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Axisymmetric Flow Over a Vertical Slender Cylinder in the Presence of Chemically Reactive Species

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Abstract

The Combined buoyancy effect due to thermal diffusion as well as species diffusion on the boundary layer flow over a slender cylinder in the presence of a chemical reaction is investigated. Using an appropriate transformation, the governing equations are transformed into a system of coupled non-linear ordinary differential equations and are solved numerically via finite difference scheme. The obtained numerical results are compared with the available results in the literature for some special cases and the results are found to be in excellent agreement. The velocity, temperature, and the concentration profiles are presented graphically and analyzed for several sets of the physical parameters. The pooled effect of the thermal and mass Grashof number is to enhance the velocity and is quite the opposite for temperature and the concentration fields.

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Abbreviations

\(a, b, a_o , b_0 , a_{11} ,b_{11}\) :

Constants

\(c_p \) :

Specific heat at constant pressure

C :

Concentration of the fluid

\(C_f\) :

Skin friction coefficient

\(C_w \) :

Concentration at the surface (\(\hbox {mol m}^{-3}\))

\(C_\infty \) :

Concentration of the fluid for away from the wall (\(\hbox {mol m}^{-3}\))

D (C):

Concentration dependent diffusion coefficient

\(D_\infty \) :

Diffusion coefficient for away from the wall

f :

Dimensionless stream function

g :

Acceleration due to gravity (\(\hbox {m/s}^{2}\))

Gr :

Thermal Grashof number

Gc :

Mass Grashof number

k(T):

Temperature-dependent thermal conductivity

\(k_w \) :

Thermal conductivity at the wall (\(\hbox {W m}^{-1}~\hbox {K}^{-1})\)

\(k_1 \) :

Chemical reaction parameter

\(k_\infty \) :

Thermal conductivity for away from the wall

l :

Reference length scale

M:

Kummer’s function

\(Nu_x \) :

Local Nusselt number

\(\Pr \) :

Prandtl number

r :

Radial coordinate

R :

Radius of the cylinder

\(\hbox {Re}_x \) :

Local Reynolds number Sc Schmidt number

\(Sh_x \) :

Local Sherwood number

T :

Fluid temperature (K)

\(T_w \) :

Surface temperature (K)

\(T_\infty \) :

Ambient temperature (K)

u :

Axial velocity component (m/s)

\(U_w \) :

Stretching velocity (m/s)

\(\hbox {v}\) :

Radial velocity component (m/s)

x :

Axial coordinate

\(\beta \) :

Thermal expansion coefficient

\(\beta ^{*}\) :

Concentration expansion coefficient

\(\gamma \) :

Transverse curvature

\(\delta \) :

Reaction rate parameter

\(\varepsilon _1 \) :

Variable thermal conductivity wall

\(\varepsilon _2 \) :

Variable diffusivity

\(\eta \) :

Similarity variable

\(\theta \) :

Dimensionless temperature

\(\mu \) :

Dynamic viscosity (m\(^{2}\)/s)

\(\nu \) :

Kinematic viscosity (m\(^{2}\)/s)

\(\rho \) :

Density (kg/m\(^{3})\)

\(\phi \) :

Dimensionless concentration

\(\psi \) :

Stream function

w :

Conditions at the stretching sheet

\(\infty \) :

Condition at infinity

\(^{\prime }\) :

differentiation with respect to \(\eta \)

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Acknowledgments

The authors appreciate the constructive comments of the reviewer which led to definite improvements in the paper.

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Authors and Affiliations

  1. Department of Mathematics, Vijayanagara Sri Krishnadevaraya University, Bellary, 583104, India

    K. V. Prasad & Hanumesh Vaidya

  2. Department of Mathematics, Department of Mechanical, Materials and Aerospace Engineering, University of Central Florida, Orlando, FL, 32816, USA

    K. Vajravelu

  3. TIFR Centre, IISC-TIFR Joint Programme in Applications of Mathematics, Indian Institute of Science, Bangalore, Karnataka, India

    P. S. Datti

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  1. K. V. Prasad
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  2. K. Vajravelu
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Correspondence to K. V. Prasad.

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Prasad, K.V., Vajravelu, K., Vaidya, H. et al. Axisymmetric Flow Over a Vertical Slender Cylinder in the Presence of Chemically Reactive Species. Int. J. Appl. Comput. Math 3, 663–678 (2017). https://doi.org/10.1007/s40819-015-0121-z

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