Analytical approximate solutions for two-dimensional viscous flow through expanding or contracting gaps with permeable walls

Dinarvand, Saeed; Rashidi, Majid; Doosthoseini, Ahmad

doi:10.2478/s11534-009-0024-x

Cited by 17 publications

(13 citation statements)

References 27 publications

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“…More recently Asghar et al [15] discussed the flow in a slowly deforming channel with weak permeability using Adomian decomposition method (AMD). Dinarvand et al [16,17] obtained analytical approximate solutions for two-dimensional viscous flow through expanding or contracting gaps with permeable walls. Si et al [18] obtained the analysis solutions for the asymmetric laminar flow in a porous channel with expanding or contracting walls using HAM.…”

Section: Introductionmentioning

confidence: 99%

The flow of a micropolar fluid through a porous channel with expanding or contracting walls

Zheng

Zhang

et al. 2011

Open Physics

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Abstract:The flow of a micropolar fluid in a porous channel with expanding or contracting walls is investigated. The governing equations are reduced to ordinary ones by using similar transformations. Homotopy analysis method (HAM) is employed to obtain the expressions for the velocity fields and microrotation fields. Graphs are sketched for the effects of some values of parameters, especially the expansion ratio, on the velocity and microrotation fields and associated dynamic characteristics are analyzed in detail. PACS

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Section: Introductionmentioning

confidence: 99%

The flow of a micropolar fluid through a porous channel with expanding or contracting walls

Zheng

Zhang

et al. 2011

Open Physics

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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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“…For example, the transport of biological fluids through expanding or contracting vessels, the synchronous pulsation of porous diaphragms, the modeling of air and blood circulation in the respiratory system, binary gas diffusion, filtration, ablation cooling, surface sublimation and the regression of the burning surface in solid rocket motors. Many investigations in this direction have been carried out by several researchers (Uchida and Aoki 1977;Dauenhauer and Majdalani 1999;Majdalani et al 2002;Majdalani and Zhou 2003;Boutros et al 2007;Dinarvand et al 2009;Si et al 2011a;Fakour et al 2015). Si et al (2011b) studied analytically the asymmetric laminar flow of micropolar fluid through porous channel with an expanding or contracting wall using homotopy analysis method (HAM).…”

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confidence: 99%

Asymmetric Flow of a Nanofluid Between Expanding or Contracting Permeable Walls With Thermal Radiation

Vijayalakshmi¹,

Srinivas²

2016

Frontiers in Heat and Mass Transfer

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In the present study, the flow and heat transfer characteristics of a nanofluid in an expanding or contracting porous channel with different permeabilities in presence of thermal radiation are investigated. Analytical solutions for the flow variables are obtained by employing homotopy analysis method (HAM). Maxwell-Garnetts and Brinkman models are considered to calculate the thermal conductivity and the viscosity of nanofluid. In this investigation, we considered water and ethylene glycol as base fluids and silver ( Ag ), copper ( Cu ), titanium dioxide ( 2 TiO ) and alumina ( 23Al O ) as nanoparticles. The effects of various emerging parameters on axial velocity, temperature, shear stress and Nusselt number distributions have been discussed. The results of present study are compared with the numerical solutions obtained by shooting technique along with Runge-Kutta fourth order scheme. We found that there is a good agreement between the analytical and the numerical solutions.

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Analytical approximate solutions for two-dimensional viscous flow through expanding or contracting gaps with permeable walls

Cited by 17 publications

References 27 publications

The flow of a micropolar fluid through a porous channel with expanding or contracting walls

The flow of a micropolar fluid through a porous channel with expanding or contracting walls

Viscous Mean Flow Approximations for Porous Tubes with Radially Regressing Walls

Asymmetric Flow of a Nanofluid Between Expanding or Contracting Permeable Walls With Thermal Radiation

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