An analytical solution for steady flow of a Quemada fluid in a circular tube

An analytical solution is obtained for steady flow of Quemada-type fluids in a circular tube driven by a constant pressure gradient. Expressions are derived for velocity distribution and for volumetric flow rate as a function of pressure gradient or wall shear stress.     

A finite element approximation of steady flow through a rotating non-aligned straight tube

A finite element solution is developed for a penalty function formulation of the equations which govern the steady motion of a Newtonian fluid through a pipe that rotates about an axis not parallel to its own. The motion in this system is driven by the Coriolis acceleration, which has components in the axial direction as well as in the transverse plane of the pipe. The relative magnitudes of these components significantly affect the qualitative and quantitative nature of the primary and secondary flow field. The present results compare favourably with those of previously reported experimental and theoretical studies over a wide range of flow regimes.     

Heat transfer to laminar flow of nongray gases through a circular tube

Analyses are presented for infrared radiative energy transfer in gases when other modes of energy transfer simultaneously occur. Fully developed laminar flow of an absorbing emitting gas in a circular tube is considered under the conditions of uniform wall heat flux. Nongray as well as gray formulations are presented, and results are obtained for illustrative cases. Appropriate limiting solutions of the governing equations are obtained and conduction-radiation interaction parameters are evaluated. The influence of variable wall emittance (gray and nongray) upon radiative energy transfer in nongray gases is investigated. In particular, nongray results are obtained, in the large path length limit, for the flow of CO₂ through stainless steel tubes of various compositions. Finally, a correlation is presented which can be utilized to extend all nongray results for the parallel plate geometry, already available in literature, to yield results for the corresponding case of a circular tube. This work was supported by the National Science Foundation through Grant No. GK-16755.     

Effect of curvature on dual solutions of flow through a curved circular tube

Dual solutions, i.e., two-vortex and four-vortex solutions, of the flow through a curved circular tube are numerically obtained by the spectral method for 0 ⩽ δ ⩽ 0.8 and 500 ⩽ Dn ⩽ 10000, where δ is the non-dimensional curvature of the tube and Dn the Dean number. It is found that the critical Dean number above which the four-vortex solution exists takes the lowest value 956 at δ = 0 and increases with δ. In terms of the Reynolds number of the flow, however, the critical Reynolds number decreases from infinity as δ increases from zero, takes the minimum value of about 250 at δ ≈ 0.52, and then increases again.     

Asymptotic solution for the hartmann problem through circular tube

Summary Asymptotic solutions valid for sufficiently large Hartmann numbers M are presented in this paper. It is found that the velocity profiles are elliptic paraboloids of revolution whose major axis are parallel to the direction of the imposed magnetic field. Also the velocity profiles along the diameter parallel to the imposed field are like those of Hartmann for parallel plates and perpendicular to the field these are almost of parabolic character.     

Laminar flow between the surfaces of two eccentric circular cylinders

The problem of laminar fluid flow in an asymmetric annular gap has been solved in earlier work in an approximation with error difficult to gauge. In the present paper, the problem is solved exactly. The velocity distribution of the flow is obtained, the mean velocity is determined, and an exact expression is found for the coefficient which determines the flow rate. An approximate expression proposed for this coefficient holds asymptotically at small eccentricities. The results are compared with experimental data.Translated from Izvestiya Akademil Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 16–20, January–February, 1984.     

A multigrid finite difference approach to steady flow between eccentric rotating cylinders

A simple finite difference scheme over a non‐uniform grid is proposed to solve the two‐dimensional, steady Navier–Stokes equations. Instead of the Newton method, a more straightforward line search algorithm is used to solve the resultant system of non‐linear equations. By adopting the multigrid methodology, a fast convergence is achieved, at least for low‐Reynolds number flow. This scheme is applied, in particular, to flow between eccentric rotating cylinders. The computed results are shown in good agreement with some analytic findings. Copyright © 2000 John Wiley & Sons, Ltd.     

Stability of a flow in a circular tube

Many studies, both theoretical and experimental, have been dedicated to the stability of flow in a circular tube (see, for example, review [1]). In every case mathematical investigation has not succeeded in obtaining an expression for hydrodynamic instability of such a flow for disturbances of sufficiently low amplitude. (An exception is [2].) Experiment also indicates the stability of such a flow [3], with a laminar mode being extended to Reynolds numbers of the order of tens of thousands. These facts are the basis for the assumption that the flow of a viscous incompressible liquid in a circular tube is stable for small perturbations. However, there is no analytical or even numerical proof of this hypothesis. Moreover, some studies, for example [2], indicate the instability of such a flow in relation to three-dimensional nonaxiosymmetric perturbations. The analysis of hydrodynamic stability with respect to three-dimensional disturbances of flow within a circular tube conducted in this study showed the stability of the flow over a wide range of wave numbers and Reynolds numbers.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 20–24, January–February, 1973.     

