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

Abstract

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.

A numerical study for multiple solutions of a singular boundary value problem arising from laminar flow in a porous pipe with moving wall

“…(1) for the large injection Reynolds number can be obtained by the Lighthill method. As indicated in [38], this is the available method which can construct a sufficiently smooth asymptotic solution for all η ∈ [0, 1]. Eq.…”

Asymptotic solutions for the asymmetric flow in a channel with porous retractable walls under a transverse magnetic field

“…Terrill and Shrestha [21,22,23] and made further extension of Suryaprakasrao's work, and obtained the asymptotic solutions for large suction and injection Reynolds numbers and all values of the Hartamnn number. Based on these works, investigators began to take account of the wall motion [24].…”