Some extremum principles for magnetohydrodynamic flow in conducting pipes

1972 ◽  
Vol 72 (2) ◽  
pp. 303-313 ◽  
Author(s):  
P. Smith
Keyword(s):  
Cross Section ◽  
Flow Rate ◽  
Hartmann Number ◽  
Circular Cross Section ◽  
Arbitrary Cross Section ◽  
Upper And Lower Bounds ◽  
Asymptotic Estimates ◽  
Conducting Liquid ◽  
Straight Pipe ◽  
Arbitrary Thickness

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.

Magnetohydrodynamic pipe flow Part2. High Hartmann number

1962 ◽  
Vol 13 (4) ◽  
pp. 513-518 ◽  
Author(s):  
J. A. Shercliff
Keyword(s):  
Magnetic Fields ◽  
Pressure Gradient ◽  
Cross Section ◽  
Pipe Flow ◽  
Hartmann Number ◽  
Gradient Flow ◽  
Transverse Magnetic ◽  
Arbitrary Cross Section ◽  
Conducting Liquid ◽  
Experimental Pressure

The paper presents an improved, second approximation for the laminar motion of a conducting liquid at high Hartmann number in non-conducting pipes of arbitrary cross-section under uniform transverse magnetic fields. A satisfactory comparison with the author's previously experimental pressure gradient/flow results is made for the case of a circular pipe.

Unsteady Laminar Duct Flow With a Given Volume Flow Rate Variation

1999 ◽  
Vol 67 (2) ◽  
pp. 274-281 ◽  
Author(s):  
D. Das ◽  
J. H. Arakeri
Keyword(s):  
Cross Section ◽  
Flow Rate ◽  
Volume Flow Rate ◽  
Circular Cross Section ◽  
Volume Flow ◽  
Rate Variation ◽  
Two Dimensional ◽  
Duct Flow ◽  
Fully Developed Flow ◽  
Gradient Variation

In this paper we give a procedure to obtain analytical solutions for unsteady laminar flow in an infinitely long pipe with circular cross section, and in an infinitely long two-dimensional channel, created by an arbitrary but given volume flow rate with time. In the literature, solutions have been reported when the pressure gradient variation with time is prescribed but not when the volume flow rate variation is. We present some examples: (a) the flow rate has a trapezoidal variation with time, (b) impulsively started flow, (c) fully developed flow in a pipe is impulsively blocked, and (d) starting from rest the volume flow rate oscillates sinusoidally. [S0021-8936(00)01702-5]

Torsion of Composite Elastic Bars of Arbitrary Cross Section

1968 ◽  
Vol 90 (3) ◽  
pp. 435-440 ◽  
Author(s):  
E. M. Sparrow ◽  
H. S. Yu
Keyword(s):  
Exact Solution ◽  
Closed Form ◽  
Elastic Properties ◽  
Cross Section ◽  
Excellent Agreement ◽  
Solution Method ◽  
Circular Cross Section ◽  
High Accuracy ◽  
Arbitrary Cross Section ◽  
Closed Form Solutions

A method of analysis is presented for determining closed-form solutions for torsion of inhomogeneous prismatic bars of arbitrary cross section, the inhomogeneity stemming from the layering of materials of different elastic properties. It is demonstrated that the solution method is very easy to apply and provides results of high accuracy. As an application, solutions are obtained for the torsion of a bar of circular cross section consisting of two materials separated by a plane interface. The results are compared with those of various limiting cases and excellent agreement is found to exist. Among the limiting cases, an exact solution was derived by Green’s functions for the problem in which the interface between the materials coincides with a diameter of the circular cross section.

Herschel-Bulkley Viscoplastic Flow in Tubes of Non-Circular Cross-Section

2016 ◽  
Author(s):  
Mario F. Letelier ◽  
Dennis A. Siginer ◽  
Felipe Godoy ◽  
César Rosas
Keyword(s):  
Cross Section ◽  
Power Index ◽  
Circular Cross Section ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Equation Of Motion ◽  
Arbitrary Cross Section ◽  
Viscoplastic Flow ◽  
The Cross ◽  
Tube Geometry

Flow of a Herschel-Bulkley (H-B) fluid in tubes of non-circular cross-section in investigated analytically. This study complements results presented in [1] where the equation of motion was solved in tubes of arbitrary cross-section for Bingham type of fluids, and the shapes of plug zones centered on the tube axis and stagnant zones attached to the corners were predicted when the cross-section is triangular and square. In this paper we investigate the effect of the power index in the H-B model on the flow for values greater and lesser than unity, considering thus the shear-thinning and shear-thickening effects, which could not be accounted for with the Bingham model. The equation of motion is solved when the cross-section is an equilateral triangle or a square by means of the shape factor method previously introduced in [2]. Thus, shear-thickening and shear-thinning effects are accounted for and related to the tube geometry in predicting the existence and the extent of undeformed regions in the flow field.

Heat-Transfer Analysis of Visco-Elastic Giesekus Fluid in a Duct Between Parallel Plates and in a Straight Pipe of a Circular Cross-Section

2015 ◽  
Author(s):  
Sara N. AlMelhi ◽  
Lyes Khezzar ◽  
Mohamed Alshehhi ◽  
Abdelkader Filali
Keyword(s):  
Heat Transfer ◽  
Cross Section ◽  
Numerical Solutions ◽  
Numerical Technique ◽  
Circular Cross Section ◽  
Heat Transfer Analysis ◽  
Rheological Parameters ◽  
Parallel Plates ◽  
Straight Pipe ◽  
Finite Element Software

This work aims to conduct numerical simulation to investigate the convective heat transfer of viscoelastic fluids obeying Giesekus model flowing either along straight pipe of circular cross-section or within the space between parallel plates with constant heat flux thermal boundary condition and neglected viscous dissipation. The numerical technique used is based on finite element software (ANSYS Polyflow 14.0) and the obtained numerical solutions are compared against the analytical solution available in literature. The effect of the rheological parameters on the heat transfer enhancement is discussed.

Oscillating Flow in Ducts of Arbitrary Cross Section

1969 ◽  
Vol 73 (706) ◽  
pp. 894-896
Author(s):  
A. M. Abu-Sitta ◽  
D. G. Drake
Keyword(s):  
Boundary Layer ◽  
Viscous Fluid ◽  
Pressure Gradient ◽  
Numerical Solution ◽  
Cross Section ◽  
Circular Cross Section ◽  
Arbitrary Cross Section ◽  
Oscillating Flow ◽  
Elliptic Case ◽  
Uniform Cross Section

The rectilinear flow of an incompressible viscous fluid along a duct of uniform cross section due to an oscillating pressure gradient has been considered by a number of investigators. The duct of circular cross .section has been treated by Richardson and Tyler and Sexl, the elliptic case by Khamrui, and the rectangular case by Drake and Fan and Chao. Recently Jeng has discussed the importance of this type of flow and has given a procedure for calculating a numerical solution for a duct of arbitrary cross-section. An interesting feature of these flows is that, at large frequencies when the flow is of boundary-layer type, the velocity at any instant has its maximum near the walls, the velocity overshooting its almost uniform distribution at the centre of the duct.

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