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On the flow of an unsteady, compressible boundary layer over an accelerating semi-infinite flat plate

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Zusammenfassung

Es wird die Grenzschicht untersucht, die sich in laminarer, kompressibler Strömung an einer ebenen Platte unter der Annahme einstellt, dass sich diese nach einer Seite ins Unendliche ausdehnt und von der Ruhe aus gleichförmig beschleunigt wird. Die Temperatur der Platte wird in vorgeschriebener Weise mit der Zeit und der Entfernung von der Vorderkante der Platte geändert, und der Effekt dieser Änderungen kurz nach dem Beginn der Bewegung wird für Punkte berechnet, die weit vom Plattenrand entfernt sind.

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Abbreviations

A :

acceleration, ft/sec2

a 1 :

20.00×10−5 ft2/sec

a 2 :

27.51×10−5 ft2/sec

b 1 :

1.07×10−11 ft-slugs/sec-lbs

b 2 :

1.30×10−11 ft-slugs/sec-lbs

g nm (z) :

defined by equation (6)

h :

specific enthalpy, ft-lbs/slug

h w :

specific enthalpy at the plate surface

h ∞ :

specific enthalpy in the free stream

j nm(z) :

defined by equation (7)

Pr :

Prandtl number

q :

heat transfer rate at the wall, ft-lbs/ft2-sec

t :

time, seconds

U :

free stream velocity relative to plate, ft/sec

u :

velocity component parallel to plate, relative to plate, ft/sec

x :

distance along the plate, measured from the leading edge, feet

y :

distance perpendicular to plate, measured from surface of plate, feet

z :

\(\eta /\sqrt {v_0 t}\)

ψ η :

u

η:

\(\int\limits_2^y {(\varrho /\varrho _0 )dy}\)

ξ:

x/A t 2

v o :

1.66×10−4 ft2/sec

ϱ:

density, slugs/ft3

ϱ 0 :

00229 slugs/ft3

μ:

viscosity, slugs/sec-ft

ω:

at the plate surface

x :

differentiation with respect tox

t :

differentiation with respect tot

η:

differentiation with respect to η

′:

differentiation with respect toz

References

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  3. N. A. Evans,Heat Transfer in the Unsteady Compressible Boundary Layer on a Flat Plate, Proc. 1960 Heat Transfer and Fluid Mechanics Institute (Stanford University, Stanford, California), pp. 77–87.

  4. S. Schreier,On the Flow of an Unsteady Compressible Boundary Layer Over a Semi-Infinite Flat Plate Whose Temperature Exceeds the Free Stream Temperature, Z. angew. Math. Phys.17, 541–544 (1966).

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  5. S. Schreier,On the Flow of an Unsteady, Compressible Boundary Layer Over a Semi-Infinite Flat Plate Whose Temperature is Varied with Time, Z. angew. Math. Phys.19, 516–519 (1968).

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  9. C. R. Illingworth,Unsteady Laminar Flow of a Gas Near an Infinite Flat Plate, Proc. Cambridge Phil. Soc.46, 603–613 (1950).

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  10. S. Schreier,On the Flow of Non-Steady Compressible Boundary Layers with Variable Transport Properties, Ph. D. Thesis (University of Maryland, 1967).

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Authors and Affiliations

  1. Dept. of Mechanical Engineering, The University of Connecticut, Storrs, Connecticut, USA

    Stefan Schreier & F. Bühler

Authors
  1. Stefan Schreier
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  2. F. Bühler
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Additional information

The computer time for this project was supported by National Aeronautics and Space Administration Grant NsG-398.

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Schreier, S., Bühler, F. On the flow of an unsteady, compressible boundary layer over an accelerating semi-infinite flat plate. Journal of Applied Mathematics and Physics (ZAMP) 20, 905–922 (1969). https://doi.org/10.1007/BF01592300

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  • DOI: https://doi.org/10.1007/BF01592300

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