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Thermal Enhancement of Radiating Magneto-Nanoliquid with Nanoparticles Aggregation and Joule Heating: A Three-Dimensional Flow

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Abstract

This article studies the effect of nanoparticle aggregation on the 3D flow of titanium nanoliquid based on ethylene glycol \( ( {\text{C}}_{ 2} {\text{H}}_{ 6} {\text{O}}_{2} - {\text{TiO}}_{2} ) \) due to an exponentially elongated surface. Thermal analysis is carried out considering linear thermal radiation, Joule heating, and mechanisms of the heat source/sink, while the aspect of the homogeneous single-order chemical reaction is included in the analysis of the solute. The variable magnetic field is also accounted. The modified Maxwell model (Maxwell–Bruggeman) is implemented to estimate the effective conductivity of the nanoliquid. The displayed equations are moderated in quantities without dimensions. The 2-point nonlinear boundary value problem (BVP) is solved by the shooting procedure. The importance of effective parameters is described through graphs. Numerical data are presented to study the friction factor, the heat transfer rate, and the mass transfer rate. It has been established that the aggregation of nanoparticles significantly improves the thermal field. Furthermore, the effect of magnetism is more in ordinary fluid than in nanofluid.

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Abbreviations

x, y, z :

Cartesian coordinate system (m)

u, v, w :

Velocity components along with x, y, and z directions, respectively (m/s)

\( \mu_{nf} \) :

The viscosity of the nanofluid (kg/ms)

\( \nu_{nf} \) :

The kinetic velocity of the nanofluid (m2/s)

\( \nu_{f} \) :

Kinematic viscosity of the base fluid (m2/s)

\( \left( {\rho c_{p} } \right)_{nf} \) :

Specific heat capacitance of the nanofluid (J/kg K)

\( \left( {\rho c_{p} } \right)_{f} \) :

Heat capacity of foundation liquid (J/kg K)

\( \left( {\rho c_{p} } \right)_{s} \) :

Heat capability of solid nanoparticle (J/kg K)

k nf :

Thermal conductivity of the nanofluid (m2/s)

k f :

Thermal conductivity of the base fluid (m2/s)

k s :

Thermal conductivity of the solid nanoparticle (m2/s)

\( \rho_{nf} \) :

The density of nanofluid (kg/m3)

\( \rho_{f} \) :

The density of the base fluid (kg/m3)

\( \rho_{s} \) :

The density of solid nanoparticle (kg/m3)

Ec:

Eckert number

Pr:

Prandtl number

Kc * :

The reaction rate of the solute

Kc :

Chemical reaction parameter

Q * :

Heat source/sink coefficient

Sc:

Schmidt number

D B :

Brownian motion coefficient (m2/s)

\( \delta \) :

Ratio parameter

Q :

Heat source/sink parameter

A :

Temperature exponent

A * :

Concentration exponent

R :

Radiation parameter

T :

Temperature K (°C)

T w :

The variable temperature at the sheet

\( T_{\infty } \) :

Free-stream temperature K (°C)

C :

Concentration

\( \phi \) :

The dimensionless nanoparticle volume fraction

\( C_{\infty } \) :

Free-stream concentration

C w :

Variable concentration at the sheet

f :

Dimensionless velocity

\( \theta \) :

Dimensionless temperature

\( \varPhi \) :

Dimensionless concentration

C f :

The local skin friction coefficient

Nux :

Local Nusselt number

Shx :

Local Sherwood number

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Acknowledgements

We express our sincere thanks to the editor and anonymous reviewers for their constructive suggestions, and one of the authors (B Mahanthesh) expresses his sincere thanks to the Management, CHRIST (Deemed to be University), Bangalore, India, for their support to complete this research work.

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Authors and Affiliations

  1. Department of Mathematics, Gandhi Institute for Technology, Bhubaneswar, Odisha, 752054, India

    K. Swain

  2. Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, Karnataka, 560029, India

    B. Mahanthesh

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  1. K. Swain
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  2. B. Mahanthesh
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Correspondence to B. Mahanthesh.

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Swain, K., Mahanthesh, B. Thermal Enhancement of Radiating Magneto-Nanoliquid with Nanoparticles Aggregation and Joule Heating: A Three-Dimensional Flow. Arab J Sci Eng 46, 5865–5873 (2021). https://doi.org/10.1007/s13369-020-04979-5

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