Lie-group method for unsteady flows in a semi-infinite expanding or contracting pipe with injection or suction through a porous wall

Boutros, Y. Z.; Abd‐el‐Malek, Mina B.; Badran, Nagwa A.; Hassan, Hossam S.

doi:10.1016/j.cam.2005.11.031

Cited by 48 publications

(44 citation statements)

References 8 publications

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“…In the interim, Dauenhauer and Majdalani [56][57][58] formulated the corresponding equation and numerical solution for the planar flow analog. The analytical solutions promoted through these efforts would later receive attention in follow-up studies aimed at devising asymptotic approximations over various ranges of the control parameters or at reconstructing the solution using alternative techniques such as the Lie-group theory [59,60] or the HomotopyAnalysis Method [61][62][63].…”

Section: Doi: 102514/1j055949mentioning

confidence: 99%

Viscous Mean Flow Approximations for Porous Tubes with Radially Regressing Walls

Saad

Majdalani

2017

AIAA Journal

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The mean gaseous motion in solid rocket motors has been traditionally described using an inviscid solution in a porous tube of fixed radius and uniform wall injection. This model, usually referred to as the Taylor-Culick profile, consists of a rotational solution that captures the bulk gaseous motion in a frictionless rocket chamber. In practice, however, the port radius increases as the propellant burns, thus leading to time-dependent effects on the mean flow. This work considers the related problem in the context of viscous motion in a porous tube and allows the radius to be time dependent. By implementing a similarity transformation in space and time, the incompressible Navier-Stokes equations are first reduced to a nonlinear fourth-order ordinary differential equation with four boundary conditions. This equation is then solved both numerically and asymptotically, using the injection Reynolds number Re and the dimensionless wall regression ratio α as primary and secondary perturbation parameters. In this manner, closedform analytical solutions are obtained for both large and small Reynolds number with small-to-moderate α. The resulting approximations are then compared with the numerical solution obtained for an equivalent third-order ordinary differential equation in which both shooting and the irregular limit that affects the fourth-order formulation are circumvented. This code is found to be capable of producing the stable solutions for this problem over a wide range of Reynolds numbers and wall regression ratios.

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Section: Doi: 102514/1j055949mentioning

confidence: 99%

Viscous Mean Flow Approximations for Porous Tubes with Radially Regressing Walls

Saad

Majdalani

2017

AIAA Journal

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“…Similar to Dauenhauer and Majdalani [11], Uchida and Aoki [20], and Boutros et al [13,14], we substitute Eqs. (6) and (7) into governing equations and consider the similarity solutions with respect to space and time, then the following ordinary equations can be obtained:…”

Section: Preliminariesmentioning

confidence: 99%

“…Furthermore, Majdalani, Zhou and Dawson [12] also obtained an asymptotic solution for the flow in a porous channel, with slowly expanding or contracting walls, by considering the permeation Reynolds number and expansion ratio as two small parameters. Boutros et al [13,14] also discussed the flow through an expanding porous channel or pipe using the Lie group method and obtained the analytical solution with the perturbation method. Recently Si et al [15] also investigated the micropolar fluid in a porous deforming channel and discussed the effects of the micropolar parameter and the expansion ratio on the velocity and microrotation distribution.…”

Section: Introductionmentioning

confidence: 99%

Perturbation solutions for a micropolar fluid flow in a semi-infinite expanding or contracting pipe with large injection or suction through porous wall

Yuan

Cao

et al. 2016

Open Physics

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Abstract:We investigate an unsteady incompressible laminar micropolar flow in a semi-infinite porous pipe with large injection or suction through a deforming pipe wall. Using suitable similarity transformations, the governing partial differential are transformed into a coupled nonlinear singular boundary value problem. For large injection, the asymptotic solutions are constructed using the Lighthill method, which eliminates singularity of solution in the high order derivative. For large suction, a series expansion matching method is used. Analytical solutions are validated against the numerical solutions obtained by Bvp4c.

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“…This technique has been applied by many researchers to solve some partial differential problems [25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

The analysis of the suction/injection on the MHD Maxwell fluid past a stretching plate in the presence of nanoparticles by Lie group method

Cao

Zheng

et al. 2015

Open Physics

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Abstract:In this paper, the magnetohydrodynamic (MHD) Maxwell fluid past a stretching plate with suction/injection in the presence of nanoparticles is investigated. The Lie symmetry group transformations are used to convert the boundary layer equations into non-linear ordinary differential equations. The dimensionless governing equations are solved numerically using Bvp4c with MATLAB, which is a collocation method equivalent to the fourth order mono-implicit Runge-Kutta method. The effects of some physical parameters, such as the elastic parameter K, the Hartmann number M, the Prandtl number Pr, the Brownian motion Nb, the thermophoresis parameter Nt and the Lewis number Le, on the velocity, temperature and nanoparticle fraction are studied numerically especially when suction and injection at the sheet are considered.

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Lie-group method for unsteady flows in a semi-infinite expanding or contracting pipe with injection or suction through a porous wall

Cited by 48 publications

References 8 publications

Viscous Mean Flow Approximations for Porous Tubes with Radially Regressing Walls

Viscous Mean Flow Approximations for Porous Tubes with Radially Regressing Walls

Perturbation solutions for a micropolar fluid flow in a semi-infinite expanding or contracting pipe with large injection or suction through porous wall

The analysis of the suction/injection on the MHD Maxwell fluid past a stretching plate in the presence of nanoparticles by Lie group method

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