Analytical solution for laminar flow through leaky tube

The laminar flow through a leaky tube is investigated, and the momentum and conservation of energy equations are solved analytically. By using the Hagen-Poiseuille velocity profile and defining unknown functions for the axial and radial velocity components, the pressure and mass transfer equations are obtained, and their profiles are plotted according to different parameters. The results indicate that the axial velocity, the radial velocity, the mass transfer parameter, and the pressure in the tube decrease as the fluid moves along the tube.     

On exact solutions of the flow equations for Bingham visco-plastic fluids through an eccentric annular cross-section

We discuss properties of solutions of the Bingham flow equations for visco-plastic fluids through an eccentric annular cross-section. Particularly, we perform arguments which are not in favor of the well-known Szabo–Hassager’s conjecture that the rigid zone is confined by circles provided the eccentricity is small (J Non-Newtonian Fluid Mech 45:149-169, 1992).     

Reinforcement of a plate with a circular hole by an eccentric circular patch

We study the reinforcement of an infinite elastic plate with a circular hole by a larger eccentric circular patch completely covering the hole and rigidly adjusted to the plate along the entire boundary of itself. We assume that the plate and the patch are in a generalized plane stress state generated by the action of some given loads applied to the plate at infinity and on the boundary of the hole. We use the power series method combined with the conformal mapping method to find the Muskhelishvili complex potentials and study the stress state on the hole boundary and on the adhesion line. We consider several examples, study how the stresses depend on the geometric and elastic parameters, and compare the problem under study with the case of a plate with a circular hole without a patch. In scientific literature, numerous methods for reinforcing plates with holes, in particular, with circular holes, have been studied. In the monographs [1, 2], the problem of reinforcing the hole edges by stiffening ribs is solved. Methods for reinforcing a circular hole by using two-dimensional patches pasted to the entire plate surface are studied in [3, 4]. The case of a plate with a circular cut reinforced by a concentric circular patch adjusted to the plate along the boundary of itself or along some other circle was studied in [5, 6]. The reinforcement of an elliptic hole by a confocal elliptic patch was considered in [7].     

Non-isothermal masstransport in a circular tube for flow of Non-Newtonian liquid

The non-isothermal mass transport in a circular tube has been investigated for an Ostwald-de-Waele liquid. The influence of the velocity profile parameter, the flow parameter, the thermal diffusion, the diffusive heat transfer as well as the ratio of the Schmidt- to the Prandtl number upon the concentration- and temperature profile along the tube have been determined. The results are compared with the plug flow case and also with the isothermal mass transport. It was found that considerable differences in the mass transport and heat transport occur through their coupling effect.

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Nichtisothermer Stofftransport in einem Rohr für die Strömung einer nicht-Newtonschen Flüssigkeit

Zusammenfassung Für eine Ostwald-de-Waele Flüssigkeit wurde der nichtisotherme Stofftransport in einem Kreiszylinderrohr untersucht. Dabei wurde der Einfluß des Geschwindigkeitsparameters, des Strömungsparameters, der Wärmediffusion, des diffusen Wärmetransportes, sowie der Einfluß des Verhältnisses von Schmidt- zur Prandtlzahl auf das Konzentrations- und Temperaturprofil entlang der Rohrlauflänge untersucht. Die Ergebnisse wurden mit dem Fall eines Kolbenprofiles und mit denen des isothermen Stofftransportes verglichen. Dabei konnten erhebliche Differenzen in der Konzentrations- und Wärmeverteilung durch den Koppelungseffekt festgestellt werden.

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Nomenclature a radius of tube - c concentration - c _i initial concentration at inlet z=0 - c _w wall concentration - D diffusion coefficient - J _m Besselfunction of first kind andm ^th order - j diffusive mass flux - K material constant - p liquid pressure - dp/dz pressure gradient along tube - q heat flux - r, ,z cylindrical coordinates - S entropy - T temperature { _{Tw wall temperature} ^{Ti initial temperature at inlet} - w axial velocity of liquid - k _T thermal diffusion ratio - N thermodynamic parameter - .=k _T/T parameter - _n zeros ofJ ₀ (_n)=0 - parameter (=0 plug flow, 1 Ostwald-de-Waele flow) - material constant { _{< 1 dilatant} ^{> 1 pseudoplastics} } - effective chemical potential - thermal conductivity - thermal diffusivity of mixture - liquid density - dynamic viscosity of Newtonian liquid - shear stress - eigenvalues     

