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Transient analysis of viscoelastic fluid past a semi-infinite vertical cylinder with respect to the Deborah and Hartmann numbers

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Abstract

This article investigates the visualizations of heatlines in a natural convection magnetohydrodynamic flow from a vertical cylinder via heat function concept. Fluid is electrically conducting in the existence of an applied magnetic field. The constitutive equations of time-dependent, coupled and highly nonlinear Jeffrey fluid model are evaluated mathematically by utilizing well-organized unconditionally stable finite-difference Crank–Nicolson method. Simulated results are given for several values of Deborah number and Hartmann number to present interesting aspects of the solution of the flow variables, friction factor and heat transfer rate. Results specify that required time to achieve time-independent state rapidly rises with the boosting values of Hartmann number. Boundary-layer flow visualization has been made using heatlines, isotherms and streamlines to perceive the understanding of heat and fluid flow. It is noticed that heat function value reduces for augmenting Hartmann number and also for all smaller physical parameter values and these heatlines become closer to the hot wall. It is also remarked that the hydromagnetic flow-field profiles concerning the Newtonian fluid show a different pattern from that of non-Newtonian Jeffrey fluid.

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Abbreviations

B 0 :

Applied magnetic field (kg s−2 A−1)

\(\bar{B}\) :

Magnetic flux (Wb)

\(\overline{{ C_{\text{f} } }}\) :

Average skin friction coefficient (–)

\(\bar{E}\) :

Electric field (V m−1)

g :

Acceleration due to gravity (m s−2)

\(\bar{H}\) :

Magnetic field (kg s−2 A−1)

\(\overline{Nu}\) :

Average Nusselt number (–)

Gr :

Grashof number (–)

Ha :

Hartmann number (–)

\(\bar{J}\) :

Current density (A m−2)

Pr :

Prandtl number (–)

r 0 :

Radius of cylinder (m)

r :

Radial coordinate (m)

R :

Dimensionless radial coordinate (–)

t′:

Time (s)

t :

Dimensionless time (–)

T′:

Temperature (K)

u, v :

Velocity components in x, r directions (ms−1)

x :

Axial coordinate (m)

U, V :

Dimensionless velocity components in X, R directions (–)

\(\bar{U}\) :

Velocity vector (m s−1)

X :

Dimensionless axial coordinate (–)

β T :

Volumetric coefficient of thermal expansion (K−1)

θ :

Dimensionless temperature (–)

β :

Deborah number (–)

α :

Thermal diffusivity (m2 s−1)

ρ :

Density (kg m−3)

Θ′:

Heat function (kg m2 s−3)

μ :

Dynamic viscosity (kg m−1 s−1)

Π :

Dimensionless heat function (–)

ψ :

Dimensionless stream function (–)

σ :

Electrical conductivity (kg−1 m−3 s3 A2)

υ :

Kinematic viscosity (m2 s−1)   

λ:

Viscoelastic Jeffrey fluid parameter (−)

w:

Condition on the wall

k:

Time step level

\(\infty\) :

Free stream condition

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Acknowledgements

The first author wishes to thank DST-INSPIRE (Code No. IF160028) for the grant of research fellowship and to Central University of Karnataka for providing the research facilities. The authors wish to express their gratitude to the reviewers who highlighted important areas for improvement in this article.

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Authors and Affiliations

  1. Department of Mathematics, Central University of Karnataka, Kalaburagi, 585 367, India

    Mahesh Kumar & G. Janardhana Reddy

  2. Department of Applied Sciences, National Institute of Technology Goa, Farmagudi, 403 401, India

    Ravi Ragoju

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  1. Mahesh Kumar
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Correspondence to G. Janardhana Reddy.

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Kumar, M., Reddy, G.J. & Ragoju, R. Transient analysis of viscoelastic fluid past a semi-infinite vertical cylinder with respect to the Deborah and Hartmann numbers. J Therm Anal Calorim 139, 507–517 (2020). https://doi.org/10.1007/s10973-019-08285-7

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