Unsteady Reversed Stagnation-Point Flow over a Flat Plate

This paper investigates the nature of the development of two-dimensional laminar flow of an incompressible fluid at the reversed stagnation-point. ". In this study, we revisit the problem of reversed stagnation-point flow over a flat plate. Proudman and Johnson (1962) first studied the flow and obtained an asymptotic solution by neglecting the viscous terms. This is no true in neglecting the viscous terms within the total flow field. In particular it is pointed out that for a plate impulsively accelerated from rest to a constant velocity V0 that a similarity solution to the self-similar ODE is obtained which is noteworthy completely analytical.




References:
[1] K. Hiemenz, "Die Grenzschicht an einem in den gleichf¨ormigen
Fl¨ussigkeitsstrom eingetauchten geraden Kreiszylinder, Dingl. Polytech,"
J, vol. 326, pp. 321-410, 1911.
[2] L. Howarth, "CXLIV. The boundary layer in three dimensional flow.-Part
II. The flow near a stagnation point," Philosophical Magazine (Series
7), vol. 42, no. 335, pp. 1433-1440, 1951.
[3] A. Davey, "Boundary-layer flow at a saddle point of attachment," Journal
of Fluid Mechanics, vol. 10, pp. 593-610, 1961.
[4] I. Proudman and K. Johnson, "Boundary-layer growth near a rear
stagnation point," Journal of Fluid Mechanics, vol. 12, no. 02, pp. 161-
168, 1962.
[5] A. Robins and J. Howarth, "Boundary-layer development at a twodimensional
rear stagnation point," Journal of Fluid Mechanics, vol. 56,
no. 01, pp. 161-171, 1972.
[6] S. Smith, "The development of the boundary layer at a rear stagnation
point," Journal of Engineering Mathematics, vol. 11, no. 2, pp. 139-144,
1977.
[7] V. K. Sin and C. K. Chio, Computation of Non-Isothermal Reversed
Stagnation-Point Flow over a Flat Plate, ch. Computational Simulations
and Applications, pp. 159-174. InTech, 2011. ISBN: 978-953-307-430-
6.
[8] F. White, "Fluid Mechanics. 5th edt," 2003.
[9] A. Shapiro, "An analytical solution of the navier-stokes equations for
unsteady backward stagnation-point flow with injection or suction,"
ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift f¨ur
Angewandte Mathematik und Mechanik, vol. 86, no. 4, pp. 281-290,
2006.
[10] D. Zwillinger, Handbook of differential equations. Academic Press,
1998.
[11] L. Shampine, I. Gladwell, and S. Thompson, Solving ODEs with
MATLAB. Cambridge Univ Pr, 2003.