This paper presents a study of visco-elastic flow of an incompressible generalized Oldroyd-B fluid between two infinite parallel plates in which the constitutive equation involves fractional order time derivative. The...This paper presents a study of visco-elastic flow of an incompressible generalized Oldroyd-B fluid between two infinite parallel plates in which the constitutive equation involves fractional order time derivative. The solutions of field equations are being obtained for the motion of the said fluid between two parallel plates where the lower plate starts to move with steady velocity and the upper plate remains fixed in the first problem and the upper plate oscillates with constant frequency and the other being at rest in the second problem. The exact solutions for the velocity field are obtained by using the Laplace transform and finite Fourier Sine transform technique in terms of Mittag Leffler and generalised functions. The analytical expression for the velocity fields are derived and the effect of fractional parameters upon the velocity field is depicted graphically.展开更多
The unsteady incompressible viscous flow of a Generalised Maxwell fluid between two coaxial rotating infinite parallel circular disks is studied by using the method of integral transforms. The motion of the fluid is c...The unsteady incompressible viscous flow of a Generalised Maxwell fluid between two coaxial rotating infinite parallel circular disks is studied by using the method of integral transforms. The motion of the fluid is created by the rotation of the upper and lower circular disks with different angular velocities. A fractional calculus approach is utilized to determine the velocity profile in series form in terms of Mittag-Leffler function. The influence of the fractional as well as the material parameters on the velocity field is illustrated graphically.展开更多
文摘This paper presents a study of visco-elastic flow of an incompressible generalized Oldroyd-B fluid between two infinite parallel plates in which the constitutive equation involves fractional order time derivative. The solutions of field equations are being obtained for the motion of the said fluid between two parallel plates where the lower plate starts to move with steady velocity and the upper plate remains fixed in the first problem and the upper plate oscillates with constant frequency and the other being at rest in the second problem. The exact solutions for the velocity field are obtained by using the Laplace transform and finite Fourier Sine transform technique in terms of Mittag Leffler and generalised functions. The analytical expression for the velocity fields are derived and the effect of fractional parameters upon the velocity field is depicted graphically.
文摘The unsteady incompressible viscous flow of a Generalised Maxwell fluid between two coaxial rotating infinite parallel circular disks is studied by using the method of integral transforms. The motion of the fluid is created by the rotation of the upper and lower circular disks with different angular velocities. A fractional calculus approach is utilized to determine the velocity profile in series form in terms of Mittag-Leffler function. The influence of the fractional as well as the material parameters on the velocity field is illustrated graphically.
