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Mass transfer effects on flow past an impulsively started infinite vertical plate with constant mass flux — an exact solution

Einfluß von Stofftransport auf die Strömung entlang einer plötzlich in Bewegung gesetzten, unendlich ausgedehnten, vertikalen Platte bei konstantem Massenfluß — eine exakte Lösung

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Abstract

An exact solution to the problem of flow past an impulsively started infinite vertical plate in the presence of a foreign mass and constant mass flux at the plate is presented by the Laplace-transform technique. The velocity, the temperature and the concentration profiles are shown on graphs. The skin-friction and the Sherwood number are also shown on graphs. The effects of different parameters likeG (the Grashof number),Gc (the modified Grashof number),Pr (the Prandtl number) andSc (the Schmidt number) are discussed.

Zusammenfassung

Mit Hilfe der Laplace-Transformation wird eine exakte Lösung für die Strömung entlang einer plötzlich in Bewegung gesetzten, unendlich ausgedehnten, vertikalen Platte hergeleitet, wobei deren Oberfläche einen aus der Umgebung gespeisten konstanten Massenstrom aufnehmen soll. Geschwindigkeits-, Temperatur- und Konzentrationsprofile sind graphisch dargestellt, ebenso Reibungsbeiwerte und Sherwood-Zahlen. Der Einfluß verschiedener Parameter, wie Grashof-Zahl, modifizierte Grashof-Zahl, Prandtl-Zahl und Schmidt-Zahl wird diskutiert.

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Abbreviations

C′:

species concentration near the plate

\(C'_\infty \) :

species concentration in the fluid far away from the plate

C p :

specific heat at constant pressure

D :

chemical molecular diffusivity

G :

grashof number

Gc :

modified Grashof number

g :

acceleration due to gravity

j″:

mass flux per unit area at the plate

K :

thermal conductivity

Nu :

Nusselt number

Pr :

Prandtl number

Sc :

Schmidt number

T′:

temperature of the fluid near the plate

\(T'_\infty \) :

temperature of the fluid far away from the plate

T′ w :

temperature of the plate

t′:

time

u′:

velocity in thex′-direction

U 0 :

velocity of the plate

x′:

coordinate axis along the plate

y′:

coordinate axis normal to the plate

β :

coefficient of volume expansion

β⋆:

coefficient of species expansion

ν :

kinematic viscosity

ρ :

density

μ :

viscosity

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Authors and Affiliations

  1. Dept. of Mathematics, Gauhati University, 731 014, Guwahati, India

    U. N. Das & S. N. Ray

  2. 31A-12, Brindavan Society, 400 014, Thane, India

    V. M. Soundalgekar

Authors
  1. U. N. Das
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  2. S. N. Ray
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  3. V. M. Soundalgekar
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Das, U.N., Ray, S.N. & Soundalgekar, V.M. Mass transfer effects on flow past an impulsively started infinite vertical plate with constant mass flux — an exact solution. Heat and Mass Transfer 31, 163–167 (1996). https://doi.org/10.1007/BF02333314

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  • DOI: https://doi.org/10.1007/BF02333314

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