Magnetohydrodynamic Flow through Ducts of Variable Cross Section

Buoyancy driven, adiabatic and compressible flow in relatively high solar chimneys is treated in the paper analytically by using one-dimensional model of flow. General equations written suitably in a non-dimensional form are used for a qualitative discussion pertaining to the mutual effects of gravity, viscosity and varying cross section of the chimney. It is shown that in case of low Mach number flow these equations possess exact solutions obtainable by ordinary mathematical methods for any given chimney shape. Also shown, and demonstrated on an example, is the procedure of evaluation of the chimney shape that satisfies a condition imposed beforehand upon the flow. For better insight into the role of various parameters the solutions are presented in the form of power series expansions.

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Effective Flow of Micropolar Fluid through a Thin or Long Pipe

Mathematical Problems in Engineering ◽

10.1155/2011/127070 ◽

2011 ◽

Vol 2011 ◽

pp. 1-18 ◽

Cited By ~ 9

Author(s):

Igor Pažanin

Keyword(s):

Cross Section ◽

Asymptotic Approximation ◽

Micropolar Fluid ◽

Variable Cross Section ◽

Asymptotic Model ◽

Variable Cross ◽

Straight Pipe ◽

Micropolar Fluid Flow ◽

Flow Through ◽

Explicit Formulae

The aim of this paper is to present the result about asymptotic approximation of the micropolar fluid flow through a thin (or long) straight pipe with variable cross section. We assume that the flow is governed by the prescribed pressure drop between pipe's ends. Such model has relevance to some important industrial and engineering applications. The asymptotic behavior of the flow is investigated via rigorous asymptotic analysis with respect to the small parameter, being the ratio between pipe's thickness and its length. In the case of circular pipe, we obtain the explicit formulae for the approximation showing explicitly the effects of microstructure on the flow. We prove the corresponding error estimate justifying the obtained asymptotic model.

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Mathematical Model Of Liquid Flow Through The Pipe Of Curcular Cross-Section

Siberian Journal of Physics ◽

10.54362/1818-7919-2016-11-4-61-67 ◽

2016 ◽

Vol 11 (4) ◽

pp. 61-67

Author(s):

Eduard Arinstein ◽

Denis Tokarev

Keyword(s):

Cross Section ◽

Cross Sections ◽

Liquid Flow ◽

Analytical Approach ◽

Variable Cross Section ◽

Cylindrical Symmetry ◽

Variable Cross ◽

Current Line ◽

Flow Velocity Profile ◽

Flow Through

This article analyses the properties of homogeneous viscous liquid flow in the pipe with variable cross-section characterized by cylindrical symmetry. The analytical approach is proposed in order to determine the flow velocity profile in the pipe’s extremium cross-sections. The conditions when dead spaces emerge in neighborhood of the maximum cross-section are identified. The particular case of problem-solving allowing prime presentation is examined for the set of current line allowing prime presentation.

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