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Free convection of copper–water nanofluid in a porous gap between hot rectangular cylinder and cold circular cylinder under the effect of inclined magnetic field

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Abstract

Natural convection heat transfer of copper–water nanofluid in a porous gap between hot internal rectangular cylinder and cold external circular cylinder under the effect of inclined uniform magnetic field has been investigated. Domain of interest is a porous sector, where horizontal and vertical adiabatic borders are the external circular cylinder radii. Governing equations formulated in dimensionless stream function, vorticity and temperature variables using the Brinkman-extended Darcy model for the porous medium, single-phase nanofluid model with Brinkman correlation for the nanofluid viscosity and Hamilton and Crosser model for the nanofluid thermal conductivity have been solved numerically by the control volume finite element method. Effects of the Rayleigh number, Hartmann number, Darcy number, magnetic field inclination angle, nanoparticles volume fraction, nanoparticles shape factor, nanoparticles material, nanofluid thermal conductivity and dynamic viscosity models and nanofluid electrical conductivity correlation on streamlines, isotherms, local and average Nusselt numbers have been studied. Obtained results have shown the heat transfer enhancement with the Rayleigh number, Darcy number, nanoparticles volume fraction and nanoparticles shape factor, while the heat transfer rate reduces with the Hartmann number and magnetic field inclination angle. At the same time, the average Nusselt number increases at about 16% when nanoparticles volume fraction rises from 0 till 4% for Ra = 105, Ha = 25, while for Ha = 0 one can find the heat transfer rate augmentation at about 9% for the same conditions. In the case of different nanofluid thermal conductivity and dynamic viscosity models, it has been found that KKL model reflects the heat transfer rate reduction with nanoparticles volume fraction, while for the Hamilton–Crosser–Brinkman model, the heat transfer rate increases. Comparison between the Maxwell correlation for the nanofluid electrical conductivity and the base fluid electrical conductivity illustrates an intensification of the convective heat transfer rate for high values of the Rayleigh number (Ra ≥ 104) in the case of Maxwell correlation for the nanofluid electrical conductivity. At the same time, the effect of the nanoparticles volume fraction becomes more significant when nanofluid electrical conductivity is a function of nanoparticles volume fraction.

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Acknowledgements

This work of the second author was conducted as a government task of the Ministry of Education and Science of the Russian Federation (Project Number 13.6542.2017/6.7). The work of the fourth author was supported from the Grant PN-III-P4-ID-PCE-2016-0036, UEFISCDI, Romania. The authors also wish to express their thanks to the very competent reviewers for the valuable comments and suggestions.

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Correspondence to A. S. Dogonchi or M. A. Sheremet or I. Pop.

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Dogonchi, A.S., Sheremet, M.A., Ganji, D.D. et al. Free convection of copper–water nanofluid in a porous gap between hot rectangular cylinder and cold circular cylinder under the effect of inclined magnetic field. J Therm Anal Calorim 135, 1171–1184 (2019). https://doi.org/10.1007/s10973-018-7396-3

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Keywords

  • Free convection
  • Water-based nanofluid
  • Inclined magnetic field
  • Porous medium
  • Isothermal cylinders
  • Control volume finite element method