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First-order chemical reaction on flow past an impulsively started vertical plate with uniform heat and mass flux

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Summary

A finite-difference solution of the transient natural convection flow of an incompressible viscous fluid past an impulsively started semi-infinite plate with uniform heat and mass flux is presented here, taking into account the homogeneous chemical reaction of first order. The velocity profiles are compared with the available theoretical solution and are found to be in good agreement. The steady-state velocity, temperature and concentration profiles are shown graphically. It is observed that due to the presence of first order chemical reaction the velocity decreases with increasing values of the chemical reaction parameter. The local as well as average skin-friction, Nusselt number and Sherwood number are shown graphically.

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Abbreviations

C′ :

concentration

C′ ∞ :

species concentration in the fluid far away from the plate

C w′ :

species concentration near the plate

C :

dimensionless concentration

D :

mass diffusion coefficient

Gc :

mass Grashof number

Gr :

thermal Grashof number

g :

acceleration due to gravity

j″ :

mass flux per unit area at the plate

K :

dimensionless chemical reaction parameter

K l :

chemical reaction parameter

k :

thermal conductivity

Nux :

dimensionless local Nusselt number

\(\overline {Nu} \) :

dimensionless average Nusselt number

Pr:

Prandtl number

q :

heat flux per unit area at the plate

Sc:

Schmidt number

Shx :

dimensionless local Sherwood number

\(\overline {Sh} \) :

dimensionless average Sherwood number

T′ :

temperature

T′ ∞ :

temperature of the fluid far away from the plate

T w′ :

temperature of the plate

T :

dimensionless temperature

t′ :

time

t :

dimensionless time

u 0 :

velocity of the plate

U, V :

dimensionless velocity components inX,Y-directions, respectively

u, v :

velocity components inx, y-directions, respectively

X :

dimensionless spatial coordinate along the plate

x :

spatial coordinate along the plate

Y :

dimensionless spatial coordinate normal to the plate

y :

spatial coordinate normal to the plate

α:

thermal diffusivity

β:

volumetric coefficient of thermal expansion

β*:

volumetric coefficient of expansion with concentration

μ:

coefficient of viscosity

ν:

kinematic viscosity

τx :

dimensionless local skin-friction

\(\bar \tau \) :

dimensionless average skin-friction

References

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Author notes

  1. R. Muthucumaraswamy

    Present address: Department of Mathematics and Computer Applications, Sri Venkateswara College of Engineering, 602 105, Sriperumbudur, India

  2. P. Ganesan

    Present address: Department of Mathematics, Anna University, 600 025, Chennai, India

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    1. R. Muthucumaraswamy
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    2. P. Ganesan
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    Muthucumaraswamy, R., Ganesan, P. First-order chemical reaction on flow past an impulsively started vertical plate with uniform heat and mass flux. Acta Mechanica 147, 45–57 (2001). https://doi.org/10.1007/BF01182351

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    • DOI: https://doi.org/10.1007/BF01182351

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