numerical simulation method(the fictitious domain method)to investigate the effects of large neutrally-buoyant particles on the turbulent flow in a pipe at low Reynolds num...In this article,we employ a fully-resolved numerical simulation method(the fictitious domain method)to investigate the effects of large neutrally-buoyant particles on the turbulent flow in a pipe at low Reynolds number and non-dilute regimes.The tube Reynolds number is fixed to be 4 900,the particle-pipe diameter ratio is 0.1,and the particle volume fraction ranges from 0.33%to 10%.Our results indicate that the presence of large particles decreases the maximum root-of-mean-square(rms)of the streamwise velocity fluctuation near the wall by weakening the intensity of large-scale streamwise vortices,although in the region very close to the wall the particles increase the rms of streamwise velocity fluctuation.On the other hand,the particles induce small-scale vortices in the near-wall region,resulting in the enhancement of the rms of radial and circumferential velocity fluctuations there.展开更多
The magnetohydrodynamic (MHD) Falkner-Skan boundary layer flow over a permeable wall in the presence of a transverse magnetic field is examined. The approximate solutions and skin friction coefficients of the MHD bo...The magnetohydrodynamic (MHD) Falkner-Skan boundary layer flow over a permeable wall in the presence of a transverse magnetic field is examined. The approximate solutions and skin friction coefficients of the MHD boundary layer flow are obtained by using a method that couples the differential transform method (DTM) with the Pade approximation called DTM-Pade. The approximate solutions are expressed in the form of a power series that can be easily computed with an iterative procedure. The approximate solutions are tabulated, plotted for the values of different parameters and compared with the numerical ones obtained by employing the shooting technique. It is found that the approximate solution agrees very well with the numerical solution, showing the reliability and validity of the present work. Moreover, the effects of various physical parameters on the boundary layer flow are presented graphically and discussed.展开更多
An analytical solution to the famous Falkner-Skan equation for the magnetohydrodynamic (MHD) flow is obtained for a special case, namely, the sink flow with a velocity power index of-1. The solution is given in a cl...An analytical solution to the famous Falkner-Skan equation for the magnetohydrodynamic (MHD) flow is obtained for a special case, namely, the sink flow with a velocity power index of-1. The solution is given in a closed form. Multiple solution branches are obtained. The effects of the magnetic parameter and the wall stretching parameter are analyzed. Interesting velocity profiles are observed with reversal flow regions even for a stationary wall. These solutions provide a rare case of the Falkner-Skan MHD flow with an analytical closed form formula. They greatly enrich the analytical solution for the celebrated Falkner-Skan equation and provide better understanding of this equation.展开更多
Based on Huang's accurate tri-sectional nonlin- ear kinematic equation (1997), a dimensionless simplified mathematical model for nonlinear flow in one-dimensional semi-infinite long porous media with low permeabili...Based on Huang's accurate tri-sectional nonlin- ear kinematic equation (1997), a dimensionless simplified mathematical model for nonlinear flow in one-dimensional semi-infinite long porous media with low permeability is presented for the case of a constant flow rate on the inner boundary. This model contains double moving boundaries, including an internal moving boundary and an external mov- ing boundary, which are different from the classical Stefan problem in heat conduction: The velocity of the external moving boundary is proportional to the second derivative of the unknown pressure function with respect to the distance parameter on this boundary. Through a similarity transfor- mation, the nonlinear partial differential equation (PDE) sys- tem is transformed into a linear PDE system. Then an ana- lytical solution is obtained for the dimensionless simplified mathematical model. This solution can be used for strictly checking the validity of numerical methods in solving such nonlinear mathematical models for flows in low-permeable porous media for petroleum engineering applications. Finally, through plotted comparison curves from the exact an- alytical solution, the sensitive effects of three characteristic parameters are discussed. It is concluded that with a decrease in the dimensionless critical pressure gradient, the sensi- tive effects of the dimensionless variable on the dimension- less pressure distribution and dimensionless pressure gradi- ent distribution become more serious; with an increase in the dimensionless pseudo threshold pressure gradient, the sensi- tive effects of the dimensionless variable become more serious; the dimensionless threshold pressure gradient (TPG) has a great effect on the external moving boundary but has little effect on the internal moving boundary.展开更多
This article concerns the self-similar solutions to the hyperbolic mean curvature flow (HMCF) for plane curves, which is proposed by Kong, Liu, and Wang and relates to an earlier proposal for general flows by LeFloc...This article concerns the self-similar solutions to the hyperbolic mean curvature flow (HMCF) for plane curves, which is proposed by Kong, Liu, and Wang and relates to an earlier proposal for general flows by LeFloch and Smoczyk. We prove that all curves immersed in the plane which move in a self-similar manner under the HMCF are straight lines and circles. Moreover, it is found that a circle can either expand to a larger one and then converge to a point, or shrink directly and converge to a point, where the curvature approaches to infinity.展开更多
