Analytic solutions of Newtonian and non-Newtonian pipe flows subject to a general time-dependent pressure gradient

Purely pulsating flow of a viscoelastic fluid in a pipe revisited: The limit of large Womersley number

“…In particular, analytical solutions for the Newtonian fluid flow in a rigid infinite pipe due to a periodic pressure gradient were considered by Womersley [1] in relation to the blood flow in arteries, although similar solutions were found earlier [2,3]. Since the blood is known to behave as a non-Newtonian fluid [4], analytical solutions for several non-Newtonian fluid models have also been obtained later for this idealized pipe flow, as well as for some other more general pulsating pipe flows, not only in relation to blood flow, but to some other physiological and industrial processes, many of them in relation to the flow enhancement effect [5][6][7][8][9][10][11][12][13][14]. Some of these works, in addition to other ones for the viscoelastic fluid flow generated by an oscillating plate [15,16], are cited below in connection to the solutions described in the present work.…”

Pulsating Flow of an Ostwald—De Waele Fluid between Parallel Plates

“…Thus, inserting the solutions given by Equations (21), (31), and (49) into Equation 16, the velocity distribution up to the second-order is obtained. The shear stress is made dimensionless with ρU 2 0 , and it is computed directly from…”

“…The first analyzed the pulsatile plane Pouseille flow of viscoelastic liquids of the memory integral type, and the second the flow of a generalized Maxwell fluid through a slit. Mc Ginty et al [21] presented solutions of pulsatile flows of Newtonian, Maxwell, and Oldroyd B fluids in a cylinder and in the gap between two cylinders. Daprà and Sacarpi [22] analyzed the later configuration for a Bingham fluid.…”

Thermal convection of a viscoelastic fluid in an open-top porous layer heated from below

“…In the present study, the viscoelastic fluid is considered as an Oldroyd-B fluid. It is assumed that¯ ≥ε > 0 [17][18][19]. Notice that whenε and¯ are both equal to zero, Eq.…”