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Heat transfer enhancement using temperature-dependent effective properties of alumina-water nanoliquid with thermo-solutal Marangoni convection: A sensitivity analysis

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Abstract

The sensitivity of the heat transport rate in the thermo-solutal Marangoni convection of \({\mathrm{Al}}_{2}{\mathrm{O}}_{3}-{\mathrm{H}}_{2}\mathrm{O}\) nanoliquid at 300 K is analyzed. The nanoliquid is modeled using the modified Buongiorno model which incorporates the Brownian motion, effective nanoliquid properties, and thermophoresis effects. The thermophysical models proposed by Khanafer and Vafai are chosen in this analysis as these correlations are in good agreement with the experimental values. External constraining factors like thermal radiation and variable magnetic field are also considered. The basic equations are solved using apposite transformation variables and Finite Difference Method (FDM). The impacts of the effectual parameters on all the profiles are analyzed. Furthermore, the heat transport is analyzed by executing a Response Surface Methodology (RSM) model with the Brownian motion parameter (\(0.1\le \mathrm{Nb}\le 0.5\)), thermophoretic parameter (\(0.1\le \mathrm{Nt}\le 0.5\)), and nanoparticle volume fraction (\(1\%\le \varphi \le 3\%\)). The modified Buongiorno model yields lower temperature and concentration profiles when compared to the conventional Buongiorno model. The heat transfer rate is the most sensitive to the Brownian motion parameter than thermophoresis and nanoparticle (NP) volume fraction parameters. The results of this study would be instrumental in improving the efficiency of the welding process, crystal growth, and coating technologies.

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Abbreviations

u, v :

Velocity of liquid in \(x\) and \(y\) directions (\(\mathrm{m}{\mathrm{ s}}^{-1}\))

T, C :

Temperature (\(K\)), Concentration

T ∞ , C ∞ :

Ambient temperature (\(K\)) and concentration

p :

Density (\(\mathrm{kg}{\mathrm{ m}}^{-3}\))

c p :

Specific heat capacity (\(\mathrm{J k}{\mathrm{g}}^{-1} {\mathrm{K}}^{-1})\)

B :

Variable magnetic field

B 0 :

Uniform magnetic field (Tesla)

A 1 , A 2 :

Positive dimensional constants

k R :

Rosseland mean absorption coefficient (\({\mathrm{m}}^{-1}\))

q r :

Radiative heat flux (\({\mathrm{Wm}}^{-2}\))

n :

Exponent

Nux :

Reduced Nusselt number

f :

Dimensionless stream function

L, ζ 1, ζ 2 :

Constants

D B :

Brownian diffusion coefficient (\({\mathrm{m}}^{2} {\mathrm{s}}^{-1}\))

D T :

Thermophoresis diffusion coefficient (\({\mathrm{m}}^{2}{\mathrm{ s}}^{-1}\))

R :

Thermal radiation parameter

M :

Magnetic parameter

Prf :

Prandtl number

Nb:

Reduced Brownian motion parameter

Nt:

Reduced thermophoretic parameter

Le:

Lewis number

r :

Solutal to thermal Marangoni number ratio

d :

Diameter (\(\mathrm{m})\)

b i :

Regression coefficients

k :

Thermal conductivity (\({\mathrm{Wm}}^{-1} {\mathrm{K}}^{-1}\))

μ :

Dynamic viscosity (\(\mathrm{kg }{\mathrm{m}}^{-1} {\mathrm{s}}^{-1}\))

v :

Kinematic viscosity (\({\mathrm{m}}^{2}{\mathrm{s}}^{-1}\))

σ e :

Electrical conductivity (\({\mathrm{Sm}}^{-1}\))

φ :

Nanoparticle volume fraction

α :

Thermal diffusivity (\({\mathrm{m}}^{2}{\mathrm{s}}^{-1}\))

σ :

Surface tension (\({\mathrm{Nm}}^{-1}\))

σ 0 :

Constant surface tension at \({T}_{\infty }\) and \({C}_{\infty }\) (\({\mathrm{Nm}}^{-1}\))

σ sb :

Stefan-Boltzmann constant

θ :

Dimensionless temperature

ϕ :

Dimensionless concentration

ψ :

Stream function

η :

Similarity variable

f :

Base fluid

nf:

Nanofluid

p :

Nanoparticle

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Acknowledgements

The authors would like to dedicate this article to Prof. S. K. Gangadhar, Professor, Department of Mathematics, CHRIST (Deemed to be University), Bangalore on the occasion of his 60th Birthday.

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

    Joby Mackolil & B. Mahanthesh

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  1. Joby Mackolil
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Correspondence to B. Mahanthesh.

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Mackolil, J., Mahanthesh, B. Heat transfer enhancement using temperature-dependent effective properties of alumina-water nanoliquid with thermo-solutal Marangoni convection: A sensitivity analysis. Appl Nanosci 13, 255–266 (2023). https://doi.org/10.1007/s13204-020-01631-4

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