Numerical solutions are obtained for non-steady, incompressible fluid flow between two parallel disks which at time t are separated by a distance H(1-αt)1/2 and a magnetic field proportional to B0(1-αt) -1/2 is appl...Numerical solutions are obtained for non-steady, incompressible fluid flow between two parallel disks which at time t are separated by a distance H(1-αt)1/2 and a magnetic field proportional to B0(1-αt) -1/2 is applied perpendicular to the disks where H denotes a representative length, BO denotes a representative magnetic field and α-1 denotes a representative time. Similarity transformations are used to convert the governing partial differential equations of motion in to ordinary differential form. The resulting ordinary differential equations are solved numerically using SOR method, Richardson extrapolation and Simpson’s (1/3) Rule. Our numerical scheme is straightforward, efficient and easy to program.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
The unsteady stagnation point flow of an incompressible viscous fluid over a rotating disk is investigated numerically in the present study. The disk impinges the oncoming flow with a time-dependent axial velocity. Th...The unsteady stagnation point flow of an incompressible viscous fluid over a rotating disk is investigated numerically in the present study. The disk impinges the oncoming flow with a time-dependent axial velocity. The three-dimensionM axisymmetric boundary-layer flow is described by the Navier-Stokes equations. The governing equations are solved numerically, and two distinct similarity solution branches are obtained. Both solution branches exhibit different flow patterns. The upper branch solution exists for all values of the impinging parameter β and the rotating parameter Ω. However, the lower branch solution breaks down at some moderate values of β The involvement of the rotation at disk allows the similarity solution to be transpired for all the decreasing values of β. The results of the velocity profile, the skin friction, and the stream lines are demonstrated through graphs and tables for both solution branches. The results show that the impinging velocity depreciates the forward flow and accelerates the flow in the tangential direction.展开更多
Laminar two-dimensional unsteady mixed-convection boundary-layer flow of a viscous incompressible fluid past asymmetric wedge with variable surface temperature embedded in a porous medium saturated with a nanofluid ha...Laminar two-dimensional unsteady mixed-convection boundary-layer flow of a viscous incompressible fluid past asymmetric wedge with variable surface temperature embedded in a porous medium saturated with a nanofluid has been studied. The employed mathematical model for the nanofluid takes into account the effects of Brownian motion and thermophoresis. The velocity in the potential flow is assumed to vary arbitrary with time. The non-Darcy effects including convective, boundary and inertial effects will be included in the analysis. The unsteadiness is due to the time-dependent free stream velocity. The governing boundary layer equations along with the boundary conditions are converted into dimensionless form by a non-similar transformation, and then resulting system of coupled non-linear partial differential equations are solved by perturbation solutions for small dimensionless time until the second order. Numerical solutions of the governing equations are obtained employing the implicit finite-difference scheme in combination with the quasi-linearization technique. To validating the method used, we compared our results with previous results in earlier papers on special cases of the problem and are found to be in agreement. Effects of various parameters on velocity, temperature and nanoparticle volume fraction profiles are graphically presented.展开更多
In the present paper, the boundary layer flow of Walters Liquid B Model over a stretching plate has been considered to solve heat flow problem with variable conductivity. First, using similarity transformation, the ve...In the present paper, the boundary layer flow of Walters Liquid B Model over a stretching plate has been considered to solve heat flow problem with variable conductivity. First, using similarity transformation, the velocity components of velocity have been obtained. Then, the heat flow problem has been considered in two ways: 1) prescribed surface temperature (PST), and 2) prescribed stretching plate heat flux (PHF) in case of variable conductivity. Due to variable conductivity, temperature profile has its two part- one mean tempera-ture and other temperature profile induced due to variable conductivity. The related results have been dis-cussed with the help of graphs.展开更多
文摘The boundary-layer flow and heat transfer in a viscous fluid containing metallic nanoparticles over a nonlinear stretching sheet are analyzed. The stretching velocity is assumed to vary as a power function of the distance from the origin. The governing partial differential equation and auxiliary conditions are reduced to coupled nonlinear ordinary differential equations with the appropriate corresponding auxiliary conditions. The resulting nonlinear ordinary differential equations (ODEs) are solved numerically. The effects of various relevant parameters, namely, the Eckert number Ec, the solid volume fraction of the nanoparticles ~, and the nonlinear stretching parameter n are discussed. The comparison with published results is also presented. Different types of nanoparticles are studied. It is shown that the behavior of the fluid flow changes with the change of the nanoparticles type.
