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A Similarity Solution of Rear Stagnation-point Flow over a Flat Plate in Two Dimensions

Chon Kit Chio

Abstract

This paper investigates the nature of the development of vortex shedding for two-dimensional unsteady flow of an incompressible fluid at the rear stagnation point.

A Similarity Solution of Rear Stagnation-point Flow over a Flat Plate in Two Dimensions

Abstract

This paper investigates the nature of the development of vortex shedding for two-dimensional unsteady flow of an incompressible fluid at the rear stagnation point.

Paper Structure

This paper contains 10 sections, 3 theorems, 36 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Flow Analysis Model
  3. Insolubility when $\kappa=0$
  4. Similarity Analysis
  5. Case of $\kappa=\frac{2}{3}$
  6. Case of $\kappa=-2$
  7. Numerical Solution
  8. Flow Patterns across a Cylinder
  9. Explicit Relation between Strouhal Number and $\kappa$
  10. Conclusion

Key Result

Lemma 1

No solution $f'(\eta)$ exists which has stationary value of 1 for finite $\eta$ when $\kappa=0$.

Figures (10)

  • Figure 1: Streamlines of rear stagnation-point flow
  • Figure 2: Numerical solution as $\kappa=-5$
  • Figure 3: Numerical solution as $\kappa=-3$
  • Figure 4: Numerical solution as $\kappa=-2$
  • Figure 5: Numerical solution as $\kappa=-1.8$
  • ...and 5 more figures

Theorems & Definitions (3)

  • Lemma 1
  • Lemma 2
  • Theorem 1