School of Science, Penn State Behrend
Erie, PA 16563-0203, USA
email: jep7@psu.edu
Joseph E. Paullet
Abstract:
Several recent papers have investigated the two-dimensional
stagnation point flow of an upper-convected Maxwell fluid by
employing a similarity change of variable
to reduce the governing PDEs to a nonlinear third order ODE boundary
value problem (BVP). In these previous works, the
BVP was studied numerically and several conjectures regarding the
existence and behavior of the solutions were made.
The purpose of this article is to mathematically verify these conjectures.
We prove the existence of a solution to the BVP for all relevant
values of the elasticity parameter.
We also prove that this solution has monotonically increasing
first derivative, thus verifying the conjecture that no
``overshoot'' of the boundary condition occurs. Uniqueness
results are presented for a large range of parameter space and bounds on the
skin friction coefficient are calculated.
Submitted August 24, 2017. Published December 6, 2017.
Math Subject Classifications: 35B15, 76D10, 76A05.
Key Words: Stagnation point; boundary value problem;
upper-convected Maxwell model.
Show me the PDF file (239 KB), TEX file for this article.
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Joseph E. Paullet School of Science, Penn State Behrend Erie, PA 16563-0203, USA email: jep7@psu.edu |
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