文摘This paper considers the problem of hydrodynamics and thermal boundary layers of Darcy flow over horizontal surface embedded in a porous medium. The solutions of such problems for the cases of uniform surface temperature and variable surface temperature have been studied and analysed in many papers. This paper, however, attempts to find similarity solutions for the Darcy flow problem with a convective boundary condition at the plate surface. It is found that the solution is possible when the heat transfer coefficient is proportional to x<sup>–2/3</sup>. The numerical solutions thus obtained are analyzed for a range of values of the parameter characterizing the hot fluid convection process. Analytical expressions are provided for local surface heat flux and total surface heat transfer rate while the flow variables are discussed graphically.
文摘Unsteady mixed convective boundary layer flow of viscous incompressible fluid along isothermal horizontal plate is analyzed through Similarity Solutions. The governing partial differential equations are transformed into ordinary differential equations using the similarity transformation and solved numerically along with shooting technique. The flow field for the fluid velocity, temperature and concentration at the plate surface are significantly influenced by the governing parameters such as unsteadiness parameter, permeability parameter, Prandtl number, Schmidt number and the other driving parameters. The results show that both fluid velocity and temperature decrease but no significant effect on concentration for the increasing values of Prandtl number. It is also exposed that velocity and concentration is higher at lower Schmidt number for low Prandtl fluid. Finally, the dependency of the Skin-friction co-efficient, Nusselt number and Sherwood number, which are of physical interest, are also illustrated in tabular form for the governing parameters.
基金provided by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD)
文摘The equation used to model the unidirectional flow of methane gas in coal seams is usually formulated as a nonlinear partial differential equation, which needs to be solved numerically with a computer program.Nevertheless, for people without access to the computer program, the conventional numerical method may be inconvenient. Thus, the objective here is to seek some method simpler than the conventional one for solving the flow problem. A commonly used model of the unidirectional methane gas flow is considered, where the methane adsorption is described by the Langmuir isotherm and the free gas is treated as real gas. By introducing the similarity solution, a simple method for solving the flow model is proposed, which can be done on a hand calculator. It is shown by two examples that the gas pressure profile obtained by the proposed method agrees well with the direct numerical solution of the flow model.
文摘Similarity solution of unsteady convective boundary layer flow along isothermal vertical plate with porous medium is analyzed. The plate surface is reactive with the fluid and generates inert specie which diffuses inside the boundary. The flux of the specie at the plate is proportional to specie concentration at the plate. The governing equations of continuity, momentum, energy and specie diffusion are transformed into ordinary differential equation by using the similarity transformation and solved numerically by using free parameter method along with shooting technique. The dimensionless velocity, temperature and concentration profiles are obtained and presented through figures for different parameters entering into the problem. The local Skin-friction co-efficient, Nusselt number and Sherwood number at the plate for physical interest are also discussed through tables.
基金The National Natural Science Foundations of China (No05131/1046, 1010503020203)
文摘The unsteady flow of viscoelastic fluid in a cylindrical pipe was investigated using the fractional Maxwell model. Two special cases of unsteady pipe flow were expressed. The first is start-up flow, and the second is oscillating flow. The exact solution of start-up flow under a constant pressure gradient was obtained by using the theories of Laplace transform and Fourier-Bessel series for fractional derivatives. The exact solution of oscillating flow was obtained by utilizing the separation of variables.
文摘The laminar analytic solutions of velocities and pressure in the central zone of the inlet region of pipe flow are given under the condition of uniform inflow, based on the Navier-Stokes equations of incompressible viscous flow.
