Oscillating flow of a simple fluid in a pipe

Resonance behaviour of viscoelastic fluid in Poiseuille flow in the presence of a transversal magnetic field

“…The velocity enhancement is given by Equation (18). In Reference [9] the resonance behaviour of A in the absence of a magnetic ÿeld = 0 has been studied.…”

“…Here we mention that in the presence of electric and magnetic ÿeld one will have very general constitutive equations for the stress, free energy, etc. (see References [17,18]) and this general constitutive equation for the stress is very complicated giving rise to highly nonlinear equations, which are not easy to solve. Actually, we are going to look at simpliÿed MHD equations, which are similar to that in the case of classical MHD equations [19][20][21].…”

Developments in the Flow of Complex Fluids in Tubes

“…Frequency dependence of the enhancement in particular is not even qualitatively predicted by any of these models. The studies by Siginer [197][198][199] who used multiple integral representations of the constitutive structure given by a series of nested integrals with tensor polynomial kernels in terms of the history of the motion G(s) originally developed by Green and Rivlin [200] and Coleman and Noll [118] predicted many features of the existing data for the first time.…”

“…However, although it is well known that Riesz theorem justifies the representation of the first Fréchet derivative δF as a single integral with the integrand linear in G oo , there are no representation theorems for higher orders, and the representation of the second δ 2 F and third δ 3 F Fréchet derivatives as double and triple integrals, bilinear and trilinear, respectively, in G oo constitutes only a partially justifiable hypothesis. Siginer [197][198][199] It should be noted that canonical representations for δ 2 F and δ 3 F are not known when the base state G o is a viscometric flow. For more on this constitutive equation as well as others mentioned above, please see Siginer [73,[197][198][199].…”

Spectral approximation for a nonlinear partial differential equation arising in thin film flow of a non-Newtonian fluid

“…The superposition of oscillatory motion on steady flows has been of much interest over the last few decades as they may give rise to flow rate enhancement and can be used to control the flow rate as well. In particular pulsatile pipe flow, in which the liquid is driven by a pressure gradient oscillating about a non-zero mean, and the flow driven by a combination of a steady pressure gradient and oscillating boundaries have been investigated by several authors, Siginer [4][5][6] among them. In the same vein the drainage of a thin liquid film down a vertical surface oscillating either in its own plane or orthogonally to the flow direction was studied first by Goshawk et al [7] for Newtonian and linearly viscoelastic fluids.…”