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Sensitivity analysis of Marangoni convection in TiO2–EG nanoliquid with nanoparticle aggregation and temperature-dependent surface tension

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Abstract

The sensitivity analysis of the magnetohydrodynamic thermal Marangoni convection of ethylene glycol (EG)-based titania (TiO2) nanoliquid is carried out by considering the effect of nanoparticle aggregation. The rate of heat transfer is explored by utilizing response surface methodology and estimating the sensitivity of the heat transfer rate toward the effective parameters: radiation parameter (1 ≤ R ≤ 3), magnetic parameter (1 ≤ M ≤ 3) and nanoparticle volume fraction \((1\% \le \phi \le 5\%\)). The heat transfer phenomenon is scrutinized with thermal radiation and variable temperature at the surface. The effective thermal conductivity and viscosity with aggregation are modeled by using the Maxwell–Bruggeman and Krieger–Dougherty models. The governing equations are solved by using the apposite similarity transformations. It is found that when the effect of aggregation is considered, the velocity profile is lower. A positive sensitivity of the Nusselt number toward thermal radiation is observed. Further, a negative sensitivity of the heat transfer rate is observed toward the magnetic field and nanoparticle volume fraction.

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Abbreviations

u, v :

Fluid velocity in x and y directions (m s−1)

T :

Temperature (K)

\(T_{\infty }\) :

Ambient temperature (K)

k :

Thermal conductivity (W m−1 K−1)

c p :

Effective specific heat coefficient of fluid (J kg−1 K−1)

B :

Variable magnetic field

B 0 :

Uniform magnetic field (T)

A :

Positive dimensional constant

k R :

Rosseland mean absorption coefficient (m−1)

q r :

Radiative heat flux (W m−2)

n :

Exponent of temperature variation

Nux :

Reduced Nusselt number

f :

Dimensionless stream function

\(L,\zeta_{1} , \zeta_{2}\) :

Constants

k a :

Thermal conductivity of the aggregates (W m−1 K−1)

D :

Fractal index

r a, r p :

Radii of aggregates and nanoparticles (m)

R :

Thermal radiation parameter

M :

Magnetic parameter

Prf :

Prandtl number

\(\rho\) :

Density (kg m−3)

\(\mu\) :

Dynamic viscosity (kg m−1 s−1)

\(\nu\) :

Kinematic viscosity (m2 s−1)

\(\sigma_{\text{e}}\) :

Electrical conductivity (S m−1)

\(\alpha\) :

Thermal diffusivity (m2 s−1)

\(\phi\) :

Nanoparticle volume fraction

\(\sigma\) :

Surface tension (N m−1)

\(\sigma_{0}\) :

Surface tension at the temperature \(T_{\infty }\) (N m−1)

\(\sigma_{\text{sb}}\) :

Stefan–Boltzmann constant

\(\theta\) :

Dimensionless temperature

\(\psi\) :

Stream function

\(\eta\) :

Similarity variable

\(\beta_{\text{i}}\) :

Regression coefficients

\(\phi_{\text{m}}\) :

Maximum volume fraction of nanoparticles

\(\phi_{\text{a}}\) :

Volume fraction of nanoparticle aggregates

\(\left[ \eta \right]\) :

Einstein coefficient

f:

Base fluid

nf:

Nanoliquid

S:

Nanoparticle

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Acknowledgements

The authors are grateful to the management of CHRIST (Deemed to be University), Bengaluru, India, for their constant support to accomplish this research work. We also thank the Editor and the anonymous reviewers for their constructive suggestions to improve the quality of this article.

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

    Joby Mackolil & B. Mahanthesh

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Mackolil, J., Mahanthesh, B. Sensitivity analysis of Marangoni convection in TiO2–EG nanoliquid with nanoparticle aggregation and temperature-dependent surface tension. J Therm Anal Calorim 143, 2085–2098 (2021). https://doi.org/10.1007/s10973-020-09642-7

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