Stokes' first problem for some non-Newtonian fluids: Results and mistakes

The well-known problem of unidirectional plane flow of a fluid in a half-space due to the impulsive motion of the plate it rests upon is discussed in the context of the second-grade and the Oldroyd-B non-Newtonian fluids. The governing equations are derived from the conservation laws of mass and momentum and three correct known representations of their exact solutions given. Common mistakes made in the literature are identified. Simple numerical schemes that corroborate the analytical solutions are constructed.Comment: 10 pages, 2 figures; accepted for publication in Mechanics Research Communications; v2 corrects a few typo

The Influence of Magnetohydrodynamic Flow and Slip Condition on Generalized Burgers’ Fluid with Fractional Derivative

         هذا البحث يهدف الى تاثير حقل مغناطيسي هيدروديناميكي للمائع بيركر القابل للانضغاط من خلال ضغط ثابت ولوح متسارع أسي. حيث افتراض عدم الانزلاق بين لوحة التسارع والمائع . حساب  التفاضل والتكامل الكسري استخدم لكتابة  معادلات الحركة لنموذج المائع , باستخدام تحويلات لابلاس وفوريير نحصل على حقل السرعة والاجهاد. اضافة الى ذلك, تم رسم الاشكال الثلاثية الابعاد لعرض تاثير حقل المغناطيسي والمعلمات المختلفة على حقل السرعة.                                                          This paper investigates the effect of magnetohydrodynamic (MHD) of an incompressible generalized burgers’ fluid including a gradient constant pressure and an exponentially accelerate plate where no slip hypothesis between the burgers’ fluid and an exponential plate is no longer valid. The constitutive relationship can establish of the fluid model process by fractional calculus, by using Laplace and Finite Fourier sine transforms. We obtain a solution for shear stress and velocity distribution. Furthermore, 3D figures are drawn to exhibit the effect of magneto hydrodynamic and different parameters for the velocity distribution

Exact Solutions of Accelerated Flows for a Generalized Burgers' Fluid, I: The Case

An analysis is presented to develop the exact solutions for the accelerated flows of a generalized Burgers' fluid when the relaxation time satisfying the condition 2 /4 . The corresponding expressions for the velocity field and associated tangential stress are obtained by using Laplace transform for the problems of flow induced by constantly accelerated plate. The obtained solutions are presented through simple or multiple integrals in terms of Bessel functions. The corresponding solutions for Burgers' fluid are recovered as special case of the solutions obtained here

Effects of MHD on the Unsteady Rotating Flow of a Generalized Maxwell Fluid with Oscillating Gradient Between Coaxial Cylinders

The aim of  this paper is studied the effect of magnetic field on the unsteady rotating flow of a generalized Maxwell fluid with fractional derivative between two infinite straight circular cylinder .The velocity field and the shear stress are obtained by means of discrete Laplace transform and finite Hankel transform. The exact solution for the velocity field and the shear stress that have been obtained by integral and series form in terms of the generalized G functions and Mitting –leffer function .the graphs are plotted to show the effects of the fractional parameter on the fluid dynamic characteristics with MHD on the velocity and shear stress

Taylor–Couette flow of a generalized second grade fluid due to a constant couple

The velocity field and the adequate shear stress, corresponding to the flow of a generalized second grade fluid in an annular region between two infinite coaxial cylinders, are determined by means of Laplace and finite Hankel transforms. The motion is produced by the inner cylinder which is rotating about its axis due to a constant torque f per unit length. The solutions that have been obtained satisfy all imposed initial and boundary conditions. For β → 1 or β → 1 and α1 → 0, the corresponding solutions for an ordinary second grade fluid, respectively, for the Newtonian fluid, performing the same motion, are obtained as limiting cases

UNSTEADY MHD THREE DIMENSIONAL FLOW OF MAXWELL FLUID THROUGH POROUS MEDIUM IN A PARALLEL PLATE CHANNEL UNDER THE INFLUENCE OF INCLINED MAGNETIC FIELD

In this paper, we discuss the unsteady hydro magnetic flow of an electrically conducting Maxwell fluid in a parallel plate channel bounded by porous medium under the influence of a uniform magnetic field of strength Ho inclined at an angle of inclination with the normal to the boundaries. The perturbations are created by a constant pressure gradient along the plates. The time required for the transient state to decay and the ultimate steady state solution are discussed in detail. The exact solutions for the velocity of the Maxwell fluid consists of steady state are analytically derived, its behaviour computationally discussed with reference to the various governing parameters with the help of graphs. The shear stresses on the boundaries are also obtained analytically and their behaviour is computationally discussed in detail