Pipe Of Arbitrary Cross-section Research Articles

Solvability of a nonstationary problem of a rigid body motion in the flow of a viscous incompressible fluid in a pipe of arbitrary cross-section

The existence of a generalized weak solution is proved for the nonstationary problem of motion of a rigid body in the flow of a viscous incompressible fluid filling a cylindrical pipe of arbitrary cross-section. The fluid flow conforms to the Navier–Stokes equations and tends to the Poiseuille flow at infinity. The body moves in accordance with the laws of classical mechanics under the influence of the surrounding fluid and the gravity force directed along the cylinder. Collisions of the body with the boundary of the flow domain are not admitted and, by this reason, the problem is considered until the body approaches the boundary.

Macrotransport in nonlinear, reactive, shear flows

In 1953, G.I. Taylor published his paper concerning the transport of acontaminant in a fluid flowing through a narrow tube. He demonstrated thatthe transverse variations in the fluid's velocity field and the transversediffusion of the solute interact to yield an effective longitudinal mixingmechanism for the transverse average of the solute. This mechanism hasbeen dubbed ``Taylor Dispersion.'' Since then, many related studies havesurfaced. However, few of these addressed the effects of nonlinear chemical reactions upon a system of solutes undergoing TaylorDispersion. In this paper, I present a mathematical model for the evolutionof the transverse averages of reacting solutes in a fluid flowing down a pipeof arbitrary cross-section. The technique for deriving the model is a generalizationof an approach by introduced by P.C. Fife. The key outcome isthat while one still finds an effective mechanism for longitudinal mixing,there is also a effective mechanism for nonlinear advection.

A nonlocal problem arising from Poiseuille flow with electrical body forces

An approximation of the electric current density for the Poiseuille flow of a viscous slightly conducting fluid in a pipe of arbitrary cross section, in which a constant charge density is prescribed at one end and a difference of potential is applied, gives rise to a nonlocal elliptic problem which presents phenomena of bifurcation. The existence and multiplicity of solutions is studied. Mathematics Subject Classification: 76W05, 35Q35, 76T20

Spatial decay estimates in the problem of entry flow for a Bingham fluid filling a pipe

The aim of this paper is to deal with the classical entry flow problem for a Bingham fluid in steady motion in a cylindrical pipe of arbitrary cross section and of finite or semi-infinite length. The problem to be treated is “end effect” involving comparison between two motions: the Poiseuille-Bingham flow (basic flow) and another flow with the same flux. Our main result is an explicit estimate which establishes the rate of decay, with axial distance from the entry, of a suitable energy functional thus providing a qualitative description of the flow development. The decay estimates are derived using differential inequality techniques. If the pipe is finite, we deduce that the energy of the perturbation decays exponentially provided the Reynold's number R satisfies a smallness condition involving the Bingham number B, the pressure gradient of the Poiseuille-Bingham flow, and the geometrical features of the cross-section. More precisely we find the exponential decay if R < R B where R B is an increasing function in B. We show that for a Bingham fluid the range of R is larger than the range for a Newtonian fluid with the same features as it is known from a phenomenological point of view. If the pipe is semi-infinite we obtain, under a mild asymptotic hypothesis on the stretching tensor, that the energy of the perturbation is finite and it decays like In z/z 2 as z → + ∞.

Resistive wall impedance as derivative of the electric capacitance for a beam pipe of arbitrary cross section.

We derive a general formula expressing the resistive wall impedance in the ultrarelativistic limit for a beam pipe of arbitrary cross section through the ``normal derivative'' of its electric capacitance. An application to the case of rectangular cross section yields a closed form expression of the corresponding longitudinal impedance in terms of elliptic integrals. \textcopyright{} 1996 The American Physical Society.

Coupling impedance of beam pipes of general cross section.

We have derived expressions for the longitudinal and transverse resistive wall coupling impedances for a beam pipe of arbitrary cross section in the ultrarelativistic limit. These expressions involve the integral of the square of the tangential magnetic fields along the wall, which can be obtained from the solution of the two-dimensional Poisson equations with a monopole and dipole singularity, respectively. Explicit results are given for beam pipes of elliptical and rectangular cross sections, including the limiting cases of a circle and a pair of parallel plates.

Decay Estimates in Steady Pipe Flow

In this paper St. Venant type results are derived for the flow of viscous fluid in a pipe of arbitrary cross section. In the spirit of earlier work of Horgan and Wheeler [SIAMJ. Appl. Math., 35 (1978), pp. 97–116], the decay to fully developed flow as a function of distance from the entry section is investigated.Here, it is not assumed that the flow is fully developed at the exit section. Weighted energy inequalities are derived that lead to estimates for the “energy” associated with the velocity field represented by the difference between the entrance flow and the fully developed flow in a portion of the pipe near the exit section. The analysis is based on a variety of differential inequality techniques and Payne’s investigation of uniqueness criteria for steady-state solutions of the Navier–Stokes equations [Simpos. Internaz. Appl. Fis. Mat., 1965, pp. 130–153].

Some extremum principles for magnetohydrodynamic flow in conducting pipes

AbstractExtremum principles are obtained for the laminar flow of a conducting liquid in a straight pipe of arbitrary cross-section with conducting walls of arbitrary thickness, which is subject to a uniform applied magnetic field. These extrema provide upper and lower bounds for the mass-flow rate in the pipe. These bounds are particularly useful in the construction of asymptotic estimates for the flow rate at high Hartmann number. The method is illustrated by its application to the pipe of circular cross-section and to pipes with thin conducting walls.

Some asymptotic extremum principles for magnetohydrodynamic pipe flow

Upper and lower bounds are obtained for the mass flow rate for the steady flow of a conducting liquid along a pipe of arbitrary cross section under the influence of a uniform transverse magnetic field. The extrema are constructed by first establishing an identity which is then used in some simple inequalities. It is shown how these bounds can be used to derive an asymptotic expansion for the flow rate at large Hartmann number. Two illustrations are included.