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Momentum and heat transfer characteristics of three-dimensional CuO/water nanofluid flow in a horizontal annulus: influences of nanoparticle volume fraction and its mean diameter

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Abstract

Both experimental and numerical studies are unanimous in enhancing heat transfer for forced convection of nanoparticle suspensions, while the available works pertaining to buoyancy-induced heat transfer in nanofluids lead to considerably diverse or even contradictory conclusions. In this work, attempt is made to explore the influences of the presence of nanoparticles, with volume fraction of \(0\le \phi \le 0. 0 4\) and mean diameter of \(28 \le D_{\text{p}} \le 82\,{\text{nm}}\), on the three-dimensional laminar natural convection in a horizontal annulus saturated with CuO/water nanofluid. Further efforts have been made to examine the discrepancies in simulation results due to the use of different models for nanofluid properties. A FORTRAN computer code based on the finite volume method is developed for the solution of the general coupled equations. Results demonstrate that the hydrothermal behaviors of nanofluid depend strongly on the complex interaction between \(\phi\) and \(D_{\text{p}}\). Compared to pure water, the nanofluids especially with lower solid volume fraction and smaller nanoparticle diameter show a superior potential for improving heat transfer. In addition, the overall heat transfer is seen to be under-predicted by the classical models without considering nanoparticles’ Brownian motion, whereas the degree of underestimation progressively diminishes as \(\phi\) and \(D_{\text{p}}\) increase. The results of the current work are believed to be useful for the efficient design of thermal equipment using nanofluid as working medium.

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Abbreviations

\(c_{{p}}\) :

Specific heat (J kg−1 K−1)

\(D_{\text{p}}\) :

Particle diameter (m)

\(En\) :

Enhancement of heat transfer

\(g\) :

Acceleration due to gravity (m s−2)

\(H\) :

Height of the annulus (m)

\(k\) :

Thermal conductivity (W m−1 K−1)

\(L\) :

Annular gap (m)

\(n\) :

Time level

\(Nu\) :

Local Nusselt number

\({{Nu}}_{{{\bar{\text{z}}}}}\) :

Axially averaged Nusselt number

\({{Nu}}_{{ 3 {\text{D}}}}\) :

Overall Nusselt number

\(p\) :

Pressure (Pa)

\({Pr}\) :

Prandtl number

\(r\) :

Radial coordinate

\(R_{\text{i}} , \, R_{\text{o}}\) :

Radii of inner and outer cylinders (m)

\(R_{\text{f}}\) :

Interfacial thermal resistance (m2 K W−1)

\({Ra}\) :

Rayleigh number

\(t\) :

Time (s)

\(T\) :

Temperature (K)

\(T_{\text{h}} , \, T_{\text{c}}\) :

Temperature of heated and cooled walls (K)

\(u\) :

Velocity component in \(r\) direction (m s−1)

\(v\) :

Velocity component in \(\varphi\) direction (m s−1)

\(V\) :

Velocity (m s−1)

\(w\) :

Velocity component in \(z\) direction (m s−1)

\(z\) :

Axial coordinate

\(\alpha\) :

Thermal diffusivity (m2 s−1)

\(\beta\) :

Thermal expansion coefficient (K−1)

\(\chi\) :

Time-dependent variable

\(\phi\) :

Volume fraction

\(\varphi\) :

Azimuthal coordinate

\(\mu\) :

Dynamic viscosity (Pa s)

\(\theta\) :

Dimensionless temperature

\(\rho\) :

Density (kg m−3)

\(\upsilon\) :

Kinematic viscosity (m2 s−1)

\({\text{i}},{\text{ o}}\) :

Inner and outer cylinder walls

\({\text{f}},{\text{ nf}},{\text{ s}}\) :

Base fluid, nanofluid and solid particle

\({ \hbox{max} }\) :

Maximum value

\({\text{opt}}\) :

Optimum value

\({\text{ref}}\) :

Reference quantity

\(*\) :

Dimensionless symbol

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Acknowledgements

The research work is supported by the Foundation of National Sustainable Development Agenda (2019sfq02), the National Natural Science Foundation of China (52076218), the China Postdoctoral Science Foundation (Nos. 2019M652800), and the Hunan Provincial Natural Science Foundation of China (2020JJ4722). The support for this work by the Postdoctoral Foundation of Central South University is also gratefully acknowledged.

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Authors and Affiliations

  1. School of Energy Science and Engineering, Central South University, Changsha, 410083, China

    Wei Wang, Gang Liu, Zheng-Hua Rao, Huan Wang & Sheng-Ming Liao

  2. School of Energy and Power Engineering, Changsha University of Science and Technology, Changsha, 410114, China

    Wei Wang

  3. Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of Energy and Power Engineering, Dalian University of Technology, Dalian, 116024, China

    Ben-Wen Li

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  1. Wei Wang
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Wang, W., Liu, G., Li, BW. et al. Momentum and heat transfer characteristics of three-dimensional CuO/water nanofluid flow in a horizontal annulus: influences of nanoparticle volume fraction and its mean diameter. J Therm Anal Calorim 147, 1757–1772 (2022). https://doi.org/10.1007/s10973-020-10395-6

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