Further Investigation of Laminar Flow in Channels with Porous Walls

Yuan, Shandong

doi:10.1063/1.1722355

Cited by 214 publications

(116 citation statements)

References 2 publications

Supporting

Mentioning

110

Contrasting

Unclassified

Order By: Relevance

“…As observed (17), it becomes unbounded as ς → 0 due to the secular term cos ς ln tan 1 2 ς. Besides this, when α = 0, the series solution, given by Yuan [39], also exhibits the similar feature (i.e. the third derivative of the series solution tends to infinite at the center of the channel).…”

Section: Solution For Large Injection Reynolds Numbersmentioning

confidence: 68%

Asymptotic solutions for laminar flow based on blood circulation through a uniformlyporous channel with retractable walls and an applied transverse magnetic field

Lin

Zhang

et al. 2017

Powder Technology

View full text Add to dashboard Cite

X. (2017). Asymptotic solutions for laminar flow based on blood circulation through a uniformlyporous channel with retractable walls and an applied transverse magnetic field. Powder Technology, 308, 398-409. DOI: 10.1016/j.powtec.2016 General rights Copyright and moral rights for the publications made accessible in Discovery Research Portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from Discovery Research Portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain.• You may freely distribute the URL identifying the publication in the public portal. Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. AbstractThis paper is concerned with asymptotic solutions of a nonlinear boundary value problem (BVP), which arises in a study of laminar flow in a uniformly porous channel with retractable walls and an applied transverse magnetic field. For different ranges of the control parameters (i.e. α, Re and M ) arising in the BVP, four cases are considered using different singular perturbation methods. For the first case, unlike those in the existing literature, we make use of the Lighthill method and successfully construct an asymptotic solution with high-order derivatives at the center of the channel. For the second case, under large suction we consider M 2 = O(1) and M 2 = O(Re), respectively, which will further extend the applying range of asymptotic solutions. In other cases, asymptotic solutions with a boundary layer are successfully constructed. In addition, numerical solutions presented for each case agree well with asymptotic solutions, which illustrates that the asymptotic solutions constructed in this paper are more reliable. Finally, the influences of some parameters on flow field are discussed to develop a better understanding of the flow problem.

show abstract

Section: Solution For Large Injection Reynolds Numbersmentioning

confidence: 68%

Asymptotic solutions for laminar flow based on blood circulation through a uniformlyporous channel with retractable walls and an applied transverse magnetic field

Lin

Zhang

et al. 2017

Powder Technology

View full text Add to dashboard Cite

show abstract

“…Here it should be noted that direct use of the method of variation of parameters will cause a singularity in the third-order derivative of f 1 [17][18][19]. In order to eliminate the singularity and to simplify the equation of f 1 , we can set…”

Section: B the Transformed Boundary Conditions At The Center Of The mentioning

confidence: 99%

“…For large injection, analytical solutions are constructed using the Lighthill method, which eliminates singularity of the solution in the high order derivative [17][18][19];a series expansion matching method is used for large suction. The accuracy of the analytical solutions for each case is compared with its numerical results.…”

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

View full text Add to dashboard Cite

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.

show abstract

“…This could be attributed to its wall-normal injection that disallowed any axial velocity contribution along the porous boundary. Returning to the viscous flow problem in a porous channel, Yuan (1956) may have been the first to develop a solution for moderate to large Reynolds numbers and either suction or injection. His solution asymptotically reproduced Taylor's in the limit of a large injection Reynolds number.…”

Section: Internal Flows Driven By Wall-normal Injectionmentioning

confidence: 99%