Acta Mechanica

, Volume 147, Issue 1–4, pp 45–57

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

  • R. Muthucumaraswamy
  • P. Ganesan
Original Papers

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.

List of symbols

C′

concentration

C′

species concentration in the fluid far away from the plate

Cw′

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

Kl

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

Tw′

temperature of the plate

T

dimensionless temperature

t′

time

t

dimensionless time

u0

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

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References

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Copyright information

© Springer-Verlag 2001

Authors and Affiliations

  • R. Muthucumaraswamy
    • 1
  • P. Ganesan
    • 2
  1. 1.Department of Mathematics and Computer ApplicationsSri Venkateswara College of EngineeringSriperumbudurIndia
  2. 2.Department of MathematicsAnna UniversityChennaiIndia

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