A problem of unsteady flow of a second grade fluid over flat plates with the impulsive and oscillating motion, starting from rest, and with the wall transpiration is considered. The exact solutions are derived by the ...A problem of unsteady flow of a second grade fluid over flat plates with the impulsive and oscillating motion, starting from rest, and with the wall transpiration is considered. The exact solutions are derived by the Laplace transform, the perturbation techniques, and an extension of the variable separation technique together with similarity arguments. These solutions are written as the sum between the permanent solutions and the transient solutions. The variations of fluid behaviors with various physical parameters are shown graphically and analyzed. The results are validated by comparing the limiting cases of the present paper with the results of the related published articles.展开更多
This paper deals with the rotational flow of a generalized second grade fluid, within a circular cylinder, due to a torsional shear stress. The fractional calculus approach in the constitutive relationship model of a ...This paper deals with the rotational flow of a generalized second grade fluid, within a circular cylinder, due to a torsional shear stress. The fractional calculus approach in the constitutive relationship model of a second grade fluid is introduced. The velocity field and the resulting shear stress are determined by means of the Laplace and finite Hankel transforms to satisfy all imposed initial and boundary conditions. The solutions corresponding to second grade fluids as well as those for Newtonian fluids are obtained as limiting cases of our general solutions. The influence of the fractional coefficient on the velocity of the fluid is also analyzed by graphical illustrations.展开更多
基金Project supported by the Research Management Centre of Universiti Teknologi Malaysia(Nos.04H27and 4F255)
文摘A problem of unsteady flow of a second grade fluid over flat plates with the impulsive and oscillating motion, starting from rest, and with the wall transpiration is considered. The exact solutions are derived by the Laplace transform, the perturbation techniques, and an extension of the variable separation technique together with similarity arguments. These solutions are written as the sum between the permanent solutions and the transient solutions. The variations of fluid behaviors with various physical parameters are shown graphically and analyzed. The results are validated by comparing the limiting cases of the present paper with the results of the related published articles.
文摘This paper deals with the rotational flow of a generalized second grade fluid, within a circular cylinder, due to a torsional shear stress. The fractional calculus approach in the constitutive relationship model of a second grade fluid is introduced. The velocity field and the resulting shear stress are determined by means of the Laplace and finite Hankel transforms to satisfy all imposed initial and boundary conditions. The solutions corresponding to second grade fluids as well as those for Newtonian fluids are obtained as limiting cases of our general solutions. The influence of the fractional coefficient on the velocity of the fluid is also analyzed by graphical illustrations.
