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Free convection nanofluid flow past a vertical isothermal cone surface in the presence of viscous dissipation and MHD with heat flux

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Abstract

This study employs a numerical solution approach to examine the impacts of viscous dissipative, MHD, among various nanofluid flows across an up straight cone with iso-thermal surface velocity and temperature. After being converted into dimensionless form, the flow field equation is numerically evaluated using an outstanding finite difference approach. Our experiment used different types of nanofluids ( Cu, Al2O3, TiO2 and Ag ) and volume fractions (0, 0.01, 0.02, 0.03, 0.04) to detect differences in heat transfer occurrence depending on temperature and velocity. Graphs have been used to show a parametric analysis for various flow field features.

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Data availability

The datasets supporting the conclusions of this article are included within the article.

Abbreviations

\(B_{0}\) :

   Magnetic field induction (W m−2)

C\(_{p}\) :

   Specific heat at constant pressure (J kg−1 K−1)

Gr\(_{L}\) :

   Thermal Grashof number (−)

g:

   Acceleration due to gravity (m s−2)

k:

   Thermal conductivity (W K−1 m −1)

L:

   Reference length (m)

\({\text{Nu}} _{X}\) :

   Non-dimensional local Nusselt number

\({\overline{Nu}}\) :

   Non-dimensional average Nusselt number

Pr:

   Prandtl number (−)

R:

   Dimensionless local radius

T′:

   Temperature (k)

T:

   Dimensionless temperature

t′:

   Time (s)

t:

   Dimensionless time

U, V:

   Dimensionless velocity in X, Y direction

u,v:

   Dimensional velocity in the direction of x, y axes (ms−1)

x:

   Spatial co-ordinate alongside the cone generator (dimensional) (m)

y:

   Spatial co-ordinate perpendicular to cone generator (dimensional) (m)

X:

   Spatial co-ordinate alongside the cone generator (non-dimensional)

Y:

   Spatial co-ordinate perpendicular to cone generator (non-dimensional)

\(\beta\) :

   Volumetric thermal expansion coefficient with temperature (K−1)

\(\epsilon\) :

   Viscous dissipation parameter (−)

\(\phi\) :

   Nanoparticles volume fraction (−)

μ:

   Dynamic viscosity (kg m−1 s−1)

\(\mu _{nf}\) :

   Nanofluid of the dynamic viscosity (kg m−1 s−1)

\(\nu\) :

   Kinematic viscosity (m−1 s−1)

\(\nu _{f}\) :

   Base fluid of the kinematic viscosity (m−1 s−1)

\(\omega\) :

   Cone apex half-angle (degree)

\(\rho\) :

   Density (kg m−3)

\(\tau _{X}\) :

   Dimensionless local skin friction

\({\overline{\tau }}\) :

   Dimensionless average skin friction

\(\hbox {f}\) :

 Base fluid condition

\(\hbox {nf}\) :

Nanofluid condition

\(\hbox {s}\) :

Nanoparticle condition

\(\hbox {w}\) :

Wall condition

\(\infty\) :

Ambient condition

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Authors and Affiliations

  1. Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Chennai, Tamil Nadu, 603203, India

    E. Ragulkumar & P. Sambath

  2. Faculty of Engineering, Kuwait College of Science and Technology, Doha District, 35004, Kuwait

    Ali J. Chamkha

Authors
  1. E. Ragulkumar
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  2. P. Sambath
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  3. Ali J. Chamkha
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Contributions

ERK, PS and AJC conceived and designed the study. ERK conducted the literature search and drafted the manuscript. PS and AJC were involved in the analysis and interpretation of data. The study was supervised by PS. All authors read and approved the final manuscript.

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Correspondence to P. Sambath.

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Ragulkumar, E., Sambath, P. & Chamkha, A.J. Free convection nanofluid flow past a vertical isothermal cone surface in the presence of viscous dissipation and MHD with heat flux. Eur. Phys. J. Plus 137, 894 (2022). https://doi.org/10.1140/epjp/s13360-022-03115-6

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