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Theoretical comparative assessment of single- and two-phase models for natural convection heat transfer of Fe3O4/ethylene glycol nanofluid in the presence of electric field

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Abstract

Natural convective heat transfer of Fe3O4/ethylene glycol nanofluids around the platinum wire as a heater in the absence and presence of the high electric field was investigated, numerically. The control volume finite element method was employed for the numerical simulation. Effects of the flow model, the volume fraction of nanoparticles, Rayleigh number, and the electric field intensity on the natural heat transfer coefficient (NHTC) of nanofluid were studied. Simulation results of single-phase and two-phase flow models showed that the two-phase model could better predict experimental data than the single-phase model due to take into account the velocity of each phase in the mixture. The two-phase model could predict a particular volume fraction of 0.02 vol%, which enhancement the volume fraction further that deteriorated heat transfer. Streamlines showed that, as the supplied voltage is increased, velocity vectors and buoyant force increase, and NHTC of nanofluid enhances. Isotherms also showed that the thickness of the thermal boundary layer decays for higher voltage of the electric field, and the natural heat transfer rate promotes. Local Nusselt number (Nuθ) changed as a function of angle around the hot wire. Nuθ increased with applying the electric field for all angles, and the highest Nuθ obtained at θ = 180° (below the wire).

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Abbreviations

\( \vec{u} \) :

Velocity vector (m s−1)

\( \vec{u}_{\text{f}} \) :

Continuous phase velocity vector (m s−1)

\( \vec{u}_{\text{p}} \) :

Dispersed phase velocity vector (m s−1)

\( \vec{u}_{\text{slip}} \) :

Relative velocity vector between the two phases (m s−1)

\( \vec{g} \) :

Gravity vector (m s−2)

P :

Hydrodynamic pressure (Pa)

\( \overrightarrow {{{\text{F}}_{1} }} \) :

Volume force (N m−3)

\( \overrightarrow {{{\text{F}}_{2} }} \) :

Electrical force (N m−3)

m dc :

Mass transfer rate from the dispersed to the continuous phase (kg m−3 s−1)

(C p)nf :

Nanofluids specific heat capacity at constant pressure (J kg−1 K−1)

(C p)f :

Base fluids specific heat capacity at constant pressure (J kg−1 K−1)

(C p)p :

Nanoparticle specific heat capacity at constant pressure (J kg−1 K−1)

k nf :

Nanofluids thermal conductivity (W m−1 K−1)

k f :

Base fluids therm2al conductivity (W m−1 K−1)

k p :

Nanoparticle thermal conductivity (W m−1 K−1)

T :

Temperature (K)

T w :

Platinum wire temperature (K)

A w :

Platinum wire surface area (m−2)

T b :

Bulk temperature (K)

\( \vec{q} \) :

Heat flux vector (W m−2)

Q :

Ohmic heating (W m−3)

S :

Strain-rate tensor

D c :

Cylinder diameter (m)

L :

Wall height (m)

H c :

Cylinder height (m)

d w :

Platinum wire diameter (m)

d p :

Particle diameter (m)

q J :

Current sources (A m−3)

ρ s :

Surface charge density (C m−2)

\( \vec{J} \) :

Current density (A m−2)

\( \overrightarrow {{J_{\text{e}} }} \) :

Externally generated current density (A m−2)

V :

Electric potential (V)

\( \vec{E} \) :

Electric field

σ :

Electrical conductivity (S m−1)

ɛ 0 :

Relative permittivity of free space (F m−1)

ρ nf :

Nanofluids density (kg m−3)

ρ f :

Continuous phase density (kg m−3)

ρ p :

Dispersed phase density (kg m−3)

μ nf :

Nanofluids viscosity (Pa s)

μ f :

Continuous phase viscosity (Pa s)

β :

Thermal expansion coefficient (K−1)

α :

Mass fraction of dispersed phase (kg kg−1)

φ f :

Volume fractions of the continuous phase

φ p :

Volume fractions of dispersed phase

τ :

Viscous stress tensor (Pa)

τ Gm :

Sum of the viscous and turbulent stresses (kg m−1 s−2)

m:

Mixture

p:

Nanoparticle

f:

Base fluid

nf:

Nanofluid

b:

Bulk

Sim:

Simulation

References

  1. Daraio C, Jin S. Synthesis and patterning methods for nanostructures useful for biological applications, nanotechnology for biology and medicine. New York: Springer; 2005.

    Google Scholar 

  2. Yu W, France DM, Routbort JL, Choi SUS. Review and comparison of nanofluid thermal conductivity and heat transfer enhancement. Heat Transf Eng. 2008;29:432–60.

