The flow near a wall suddenly set in motion for a viscoelastic fluid with the generalized Oldroyd-B model is studied. The fractional calculus approach is used in the constitutive relationship of fluid model. Exact ana...The flow near a wall suddenly set in motion for a viscoelastic fluid with the generalized Oldroyd-B model is studied. The fractional calculus approach is used in the constitutive relationship of fluid model. Exact analytical solutions of velocity and stress are obtained by using the discrete Laplace transform of the sequential fractional derivative and the Fox H-function. The obtained results indicate that some well known solutions for the Newtonian fluid, the generalized second grade fluid as well as the ordinary Oldroyd-B fluid, as limiting cases, are included in our solutions.展开更多
The high-order implicit finite difference schemes for solving the fractional- order Stokes＇ first problem for a heated generalized second grade fluid with the Dirichlet boundary condition and the initial condition ar...The high-order implicit finite difference schemes for solving the fractional- order Stokes＇ first problem for a heated generalized second grade fluid with the Dirichlet boundary condition and the initial condition are given. The stability, solvability, and convergence of the numerical scheme are discussed via the Fourier analysis and the matrix analysis methods. An improved implicit scheme is also obtained. Finally, two numerical examples are given to demonstrate the effectiveness of the mentioned schemes展开更多
This paper presents a study of the finite depth Stokes＇ first problem for a thixotropic layer. The yield behavior of the thixotropic fluid in this problem is investigated for the first time. The main physical feature...This paper presents a study of the finite depth Stokes＇ first problem for a thixotropic layer. The yield behavior of the thixotropic fluid in this problem is investigated for the first time. The main physical features of this problem are discussed, including the flow field, the wall stress, and the depth of the yield region. It is shown that the yield region appears near the wall, and the yield surface moves from the wall into the flow region and moves back to the wall finally. In contrast to the solution of the Newtonian fluid, the velocity of the thixotropic layer generally does not increase with time monotonously during the start-up process. The classical solution of the Newtonian fluid can be recovered from our results in extreme cases.展开更多
This work is related to the flow of a magnetohydrodynamic Burgers fluid.The flow of an incompressible conducting Burgers fluid in the presence of a uniform transverse magnetic field over a plate that is moved suddenly...This work is related to the flow of a magnetohydrodynamic Burgers fluid.The flow of an incompressible conducting Burgers fluid in the presence of a uniform transverse magnetic field over a plate that is moved suddenly is considered.By the application of the Laplace and Fourier sine transforms techniques,the exact analytical expressions for the velocity field and associated shear stress are determined in simple forms.They are written as a sum of steady-state and transient solutions.The graphical results are plotted for different values of indispensable parameters and some interesting results are concluded.The corresponding solutions for the hydrodynamic Burgers fluid appear as the limiting cases of the obtained solutions.展开更多
基金The project supported by the National Natural Science Foundation of China(10272067)the Doctoral Program Foundation of the Education Ministry of China(20030422046)+1 种基金the Natural Science Foundation of Shandong Province,China(Y2006A 14)the Research Foundation of Shandong University at Weihai.
文摘The flow near a wall suddenly set in motion for a viscoelastic fluid with the generalized Oldroyd-B model is studied. The fractional calculus approach is used in the constitutive relationship of fluid model. Exact analytical solutions of velocity and stress are obtained by using the discrete Laplace transform of the sequential fractional derivative and the Fox H-function. The obtained results indicate that some well known solutions for the Newtonian fluid, the generalized second grade fluid as well as the ordinary Oldroyd-B fluid, as limiting cases, are included in our solutions.
基金supported by the National Natural Science Foundation of China (No. 10971175)the Scientific Research Fund of Hunan Provincial Education Department (No. 09A093)
文摘The high-order implicit finite difference schemes for solving the fractional- order Stokes＇ first problem for a heated generalized second grade fluid with the Dirichlet boundary condition and the initial condition are given. The stability, solvability, and convergence of the numerical scheme are discussed via the Fourier analysis and the matrix analysis methods. An improved implicit scheme is also obtained. Finally, two numerical examples are given to demonstrate the effectiveness of the mentioned schemes
文摘This paper presents a study of the finite depth Stokes＇ first problem for a thixotropic layer. The yield behavior of the thixotropic fluid in this problem is investigated for the first time. The main physical features of this problem are discussed, including the flow field, the wall stress, and the depth of the yield region. It is shown that the yield region appears near the wall, and the yield surface moves from the wall into the flow region and moves back to the wall finally. In contrast to the solution of the Newtonian fluid, the velocity of the thixotropic layer generally does not increase with time monotonously during the start-up process. The classical solution of the Newtonian fluid can be recovered from our results in extreme cases.
文摘This work is related to the flow of a magnetohydrodynamic Burgers fluid.The flow of an incompressible conducting Burgers fluid in the presence of a uniform transverse magnetic field over a plate that is moved suddenly is considered.By the application of the Laplace and Fourier sine transforms techniques,the exact analytical expressions for the velocity field and associated shear stress are determined in simple forms.They are written as a sum of steady-state and transient solutions.The graphical results are plotted for different values of indispensable parameters and some interesting results are concluded.The corresponding solutions for the hydrodynamic Burgers fluid appear as the limiting cases of the obtained solutions.
