On some unsteady flows of a non-Newtonian fluid

Abstract

Some properties of unsteady unidirectional flows of a fluid of second grade are considered for flows impulsively started from rest by the motion of a boundary or two boundaries or by sudden application of a pressure gradient. Flows considered are: unsteady flow over a plane wall, unsteady Couette flow, flow between two parallel plates suddenly set in motion with the same speed, flow due to one rigid boundary moved suddenly and one being free, unsteady Poiseuille flow and unsteady generalized Couette flow. The results obtained are compared with those of the exact solutions of the NavierStokes equations. It is found that the stress at time zero on the stationary boundary for the flows generated by impulsive motion of a boundary or two boundaries is finite for a fluid of second grade and infinite for a Newtonian fluid. Furthermore, it is shown that for unsteady Poiseuille flow the stress at time zero on the boundary is zero for a Newtonian fluid, but it is not zero for a fluid of second grade.

Some Unsteady Flows of a Jeffrey Fluid between Two Side Walls over a Plane Wall

“…In the absence of a pressure gradient in the flow direction the balance of linear momentum (4) along with (5), (7), and (8) yield the governing equation…”

Applications of the Numerical Inversion of the Laplace transform to unsteady problems of the third grade fluid

“…Various complex fluids such as Oils, polymer melts, different type of drilling muds and clay coatings and many emulsions are included in the category of non-Newtonian fluids. Flows of non-Newtonian fluids have been studies by many [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. One of the very important models suggested for non-Newtonian fluids is called the third-grade fluid model [22,23].…”

On exact solutions of Stokes second problem for a Burgers’ fluid, I. The case γ < λ2/4

“…Therefore, it has been now recognized in industrial and technological applications that non-Newtonian fluids are more appropriate than Newtonian fluids. Some recent studies regarding these fluids are made in the references [1][2][3][4][5][6][7][8][9][10]. In non-Newtonian fluids, relation connecting shear stress and shear rate is not usually linear; that the viscosity of a non-Newtonian fluid is not constant at a given temperature and pressure but depends on the rate of shear or on the previous kinematic history of the fluid.…”