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Magnetohydrodynamics Flow of Non-Newtonian Fluid from a Vertical Permeable Cone in the Presence of Thermal Radiation and Heat Generation/Absorption

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Abstract

The nonlinear, steady state magnetohydrodynamics natural convection boundary layer flow, heat and mass transfer of an viscoelastic incompressible Jeffrey’s fluid from a vertical permeable cone with thermal radiation and heat generation/absorption effects is investigated in this article. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a versatile, implicit finite-difference Keller box technique. The Rosseland diffusion algebraic approximation is utilized to simulate thermal radiation effects. The surface of the cones is maintained at a constant temperature and concentration with mass flux present. Excellent correlation of the present results with previous studies is obtained to validate the numerical code. The influence of Deborah number (De), ratio of relaxation to retardation times (\(\lambda \)), radiation parameter (F), heat generation/absorption parameter (\(\Delta \)), suction/injection parameter (\(f_{w}\)), magnetic parameter (M) and dimensionless tangential coordinate (\(\xi \)) on velocity, temperature and concentration evolution in the boundary layer regime are examined in detail. Also, the effects of these parameters on local skin friction, heat transfer rate and mass transfer rate are investigated.

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Abbreviations

A :

Half angle of the cone

B :

Material parameter

\(B_{0}\) :

Constant imposed magnetic field

C :

Concentration

\(C_{f}\) :

Skin friction coefficient

\(c_{p }\) :

Specific heat parameter

\(\textit{De}\) :

Deborah number

\(D_{m }\) :

Mass (species) diffusivity

f :

Non-dimensional steam function

\(f_{w}\) :

Suction/injection parameter

F :

Thermal Radiation

g :

Acceleration due to gravity

\(Gr_{x}\) :

Grashof (free convection) number

K :

Thermal diffusivity

k :

Thermal conductivity of the fluid

\(k^{*}\) :

Mean absorption coefficient

M :

Magnetic parameter

N :

Concentration to thermal buoyancy ratio parameter

\(\textit{Nu}\) :

Heat transfer rate (Local Nusselt number)

\(\textit{Pr}\) :

Prandtl number

\(q_{r}\) :

Radiative heat flux

r :

Local radius of the cone

S :

Cauchy stress tensor

\(\textit{Sc}\) :

Local Schmidt number

\(\textit{Sh}\) :

Mass transfer rate (Local Sherwood number)

T :

Temperature of the fluid

u, v :

Non-dimensional velocity components along the x- and y-directions, respectively

x :

Stream wise coordinate

y :

Transverse coordinate

\(\alpha \) :

Thermal diffusivity

\(\beta \) :

Coefficient of thermal expansion

\(\beta ^{*}\) :

Coefficient of concentration expansion

\(\lambda \) :

Ratio of relaxation to retardation times

\(\lambda _1\) :

Retardation time

\(\eta \) :

Dimensionless radial coordinate

\(\mu \) :

Dynamic viscosity

\(\nu \) :

Kinematic viscosity

\(\theta \) :

Non-dimensional temperature

\(\phi \) :

Non-dimensional concentration

\(\rho \) :

Density of fluid

\(\xi \) :

Dimensionless tangential coordinate

\(\psi \) :

Dimensionless stream function

\(\Delta \) :

Heat generation (source)/heat absorption (sink) parameter

\(\sigma ^{*}\) :

Stefan–Boltzmann constant

w :

Surface conditions on cone surface

\(\infty \) :

Free stream conditions

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Acknowledgments

The authors are grateful to both reviewers and their comments which have served to significantly improve the interpretative and other aspects of the present article.

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Authors and Affiliations

  1. Department of Mathematics, Jawaharlal Nehru Technological University Anantapur, Anantapuramu, 515002, India

    S. Abdul Gaffar & E. Keshava Reddy

  2. Department of Mathematics, Madanapalle Institute of Technology and Science, Madanapalle, 517325, India

    V. Ramachandra Prasad

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Abdul Gaffar, S., Prasad, V.R. & Reddy, E.K. Magnetohydrodynamics Flow of Non-Newtonian Fluid from a Vertical Permeable Cone in the Presence of Thermal Radiation and Heat Generation/Absorption. Int. J. Appl. Comput. Math 3, 2849–2872 (2017). https://doi.org/10.1007/s40819-016-0262-8

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