On Dual Solutions of Stagnation Point Flow of a Viscoelastic Fluid

Abstract

Es wird die laminare zweidimensionale Strömung eines inkompressiblen viskoelastischen Fluids in der Nähe eines Staupunktes betrachtet. Eine Näherungslösung, die die orthogonale Kollokationspunktmethode mit Laguerreschen Polynomen benutzt, wird entwickelt. Sie unterstreicht die Nichtexistenz von Lösungen über den kritischen Wert des viskoelastischen Fluidparameters hinaus und die Existenz dualer Lösungen für den Parameterwert kleiner als dieser kritische Wert. Eine lineare Stabilitätsbetrachtung der zwei Lösungen wird vorgestellt. Die Lösung, die zum kleineren Wert der Schubspannungen gehört, ergibt sich als stabile Lösung, während die andere Lösung sich als instabil erweist.

Dual solutions of magnetohydrodynamic boundary layer flow and a linear temporal stability analysis

“…Ariel and Teipel 25 obtained the smallest eigenvalue with the help of the finite difference method and a root finding algorithm in their article. We, therefore, use their method in this present study to determine the smallest eigenvalue γ 1 .…”

“…We, therefore, use their method in this present study to determine the smallest eigenvalue γ 1 . Following them, 25 we take (28) again, then (25) thus be replaced by the following system …”

“…24 studied boundary layer flow over an exponentially shrinking sheet and tested the stability of the obtained dual solution branches. Ariel and Teipel 25 used the FDM technique in their flow model to determine the smallest eigenvalue for the stability of the multiple solutions that are tested by the sign of the smallest eigenvalue.…”

“…We have also tested the stability of these dual solutions by adopting the technique of Merkin. 19 Then we follow the numerical scheme of Ariel and Teipel 25 to obtain the smallest eigenvalue. On the other hand, we have also carried out the shooting method with fourth order Runge-Kutta method to validate our numerical computations, which shows an excellent agreement up to the desired accuracy.…”

Effect of heat generation on free convection boundary layer flow of a viscoelastic fluid past a horizontal circular cylinder with constant surface heat flux

“…Ariel et. al [6] investigated the laminar two-dimensional viscoelastic flow near a stagnation point using the orthogonal collocation point method with Laguerre polynomials. A large number of physical phenomena also involve natural convection that is driven by heat generation.…”