文摘According to a mathematical model for dense two-phase flows presented in the previous pape[1],a dense two-phase flow in a vertical pipeline is analytically solved, and the analytic expressions of velocity of each continuous phase and dispersed phase are respectively derived. The results show that when the drag force between twophasesdepends linearly on their relative velocity, the relative velocity profile in the pipeline coincides with Darcy's law except for the thin layer region near the pipeline wall, and that the theoretical assumptions in the dense two-phase flow theory mentioned are reasonable.
文摘This paper aims to present complete series solution of non-similarity boundary-layer flow of an incompressible viscous fluid over a porous wedge. The corresponding nonlinear partial differential equations are solved analytically by means of the homotopy analysis method (HAM). An auxiliary parameter is introduced to ensure the convergence of solution series. As a result, series solutions valid for all physical parameters in the whole domain are given. Then, the effects of physical parameters γ and Prandtl number Pr on the local Nusselt number and momentum thickness are investigated. To the best of our knowledge, it is the first time that the series solutions of this kind of non-similarity boundary-layer flows are reported.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11072217, 10872181)the Fundamental Research Funds for the Central Universities (Grant Nos. 2009QNA4036, 2010QNA4015)
文摘In this article,we employ a fully-resolved numerical simulation method(the fictitious domain method)to investigate the effects of large neutrally-buoyant particles on the turbulent flow in a pipe at low Reynolds number and non-dilute regimes.The tube Reynolds number is fixed to be 4 900,the particle-pipe diameter ratio is 0.1,and the particle volume fraction ranges from 0.33%to 10%.Our results indicate that the presence of large particles decreases the maximum root-of-mean-square(rms)of the streamwise velocity fluctuation near the wall by weakening the intensity of large-scale streamwise vortices,although in the region very close to the wall the particles increase the rms of streamwise velocity fluctuation.On the other hand,the particles induce small-scale vortices in the near-wall region,resulting in the enhancement of the rms of radial and circumferential velocity fluctuations there.
基金supported by the National Natural Science Foundation of China (Nos. 50936003 and 51076012)the Open Project of State Key Laboratory for Advanced Metals and Materials (No. 2009Z-02)
文摘The magnetohydrodynamic (MHD) Falkner-Skan boundary layer flow over a permeable wall in the presence of a transverse magnetic field is examined. The approximate solutions and skin friction coefficients of the MHD boundary layer flow are obtained by using a method that couples the differential transform method (DTM) with the Pade approximation called DTM-Pade. The approximate solutions are expressed in the form of a power series that can be easily computed with an iterative procedure. The approximate solutions are tabulated, plotted for the values of different parameters and compared with the numerical ones obtained by employing the shooting technique. It is found that the approximate solution agrees very well with the numerical solution, showing the reliability and validity of the present work. Moreover, the effects of various physical parameters on the boundary layer flow are presented graphically and discussed.
文摘An analytical solution to the famous Falkner-Skan equation for the magnetohydrodynamic (MHD) flow is obtained for a special case, namely, the sink flow with a velocity power index of-1. The solution is given in a closed form. Multiple solution branches are obtained. The effects of the magnetic parameter and the wall stretching parameter are analyzed. Interesting velocity profiles are observed with reversal flow regions even for a stationary wall. These solutions provide a rare case of the Falkner-Skan MHD flow with an analytical closed form formula. They greatly enrich the analytical solution for the celebrated Falkner-Skan equation and provide better understanding of this equation.
基金supported by the National Natural Science Foundation of China(11102237)Program for Changjiang Scholars and Innovative Research Team in University(IRT1294)+1 种基金Specialized Research Fund for the Doctoral Program of Higher Education(20110133120012)China Scholarship Council(CSC)
文摘Based on Huang's accurate tri-sectional nonlin- ear kinematic equation (1997), a dimensionless simplified mathematical model for nonlinear flow in one-dimensional semi-infinite long porous media with low permeability is presented for the case of a constant flow rate on the inner boundary. This model contains double moving boundaries, including an internal moving boundary and an external mov- ing boundary, which are different from the classical Stefan problem in heat conduction: The velocity of the external moving boundary is proportional to the second derivative of the unknown pressure function with respect to the distance parameter on this boundary. Through a similarity transfor- mation, the nonlinear partial differential equation (PDE) sys- tem is transformed into a linear PDE system. Then an ana- lytical solution is obtained for the dimensionless simplified mathematical model. This solution can be used for strictly checking the validity of numerical methods in solving such nonlinear mathematical models for flows in low-permeable porous media for petroleum engineering applications. Finally, through plotted comparison curves from the exact an- alytical solution, the sensitive effects of three characteristic parameters are discussed. It is concluded that with a decrease in the dimensionless critical pressure gradient, the sensi- tive effects of the dimensionless variable on the dimension- less pressure distribution and dimensionless pressure gradi- ent distribution become more serious; with an increase in the dimensionless pseudo threshold pressure gradient, the sensi- tive effects of the dimensionless variable become more serious; the dimensionless threshold pressure gradient (TPG) has a great effect on the external moving boundary but has little effect on the internal moving boundary.
