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Mass transfer effects on flow past a vertical oscillating plate with variable temperature

Einfluß von Stoffübergang auf die Strömung entlang einer senkrechten oszillierenden Platte veränderlicher Temperaturen

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Abstract

An exact solution to the flow of a viscous incompressible fluid past an infinite vertical oscillating plate, in the presence of a foreign mass has been derived by the Laplace-transform technique when the plate temperature is linearly varying as time. The velocity profiles are shown on graphs and the numerical values of the skin-friction are listed in a table. It is observed that the skin-friction increases with increasingSc, ωt orGr but decreases with increasingGm ort, whereSc (the Schmidt number), ω (frequency),t (time),Gr (the Grashof number) andGm is (the modified Grashof number) andt.

Zusammenfassung

Mit Hilfe der Laplace-Transformation wird eine exakte Lösung für die Strömung einer zähen, inkompressiblen Flüssigkeit entlang einer unendlich ausgedehnten, senkrechten, oszillierenden Platte gewonnen, wobei die Einwirkung eines Feststoffs Berücksichtigung findet und die Plattentemperatur linear mit der Zeit veränderlich sein soll. Die Geschwindigkeitsprofile sind in Diagrammen dargestellt und die numerischen Werte der Reibungsschubspannung in einer Tabelle. Letztere wächst mit der Schmidt-ZahlSc, der Grashof-ZahlGr und dem Produkt aus Frequenz ω und Zeitt; sie nimmt ab, wennGm (die modifizierte Grashof-Zahl) undt zunehmen.

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Abbreviations

C′ :

species concentration in the fluid near the plate

C −∞ :

species concentration in the fluid away from the plate

C ′ W :

species concentration at the plate

C p :

specific heat at constant pressure

D :

chemical molecular diffusivity

Gm :

modified Grashof number

Gr :

Grashof number

g :

acceleration due to gravity

K :

thermal conductivity

P :

Prandtl number

Sc :

Schmidt number

T′ :

Temperature of the fluid near the plate

T ′ W :

temperature of the plate

T ′∞ :

temperature of the fluid far away from the plate

t′ :

time

u′ :

velocity of the fluid in the upward direction

U 0 :

amplitude of oscillation

x′ :

coordinate axis along the plate in the vertically upward direction

y′ :

coordinate axis normal to the plate

τ′:

skin-friction

μ:

viscosity

β:

coefficient of volume expansion

β* :

coefficient of species expansion

ρ:

density

ω:

frequency

References

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Author notes

  1. V. M. Soundalgekar

    Present address: Brindavan Society, 31A-12, 400 601, Thane, India

Authors and Affiliations

  1. Dept. of Mathematics, Institute of Science, 431 001, Aurangabad, DN, India

    R. M. Lahurikar & S. G. Pohanerkar

  2. Dept. of Mathematics, Yeshawant College, 431 602, Nanded, India

    N. S. Birajdar

Authors
  1. V. M. Soundalgekar
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  2. R. M. Lahurikar
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  3. S. G. Pohanerkar
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  4. N. S. Birajdar
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Soundalgekar, V.M., Lahurikar, R.M., Pohanerkar, S.G. et al. Mass transfer effects on flow past a vertical oscillating plate with variable temperature. Heat and Mass Transfer 30, 309–312 (1995). https://doi.org/10.1007/BF01463921

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  • DOI: https://doi.org/10.1007/BF01463921

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