    Article  CAS  Google Scholar 

  3. Webb RL. Principles of enhanced heat transfer. New York: Taylor & Francis Group; 2005.

    Google Scholar 

  4. Pena NLCD, Rivera-Solorio CI, Payan-Rodríguez LA, García-Cuellar AJ, Lopez-Salinas JL. Experimental analysis of natural convection in vertical annuli filled with AlN and TiO2/mineral oil-based nanofluids. Int J Therm Sci. 2017;111:138–45.

    Article  Google Scholar 

  5. Khanafer K, Vafai K, Lightstone M. Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. Int J Heat Mass Transf. 2003;46:3639–53.

    Article  CAS  Google Scholar 

  6. Lai FH, Yang YT. Lattice Boltzmann simulation of natural convection heat transfer of Al2O3/water nanofluids in a square enclosure. Int J Therm Sci. 2011;50:1930–41.

    Article  CAS  Google Scholar 

  7. Wang G, Meng X, Zeng M, Ozoe H, Wang QW. Natural convection heat transfer of copper-water nanofluid in a square cavity with time-periodic boundary temperature. Heat Transfer Eng. 2014;35:6–8.

    Google Scholar 

  8. Kouloulias K, Sergis A, Hardalupas Y. Assessing the flow characteristics of nanofluids during turbulent natural convection, Journal of Thermal Analysis and Calorimetry. J Therm Anal Calorim. 2019;135:3181–9.

    Article  Google Scholar 

  9. Ho CJ, Liu WK, Chang YS, Lin CC. Natural convection heat transfer of alumina-water nanofluid in vertical square enclosures: an experimental study. Int J Therm Sci. 2010;49:1345–53.

    Article  CAS  Google Scholar 

  10. Ali M, Zeitoun O, Almotairi S, Al-Ansary H. The effect of alumina-water nanofluid on natural convection heat transfer inside vertical circular enclosures heated from above. Heat Transf Eng. 2013;34:1289–99.

    Article  CAS  Google Scholar 

  11. Beheshti A, Shanbedi M, Zeinali Heris S. Heat transfer and rheological properties of transformer oil-oxidized MWCNT nanofluid. J Therm Anal Calorim. 2014;118:1451–60.

    Article  CAS  Google Scholar 

  12. Nnanna AGA. Experimental model of temperature-driven nanofluid. J Heat Transf Trans ASME. 2007;129:697–704.

    Article  CAS  Google Scholar 

  13. Torki M, Etesami N. Experimental investigation of natural convection heat transfer of SiO2/water nanofluid inside inclined enclosure. J Therm Anal Calorim. 2020;139:1565–74.

    Article  CAS  Google Scholar 

  14. Samadzadeh A, Heris SZ, Hashim I, Mahian O. An experimental investigation on natural convection of non-covalently functionalized MWCNTs nanofluids: effects of aspect ratio and inclination angle. Int Commun Heat Mass Transfer. 2020;111:104473.

    Article  CAS  Google Scholar 

  15. Heris SZ, Pour MB, Mahian O, Wongwises S. A comparative experimental study on the natural convection heat transfer of different metal oxide nanopowders suspended in turbine oil inside an inclined cavity. Int J Heat Mass Transf. 2014;73:231–8.

    Article  CAS  Google Scholar 

  16. Mahian O, Kianifar A, Heris SZ, Wongwises S. Natural convection of silica nanofluids in square and triangular enclosures: theoretical and experimental study. Int J Heat Mass Transf. 2016;99:792–804.

    Article  CAS  Google Scholar 

  17. Laohalertdecha S, Naphon P, Wongwises S. A review of electrohydrodynamic enhancement of heat transfer. Renew Sustain Energy Rev. 2007;11:858–76.

    Article  CAS  Google Scholar 

  18. Das SK, Choi SUS, Yu W, Pradeep T. Nanofluids: science and technology. Hoboken: Wiley; 2008.

    Google Scholar 

  19. Masuda H, Ebata A, Teramae K. Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles. Dispersion of Al2O3, SiO2 and TiO2 ultra-fine particles. Netsu Bussei. 1993;7:227–33.

    Article  CAS  Google Scholar 

  20. Goharkhah M, Ashjaee M, Shahabadi M. Experimental investigation on convective heat transfer and hydrodynamic characteristics of magnetite nanofluid under the influence of an alternating magnetic field. Int J Therm Sci. 2016;99:113–24.

    Article  CAS  Google Scholar 

  21. Kasaeipoor A, Ghasemi B, Aminossadati S. Convection of Cu-water nanofluid in a vented T-shaped cavity in the presence of magnetic field. Int J Therm Sci. 2015;94:50–60.

    Article  CAS  Google Scholar 

  22. Dogonchi AS, Ismael MA, Chamkha AJ, Ganji DD. Numerical analysis of natural convection of Cu–water nanofluid filling triangular cavity with semicircular bottom wall. J Therm Anal Calorim. 2019;135:3485–97.

