Title

Hydromagnetic Stagnation Point Flow Of A Viscous Fluid Over A Stretching Or Shrinking Sheet

Keywords

Analytical solution; Existence theorem; Shrinking sheet; Similarity solution; Stagnation point flow; Stretching sheet; Uniqueness theorem

Abstract

We establish the existence and uniqueness results over the semi-infinite interval [0,∞) for a class of nonlinear third order ordinary differential equations of the form f‴(η) + f(η)f″(η) - ( f(η)) Mf(η) + C(C + M ) = 0, f(0) = s, f(0) = χ, lim η → ∞ f'(η) = C. Such nonlinear differential equations arise in the stagnation point flow of a hydromagnetic fluid. In particular, we establish the existence and uniqueness results, and properties of physically meaningful solutions for all values of the physical parameters M, s, χ and C. Furthermore, a method of obtaining analytical solutions for this general class of differential equations is outlined. From such a general method, we are able to obtain an analytical expression for the shear stress at the wall in terms of the physical parameters of the model. Numerical solutions are then obtained (by using a boundary value problem solver) and are validated by the analytical solutions. Also the numerical results are used to illustrate the properties of the velocity field and the shear stress at the wall. Some exact solutions are also obtained in certain special cases. © 2010 Springer Science+Business Media B.V.

Publication Date

1-1-2012

Publication Title

Meccanica

Volume

47

Issue

1

Number of Pages

31-50

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s11012-010-9402-0

Socpus ID

84855678653 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84855678653

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