Measuring small internal pressures along a tube during steady flow

A tube that can accurately measure small strains and pressure profiles during flow of non-Newtonian paste explosives has been designed and strain gaged. Equiangular rosette strain gages were installed along the length of a 6-mm-diam, 0.46-m-long thin-walled aluminum tube. The rosettes were oriented in the classical stress-gage configuration to measure circumferential stress and, hence, internal pressure independent of other stresses. The tube was static calibrated on a floating-piston pressure calibrator. Steady flow calibration was accomplished by extruding a viscous Newtonian silicone oil. Inlet pressure ranged from 0.52 to 2.1 MPa (75 to 300 psi). For the low-pressure 0.52-MPa silicone-oil extrusion, the full-scale strain levels varied from 6 to 53 μm/m. For all eight strain-gage stations, the maximum deviation from a linear pressure profile was equivalent to 0.5 μm/m. A pulsed-current-excitation signal-conditioning and digital data-acquisition system provided the necessary stability and precision to measure these unusually low-strain levels accurately.     

Stokes flow through a permeable tube

Pressure-driven Stokes flow through a circular tube with a permeable wall is considered as a model of blood flow through a capillary vessel. Fluid penetrates the tube wall over a test section according to Starling law relating the normal fluid velocity to the transmural pressure defined as the difference between the wall and the uniform ambient pressure. The problem is formulated using the integral representation for Stokes flow, and the solution is computed with high accuracy using a boundary-element method for specified values of the wall permeability and percentage of fluid escaping through the walls. The results illustrate the structure of the flow and validate the predictions of a model based on the assumption of locally unidirectional flow for sufficiently small permeability.     

Ion slip effect on a steady flow through a circular pipe of a dusty conducting Oldroyd 8-constant fluid

In this paper, a steady magnetohydrodynamic (MHD) flow of a dusty incompressible electrically conducting Oldroyd 8-constant fluid through a circular pipe is examined with considering the ion slip effect. A constant pressure gradient in the axial direction and an external uniform magnetic field in the perpendicular direction are applied. A numerical solution is obtained for the governing nonlinear momentum equations by using finite differences. The effect of the ion slip, the non-Newtonian fluid characteristics, and the particle-phase viscosity on the velocity, volumetric flow rates, and skin friction coefficients of both the fluid and particle phases is reported.     

Forced convection performance of a MEPCM suspension through an iso-flux heated circular tube: an experimental study

The paper examines experimentally forced convection performance of a microencapsulated phase change material (MEPCM) suspension through an iso-flux heated circular tube. Forced convection experiments have been undertaken using the pure water or MEPCM suspensions as the working fluid. The heat transfer performance of the MEPCM suspension was gauged in terms of local/average heat transfer coefficients and temperature control effectiveness along the tube wall compared with that obtained for the pure water.     

Numerical investigation of steady suction control of flow around a circular cylinder

This paper numerically investigates the effectiveness of the control of steady suction on a stationary circular cylinder with several isolated suction holes on the surface at a subcritical Reynolds number. The control effectiveness as a function of the azimuthal position, spanwise spacing and suction flow rate of the suction holes on the control of the aerodynamic forces on the cylinder and the suppression of alternate vortex shedding are taken into account. The study of the azimuthal location of the suction holes indicates that azimuthal angles of θ=90° and 270°, which are close to the separation point, provide the most substantial decreases in the aerodynamic forces. When restricted to the most effective azimuthal angle, a remarkable control effectiveness can be achieved when the axial spacing between two neighboring suction holes is less than a minimum value even under a small suction momentum coefficient. However, if the axial spacing exceeds the minimum spacing, the control effectiveness will not be saturated even under a very large suction momentum coefficient. Thus, the cause of the effective aerodynamic force control is suggested to be a result of obvious three-dimensional phenomenon in the near wake, which is characterized by the generation of a convergent flow between two neighboring suction hole sections and a stronger, larger three-dimensional vortex pair adjacent to the convergent flow. It has been suggested that this strongly three-dimensional flow pattern is induced by the strong interaction between two neighboring but counter-rotating three-dimensional vortices separately produced by two neighboring suction holes. Moreover, the effects of such three-dimensional flow patterns are investigated in detail based on variations in the flow field and sectional aerodynamic forces in different cross sections. Finally, the upper limit of the axial spacing between two neighboring suction holes to form such a three-dimensional flow pattern is suggested to be between 0.75 D and 1.5 D when the suction flow rate exceeds a certain value.