Effect of non-uniform heating and viscous dissipation on natural convective flow of Casson fluid over a vertical cone

Indian Journal of Physics (2021)Cite this article

Abstract

The non-Newtonian fluid flows find its applications in the production of paints, pharmaceutical products, synthetic lubricant and biological fluid. Because of the significance of this aspect, the present paper describes the consequence of non-uniform surface heating on the natural convection of the Casson fluid past a vertical cone with a viscous dissipation effect. Firstly, the governing partial differential equations are derived in the dimensionless form. After that, the numerical solution is obtained using the Crank–Nicolson technique of the finite difference method. The obtained numerical solutions for the temperature profiles, velocity profiles, local Nusselt number and local skin friction are displayed by employing the graphs in order to judge the impact of the governing physical parameters of the model such as the Casson fluid parameter, Grashof number, Eckert number and semi-vertical angle of the cone. The major result is found that the velocity and temperature profiles are more at the center of the lateral side of the cone.

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Abbreviations

\(C_{p}\) :

Specific heat at constant pressure \(\left[ {{\text{JM}}^{ - 1} {\text{K}}^{ - 1} } \right]\)

\(Ec\) :

Eckert number

\(Gr\) :

Grashof number

\(Nu\) :

Local Nusselt number at surface of the cone

\(Pr\) :

Prandtl number

\(t^{\prime}\) :

Time \(\left[ {\text{T}} \right]\)

\(t\) :

Dimensionless time

\(T^{\prime}\) :

Temperature \(\left[ {\text{K}} \right]\)

\(u^{\prime}, v^{\prime}\) :

Velocity components in \(x^{\prime} {\text{and }}y^{\prime}\) directions, respectively \(\left[ {{\text{LT}}^{ - 1} } \right]\)

\(u,v\) :

Dimensionless velocity components in \(x {\text{and }}y\) directions, respectively

\(x^{\prime}, y^{\prime}\) :

Co-ordinate axes \(\left[ {\text{L}} \right]\)

\(x, y\) :

Dimensionless co-ordinate axes

\(\beta\) :

Casson parameter

\(\rho\) :

Density of fluid \(\left[ {{\text{ML}}^{ - 3} } \right]\)

\(\theta\) :

Dimensionless temperature

\(\mu\) :

Dynamic viscosity \(\left[ {{\text{NTL}}^{ - 2} } \right]\)

\(g\) :

Gravitational acceleration \(\left[ {{\text{LT}}^{ - 2} } \right]\)

\(\nu\) :

Kinematic viscosity of fluid \(\left[ {{\text{L}}^{2} {\text{T}}^{ - 1} } \right]\)

\(\tau\) :

Local skin-friction

\(\beta_{T}\) :

Thermal expansion coefficient \(\left[ {{\text{K}}^{ - 1} } \right]\)

\(\kappa\) :

Thermal conductivity of fluid \(\left[ {{\text{WL}}^{ - 1} {\text{K}}^{ - 1} } \right]\)

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Acknowledgements

Author Arun Kumar Singh thankfully acknowledges the financial relief from UGC, New Delhi, as a Research Fellowship during this work.

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Affiliations

  1. Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, 221005, India

    Arun K. Singh & Ashok K. Singh

  2. Department of Mathematics, Central University of Rajasthan, Ajmer, 305817, India

    A. Kumar

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  1. Arun K. Singh
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Correspondence to A. Kumar.

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Singh, A.K., Kumar, A. & Singh, A.K. Effect of non-uniform heating and viscous dissipation on natural convective flow of Casson fluid over a vertical cone. Indian J Phys (2021). https://doi.org/10.1007/s12648-020-01984-0

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Keywords

  • Natural convection
  • Vertical cone
  • Casson fluid
  • Non-uniform heating
  • Viscous dissipation