基金supported in part by a grant from China Scholarship Councilthe National Natural Science Foundation of China(11301006)the Anhui Provincial Natural Science Foundation(1408085MA01)
文摘This article concerns the self-similar solutions to the hyperbolic mean curvature flow (HMCF) for plane curves, which is proposed by Kong, Liu, and Wang and relates to an earlier proposal for general flows by LeFloch and Smoczyk. We prove that all curves immersed in the plane which move in a self-similar manner under the HMCF are straight lines and circles. Moreover, it is found that a circle can either expand to a larger one and then converge to a point, or shrink directly and converge to a point, where the curvature approaches to infinity.
文摘Numerical solutions are obtained for non-steady, incompressible fluid flow between two parallel disks which at time t are separated by a distance H(1-αt)1/2 and a magnetic field proportional to B0(1-αt) -1/2 is applied perpendicular to the disks where H denotes a representative length, BO denotes a representative magnetic field and α-1 denotes a representative time. Similarity transformations are used to convert the governing partial differential equations of motion in to ordinary differential form. The resulting ordinary differential equations are solved numerically using SOR method, Richardson extrapolation and Simpson’s (1/3) Rule. Our numerical scheme is straightforward, efficient and easy to program.
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.
文摘The unsteady stagnation point flow of an incompressible viscous fluid over a rotating disk is investigated numerically in the present study. The disk impinges the oncoming flow with a time-dependent axial velocity. The three-dimensionM axisymmetric boundary-layer flow is described by the Navier-Stokes equations. The governing equations are solved numerically, and two distinct similarity solution branches are obtained. Both solution branches exhibit different flow patterns. The upper branch solution exists for all values of the impinging parameter β and the rotating parameter Ω. However, the lower branch solution breaks down at some moderate values of β The involvement of the rotation at disk allows the similarity solution to be transpired for all the decreasing values of β. The results of the velocity profile, the skin friction, and the stream lines are demonstrated through graphs and tables for both solution branches. The results show that the impinging velocity depreciates the forward flow and accelerates the flow in the tangential direction.
文摘Laminar two-dimensional unsteady mixed-convection boundary-layer flow of a viscous incompressible fluid past asymmetric wedge with variable surface temperature embedded in a porous medium saturated with a nanofluid has been studied. The employed mathematical model for the nanofluid takes into account the effects of Brownian motion and thermophoresis. The velocity in the potential flow is assumed to vary arbitrary with time. The non-Darcy effects including convective, boundary and inertial effects will be included in the analysis. The unsteadiness is due to the time-dependent free stream velocity. The governing boundary layer equations along with the boundary conditions are converted into dimensionless form by a non-similar transformation, and then resulting system of coupled non-linear partial differential equations are solved by perturbation solutions for small dimensionless time until the second order. Numerical solutions of the governing equations are obtained employing the implicit finite-difference scheme in combination with the quasi-linearization technique. To validating the method used, we compared our results with previous results in earlier papers on special cases of the problem and are found to be in agreement. Effects of various parameters on velocity, temperature and nanoparticle volume fraction profiles are graphically presented.
文摘In the present paper, the boundary layer flow of Walters Liquid B Model over a stretching plate has been considered to solve heat flow problem with variable conductivity. First, using similarity transformation, the velocity components of velocity have been obtained. Then, the heat flow problem has been considered in two ways: 1) prescribed surface temperature (PST), and 2) prescribed stretching plate heat flux (PHF) in case of variable conductivity. Due to variable conductivity, temperature profile has its two part- one mean tempera-ture and other temperature profile induced due to variable conductivity. The related results have been dis-cussed with the help of graphs.