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Mixed Convective Flow of a Casson Fluid over a Vertical Stretching Sheet

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Abstract

A coupled nonlinear boundary value problem arising from a mixed convective flow of a non-Newtonian fluid at a vertical stretching sheet with variable thermal conductivity is investigated in this paper. Casson fluid model is used to describe the non-Newtonian fluid behavior. Using a similarity transformation, the governing equations are transformed into a system of coupled, nonlinear ordinary differential equations and the analytical solutions for the velocity and temperature fields are obtained via a semi-analytical algorithm based on the optimal homotopy analysis method. To validate the method, comparisons are made with the available results in the literature for some special cases and the results are found to be in excellent agreement. The characteristics of the velocity and the temperature fields in the boundary layer have been analyzed for several sets of values of the Casson parameter, the Prandtl number, the temperature dependent thermal conductivity parameter, the velocity exponent parameter and the mixed convection parameter. The presented results through graphs and tables reveal substantial effects of the pertinent parameters on the flow and heat transfer characteristics. Furthermore, an error analysis is offered using an exact residual error and average residual error methods.

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Abbreviations

\(U_{0}\) :

Stretching rate

\(u \hbox { and } v\) :

Fluid velocity components along the x and y axes respectively

A, C :

Constants

\(e_{ij}\) :

ijth component of deformation rate

n :

Velocity exponent parameter

r :

Temperature exponent parameter

\(c_p\) :

Specific heat at constant pressure

\(C_{fx}\) :

Skin friction coefficient

f :

Dimensionless stream function

g :

Acceleration due to gravity

\(Gr_x\) :

Local Grashof number

k(T):

Temperature-dependent thermal conductivity

\(k_\infty \) :

Thermal conductivity for away from the wall

\(Nu_x\) :

Local Nusselt number

\(\Pr \) :

Prandtl number

\(\hbox {P}_{\mathrm{y}}\) :

Yield stress of fluid

\(\hbox {Re}_x\) :

Local Reynolds number

T :

Fluid temperature

\(T_w\) :

Wall temperature

\(T_\infty \) :

Ambient temperature

u :

Axial velocity component

\(U_w\) :

Stretching velocity

\(\hbox {v}\) :

Radial velocity component

x, y :

Cartesian coordinates along the surface and normal to it respectively

\(\tau _{ij}\) :

Stress teansor

\(\pi \) :

Product of the component of deformation rate with itself

\(\pi _c\) :

Critical value of

\(\beta \) :

Casson parameter

\(\beta _T\) :

Thermal expansion coefficient

\(\gamma \) :

Kinematic viscosity

\(\varepsilon \) :

Variable thermal conductivity parameter

\(\eta \) :

Similarity variable

\(\theta \) :

Dimensionless temperature

\(\mu \) :

Coefficient of viscosity

\(\mu _B\) :

Plastic dynamic viscosity

\(\lambda \) :

Buoyancy parameter

\(\psi \) :

Stream function

w :

Conditions at the stretching sheet

\(\infty \) :

Condition at infinity

‘:

Differentiation with respect to \(\eta \)

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Acknowledgments

The authors appreciate the constructive comments of the reviewers which led to definite improvements in the paper. CON was financially supported by the Research Grants Council of the Hong Kong Special Administrative Region, China, through General Research Fund Project No. 17206615.

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Authors and Affiliations

  1. Department of Mathematics, University of Central Florida, Orlando, FL, 32816, USA

    K. Vajravelu

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

    K. Vajravelu

  3. Department of Mathematics, VSK University, Vinayaka Nagar, Bellary, Karnataka, 583 105, India

    K. V. Prasad, Hanumesh Vaidya & Neelufer Z. Basha

  4. Department of Mechanical Engineering, The University of Hong Kong, Pokfulam, Hong Kong

    Chiu-On Ng

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  1. K. Vajravelu
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Correspondence to Chiu-On Ng.

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Vajravelu, K., Prasad, K.V., Vaidya, H. et al. Mixed Convective Flow of a Casson Fluid over a Vertical Stretching Sheet. Int. J. Appl. Comput. Math 3, 1619–1638 (2017). https://doi.org/10.1007/s40819-016-0203-6

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  • DOI: https://doi.org/10.1007/s40819-016-0203-6

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