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Applied Mathematics and Mechanics

, Volume 34, Issue 2, pp 139–152 | Cite as

Viscous and Ohmic heating effects in doubly stratified free convective flow over vertical plate with radiation and chemical reaction

  • P. GanesanEmail author
  • R. K. Suganthi
  • P. Loganathan
Article

Abstract

An analysis is carried out to study the combined effects of viscous and Ohmic heating in the transient, free convective flow of a viscous, incompressible, and doubly stratified fluid past an isothermal vertical plate with radiation and chemical reactions. The governing boundary layer equations are solved numerically by an implicit finite difference scheme of the Crank-Nicolson type. The influence of different parameters on the velocity, the temperature, the concentration, the skin friction, the Nusselt number, and the Sherwood number is discussed with graphical illustrations. It is observed that an increase in either the thermal stratification or the mass stratification parameter decreases the velocity. An increase in the thermal stratification increases the concentration and decreases the temperature while an opposite effect is observed for an increase in the mass stratification. An augmentation in viscous and Ohmic heating increases the velocity and temperature while decreases the concentration. The results are found to be in good agreement with the existing solutions in literature.

Key words

thermal stratification mass stratification Ohmic dissipation viscous dissipation chemical reaction radiation 

Nomenclature

x

spatial coordinate along the plate

X

dimensionless spatial coordinate along the plate

y

spatial coordinate normal to the plate

Y

dimensionless spatial coordinate normal to the plate

u

velocity component along the plate

U

dimensionless velocity component along the X-direction

υ

velocity component normal to the plate

V

dimensionless velocity component along the Y -direction

L

characteristic length

t′

time

t

dimensionless time

T′

temperature of the fluid

T

dimensionless temperature

C′

concentration of the fluid

C

dimensionless concentration

k

thermal conductivity

Ec

Eckertnumber

M

magnetic parameter

ST

thermal stratification parameter

SM

mass stratification parameter

D

mass diffusion coefficient

Gr

thermal Grashof number

g

acceleration due to gravity

R

radiation parameter

K′c

chemical reaction parameter

Kc

dimensionless chemical reaction parameter

N

buoyancy ratio parameter

Pr

Prandtl number

Sc

Schmidt number

qr

radiative heat flux

NuX

local Nusselt number

\(\overline {Nu} _X\)

average Nusselt number

ShX

local Sherwood number

\(\overline {Sh} _X\)

average Sherwood number

Greek symbols

α

thermal diffusivity

β

volumetric coefficient of thermal expansion

β*

volumetric coefficient of expansion with concentration

ν

kinematic viscosity

τX

local skin friction

\(\bar \tau _X\)

average skin friction

Chinese Library Classification

O362 

2010 Mathematics Subject Classification

76D55 76R10 76R50 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsAnna University ChennaiChennaiIndia

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