    Article  CAS  Google Scholar 

  23. Dogonchi AS, Nayak MK, Karimi N, Chamkha AJ, Ganji DD. Numerical simulation of hydrothermal features of Cu–H2O nanofluid natural convection within a porous annulus considering diverse configurations of heater. J Therm Anal Calorim. 2020. https://doi.org/10.1007/s10973-020-09419-y.

    Article  Google Scholar 

  24. Asadzadeh F, Esfahany MN, Etesami N. Natural convective heat transfer of Fe3O4/ethylene glycol nanofluid in electric field. Int J Therm Sci. 2012;62:114–9.

    Article  CAS  Google Scholar 

  25. Rohsenow W, Hartnett J, Cho Y. Handbook of heat transfer. New York: McGraw-Hill; 1998.

    Google Scholar 

  26. Shu H, Lai F. Effect of electrical field on buoyancy-induced flows in an enclosure. In: Industry Applications Conference, Orlando, FL, USA, 1995.

  27. Sheikholeslami M, Hayat T, Alsaedi A, Abelman S. Numerical analysis of EHD nanofluid force convective heat transfer considering electric field dependent viscosity. Int J Heat Mass Transf. 2017;108:2558–65.

    Article  CAS  Google Scholar 

  28. Voller VR. Basic control volume finite element methods for fluids and solids. Singapore: World Scientific; 2009.

    Book  Google Scholar 

  29. Worraker WJ, Richardson AT. The effect of temperature-induced variations in charge carrier mobility on a stationary electrohydrodynamic instability. J Fluid Mech. 1979;93:29–45.

    Article  Google Scholar 

  30. Martin PJ, Richardson AT. Conductivity models of electrothermal convection in a plane layer of dielectric liquid. J. Heat Transf. 1984;106:131–6.

    Article  Google Scholar 

  31. Cheng D. Field and wave electromagnetics. Massachusetts: Addison-Wesley; 1989.

    Google Scholar 

  32. Jin J. The finite element method in electromagnetics. New York: Wiley; 1993.

    Google Scholar 

  33. Batchelor GK. An introduction to fluid dynamics. Cambridge: Cambridge University Press; 1967.

    Google Scholar 

  34. Pak BC, Cho YI. Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles. Exp Heat Transf Int J. 1998;11:151–70.

    Article  CAS  Google Scholar 

  35. Mahmoudi AH, Pop I, Shahi M. Effect of magnetic field on natural convection in a triangular enclosure filled with nanofluid. Int J Therm Sci. 2012;59:126–40.

    Article  CAS  Google Scholar 

  36. Moraveji MK, Ardehali RM. CFD modeling (comparing single and two-phase approaches) on thermal performance of Al2O3/water nanofluid in mini-channel heat sink. Int Commun Heat Mass Transf. 2013;44:157–64.

    Article  CAS  Google Scholar 

  37. Saghir MZ, Ahadi A, Mohamad A, Srinivasan S. Water aluminum oxide nanofluid benchmark model. Int J Therm Sci. 2016;109:148–58.

    Article  CAS  Google Scholar 

  38. Hosseinizadeh SF, Raienatai Darzi AA, Tan FL. Numerical investigations of unconstrained melting of nano-enhanced phase change material (NEPCM) inside a spherical container. Int J Therm Sci. 2012;51:77–83.

    Article  CAS  Google Scholar 

  39. Manninen M, Taivassalo V, Kallio S. On the mixture model for multiphase flow. Espoo: VTT Publications; 1996.

    Google Scholar 

  40. Crowe CT, Schwarzkopf JD, Sommerfeld M, Tsuji Y. Multiphase flows with droplets and particles. New York: Taylor & Francis Group; 2011.

    Book  Google Scholar 

  41. Schiller L, Naumann A. A drag coefficient correlation. Amsterdam: Z. Ver. Duutsch. Ing; 1935.

    Google Scholar 

  42. Incropera F, DeWitt D, Bergman T, Lavine A. Fundamentals of heat and mass transfer. New York: Wiley; 2006.

    Google Scholar 

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Acknowledgements

Partial financial support of Isfahan University of Technology is appreciated.

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Authors and Affiliations

  1. Department of Chemical Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    N. Etesami & S. Tavakoli

  2. Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, 11365-9465, Iran

    S. Tavakoli & M. R. Pishvaie

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  1. N. Etesami
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  3. M. R. Pishvaie
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Correspondence to N. Etesami.

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Etesami, N., Tavakoli, S. & Pishvaie, M.R. Theoretical comparative assessment of single- and two-phase models for natural convection heat transfer of Fe3O4/ethylene glycol nanofluid in the presence of electric field. J Therm Anal Calorim 146, 981–992 (2021). https://doi.org/10.1007/s10973-020-10059-5

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