Analytical approach for solving two-dimensional laminar viscous flow between slowly expanding and contracting walls

Rahimi, E.; Rahimifar, A.; Mohammadyari, Reza; Rahimipetroudi, Iman; Rahimi-Esbo, M.

doi:10.1016/j.asej.2015.07.013

Cited by 10 publications

(7 citation statements)

References 16 publications

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“…The first attempt to study viscous flow inside a permeable pipe of contracting cross area was made by Uchida and Aoki (1977) and the problems associated with it were illuminated by Bujurke et al (1998), both numerically and analytically. Goto and Uchida (1990) presented a theoretical framework of unsteady incompressible laminar flows in a pipe where suction or injection took place at the walls of the pipe, with the radius of the pipe being variant with respect to time and many researchers subsequently investigated the fluid flow behavior between expanding or contracting walls analytically as well as numerically under various fluid flow conditions (Majdalani and Zhou, 2003;Si et al, 2010;Jafaryar et al, 2014;Rahimi et al, 2015). On the other hand, the most promising implications of nanofluids is the enhancement of heat transfer in modern engineering systems (Shi et al, 2011;Bég et al, 2013;Kleinstreuer et al, 2008).…”

Section: Introductionmentioning

confidence: 99%

Physicochemical and rheological properties of titania and carbon nanotubes in a channel with changing walls

Raza

Rohni

Omar

et al. 2016

MMMS

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Purpose The purpose of this paper is to investigate some multiple solutions for carbon nanotubes (CNTs) in a porous channel with changing walls. Moreover, the intention of the study is to examine the physicochemical and rheological properties of titania and CNTs. Design/methodology/approach The mathematical modeling is performed for the laws of conservation of mass, momentum and energy profiles. Governing partial differential equations are transformed into ordinary differential equations by applying suitable similarity transformation and then solved numerically with the help of shooting technique. Findings The effects of different physical parameters on the rheology of nanofluids are discussed graphically and numerically, in order to make the analysis more interesting. The present study revealed that multiple solutions of nanofluids in a channel with changing walls are obtained only for the case of suction. Originality/value Some new branches of the solution for nanofluids in a channel with changing walls are obtained in this research, which has never been reported before. Combined effects of physicochemical and rheology of titania and carbon nanotubes are investigated briefly. The effects of physical parameters on velocity and temperature profile are examined in detail which is more realistic than real-world problem.

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Section: Introductionmentioning

confidence: 99%

Physicochemical and rheological properties of titania and carbon nanotubes in a channel with changing walls

Raza

Rohni

Omar

et al. 2016

MMMS

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“…Subject to the boundary conditions Here = is the cross flow Reynolds number and > 0 is for suction and < 0 for injection through the walls [8], [27] and [28].…”

Section: Problem Formulationmentioning

confidence: 99%

“…In addition, Majdalani et al [5], Dauenhauer and Majdalani [6], Majdalani and Zhou [7] investigated the problem of laminar flow in a channel with porous expanding walls numerically as well as asymptotically. Later, analytical solutions were obtained by Rahimi et al [8] for the case of expanding and contracting porous channel walls. Reddy et al [9] were used perturbation technique to analysis the effects of heat and mass transfer on the asymmetric flow in a porous channel with http://www.ispacs.com/journals/cna/2017/cna-00291/ International Scientific Publications and Consulting Services expanding or contracting walls.…”

Section: Introductionmentioning

confidence: 99%

Unsteady Flow of a Casson Fluid between Two Orthogonally Moving Porous Disks: A Numerical Investigation

Raza¹,

Rohni²,

Omar³

2017

Communications in Numerical Analysis

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The purpose of the present paper is to study the unsteady two dimensional laminar incompressible flow of non-Newtonian fluid between two orthogonally moving porous disks using the Casson fluid model that is used to characterize the non-Newtonian fluid behavior. Governing partial differential equations are reduced into nonlinear ordinary differential equations by using suitable similarity transformation and then solved numerically by Runge-Kutta-Fehlberg technique. The numerical results are found excellent agreement with the literature published before. Trusting to this validity, effects of different physical parameters are discussed. The study reveals that velocity of the fluid particles increases with an increase in the disk expanding ratio.

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“…Here R " av w υ is the cross flow Reynolds number and R ą 0 is for injection and R ă 0 for suction through the walls [8,28,29].…”

Section: Problem Formulationmentioning

confidence: 99%

“…In addition, Majdalani et al [5], Dauenhauer and Majdalani [6], Majdalani and Zhou [7] investigated the problem of laminar flow in a channel with porous expanding walls numerically as well as asymptotically. Later, analytical solutions were obtained by Rahimi et al [8] for the case of expanding and contracting porous channel walls. Reddy et al [9] used perturbation techniques to analyze the effects of heat and mass transfer on the asymmetric flow in a porous channel with expanding or contracting walls.…”

Section: Introductionmentioning

confidence: 99%

A Note on Some Solutions of Copper-Water (Cu-Water) Nanofluids in a Channel with Slowly Expanding or Contracting Walls with Heat Transfer

Raza¹,

Rohni²,

Omar³

2016

MCA

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Abstract:A study has been carried out to examine the occurrence of multiple solutions for Copper-Water nanofluids flows in a porous channel with slowly expanding and contracting walls. The governing equations are first transformed to similarity equations by using similarity transformation. The resulting equations are then solved numerically by using the shooting method. The effects of wall expansion ratio and solid volume fraction on velocity and temperature profile have been studied. Numerical results are presented graphically for the variations of different physical parameters. The study reveals that triple solutions exist only for the case of suction.

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Analytical approach for solving two-dimensional laminar viscous flow between slowly expanding and contracting walls

Cited by 10 publications

References 16 publications

Physicochemical and rheological properties of titania and carbon nanotubes in a channel with changing walls

Physicochemical and rheological properties of titania and carbon nanotubes in a channel with changing walls

Unsteady Flow of a Casson Fluid between Two Orthogonally Moving Porous Disks: A Numerical Investigation

A Note on Some Solutions of Copper-Water (Cu-Water) Nanofluids in a Channel with Slowly Expanding or Contracting Walls with Heat Transfer

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