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
Stokes, G. G.: On the effect of internal friction of fluids on the motion of pendulums. Cambridge Phil. Trans.IX, 8–106 (1851).
Soundalgekar, V. M.: Free convection effects on the Stokes problem for an infinite vertical plate. ASME J. Heat Transfer99, 499–501 (1977).
Soundalgekar, V. M.: Effects of mass transfer and free convection on the flow past an impulsively started vertical plate. ASME J. Appl. Mech.46, 757–760 (1979).
Soundalgekar, V. M., Patil, M. R.: Stokes problem for a vertical plate with constant heat flux. Astrophys. Space Sci.70, 179–182 (1980).
Muthukumaraswamy, R., Ganesan, P.: Unsteady flow past an impulsively started vertical plate with heat and mass transfer. Heat Mass Transfer34, 187–193 (1998).
Soundalgekar, V. M., Birajdar, N. S., Darwekar, V. K.: Mass transfer effects on the flow past an impulsively started infinite vertical plate with variable temperature or constant heat flux. Astrophysics Space Sci.100, 159–164 (1984).
Das, U. N., Deka, R. K., Soundalgekar, V. M.: Effects of mass transfer on flow past an impulsively started infinite vertical plate with constant heat flux and chemical reaction. Forschung im Ingenieurwesen-Engineering Research60, 284–287 (1994).
Carnahan, B., Luther, H. A., Wilkes, J. O.: Applied numerical methods. New York: Wiley 1969.
Byron Bird, R., Warren, E. S., Lightfoot, E. N.: Transport phenomena. New York: Wiley 1960.
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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