Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-28T04:01:27.864Z Has data issue: false hasContentIssue false
  • English
  • Français

Rayleigh–Bénard instability in nanofluids: effect of gravity settling

Published online by Cambridge University Press:  26 October 2022

Min-Hsing Chang Open the ORCID record for Min-Hsing Chang [Opens in a new window]  and
An-Cheng Ruo Open the ORCID record for An-Cheng Ruo [Opens in a new window]
Min-Hsing Chang
Affiliation:
Department of Mechanical and Materials Engineering, Tatung University, Taipei 104, Taiwan
An-Cheng Ruo*
Affiliation:
Department of Mechanical and Electro-Mechanical Engineering, National Ilan University, Yilan 260, Taiwan
*
†Email address for correspondence: acruo@niu.edu.tw
Get access Rights & Permissions [Opens in a new window]

Abstract

Understanding the mechanism of thermal instability in nanofluids is of fundamental importance to explore the reasons behind the enhancement of heat transfer efficiency. Since Buongiorno (ASME J. Heat Transfer, vol. 128, 2006, pp. 240–250) proposed his theoretical model of nanofluids, most studies focusing on the thermal instability analysis exclusively considered Brownian motion and thermophoresis as the main diffusion mechanisms of nanoparticles. All the analyses concluded that a nanofluid layer is much more unstable than its pure counterpart as it is heated from below. However, a recent experimental observation on Rayleigh–Bénard convection appears to contradict the theoretical prediction, implying that some mechanisms neglected in the previous model may have a significant impact on the onset of thermal convection. In the present study, we revise the convective transport model of nanofluids proposed by Buongiorno and find that the gravitational settling of nanoparticles is a crucial factor influencing the thermal instability behaviour of nanofluids. By performing a linear stability analysis based on the novel model, the effect of gravity settling exhibits a stabilizing mechanism to resist the destabilizing effect of thermophoresis. Furthermore, the onset of instability can be delayed once the nanoparticle diameter exceeds a certain threshold, which explains the phenomenon observed in experiments. Particularly, the oscillatory mode is found to emerge and dominate the flow instability when the gravity settling effect is competitive with the effect of thermophoresis.

JFM classification

Complex Fluids: Suspensions Convection: Buoyancy-driven instability Micro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 950 , 10 November 2022 , A37
Check for updates
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ahuja, J. & Sharma, J. 2020 Rayleigh–Bénard instability in nanofluids: a comprehensive review. Micro Nano Syst. Lett. 8, 21.CrossRefGoogle Scholar
Ambreen, T. & Kim, M.-H. 2020 Influence of particle size on the effective thermal conductivity of nanofluids: a critical review. Appl. Energy 264, 114684.CrossRefGoogle Scholar
Angayarkanni, S.A. & Philip, J. 2015 Review on thermal properties of nanofluids: recent developments. Adv. Colloid Interface Sci. 225, 146–176.CrossRefGoogle ScholarPubMed
Avramenko, A.A., Blinov, D.G. & Shevchuk, I.V. 2011 Self-similar analysis of fluid flow and heat-mass transfer of nanofluids in boundary layer. Phys. Fluids 23, 082002.CrossRefGoogle Scholar
Bashirnezhad, K., Bazri, S., Safaei, M.R., Goodarzi, M., Dahari, M., Mahian, O., Dalkılıça, A.S. & Wongwises, S. 2016 Viscosity of nanofluids: a review of recent experimental studies. Intl Commun. Heat Mass Transfer 73, 114–123.CrossRefGoogle Scholar
Berger Bioucas, F.E., Rausch, M.H., Schmidt, J., Bück, A., Koller, T.M. & Fröba, A.P. 2020 Effective thermal conductivity of nanofluids: measurement and prediction. Intl J. Thermophys. 41, 55.CrossRefGoogle Scholar
Boyd, J.P. 1989 Chebyshev & Fourier Spectral Methods. Springer.CrossRefGoogle Scholar
Buongiorno, J. 2006 Convective transport in nanofluids. Trans. ASME J. Heat Transfer 128, 240–250.CrossRefGoogle Scholar
Canuto, C., Hussaini, M.Y., Quarteroni, A. & Zang, T.A. 2007 Spectral Methods-Evolution to Complex Geometries and Applications to Fluid Dynamics. Springer.CrossRefGoogle Scholar
Chebbi, R. 2017 A theoretical model for thermal conductivity of nanofluids. Mater. Exp. 7, 51–58.CrossRefGoogle Scholar
Choi, S.U.S. & Eastman, J.A. 1995 Enhancing thermal conductivity of fluids with nanoparticles. ASME –Publ. –Fed. 231, 99–106.Google Scholar
Dastvareh, B. & Azaiez, J. 2018 Thermophoretic effects on instabilities of nanoflows in porous media. J. Fluid Mech. 857, 173–199.CrossRefGoogle Scholar
Ding, Y., Alias, H., Wen, D. & Williams, R.A. 2006 Heat transfer of aqueous suspensions of carbon nanotubes (CNT nanofluids). Intl J. Heat Mass Transfer 49, 240–250.CrossRefGoogle Scholar
Eastman, J.A., Choi, S.U.S., Li, S., Yu, W. & Thompson, L.J. 2001 Anomalously increased effective thermal conductivities of ethylene-glycol-based nanofluids containing copper nanoparticles. Appl. Phys. Lett. 6, 718–720.CrossRefGoogle Scholar
Garoosi, F., Jahanshaloo, L., Rashidi, M.M., Badakhsh, A. & Ali, M.E. 2015 Numerical simulation of natural convection of the nanofluid in heat exchangers using a Buongiorno model. Appl. Math. Comput. 254, 183–203.Google Scholar
Gonçalves, I., Souza, R., Coutinho, G., Miranda, J., Moita, A., Pereira, J.E., Moreira, A. & Lima, R. 2021 Thermal conductivity of nanofluids: a review on prediction models, controversies and challenges. Appl. Sci. 11, 2525.CrossRefGoogle Scholar
Gutkowicz-Krusin, D., Collins, M.A. & Ross, J. 1979 Rayleigh–Bénard instability in nonreactive binary fluids. I. Theory. Phys. Fluids 22, 1443.CrossRefGoogle Scholar
Haddad, Z., Abu-Nada, E., Oztop, H.F. & Mataoui, A. 2012 Natural convection in nanofluids: are the thermophoresis and Brownian motion effects significant in nanofluid heat transfer enhancement? Intl J. Therm. Sci. 57, 152–162.CrossRefGoogle Scholar
Keblinski, P., Phillpot, S.R., Choi, S.U. & Eastman, J.A. 2002 Mechanisms of heat flow in suspensions of nano-sized particles (nanofluids). Intl J. Heat Mass Transfer 45, 855–863.CrossRefGoogle Scholar
Keblinski, P., Prasher, R. & Eapen, J. 2008 Thermal conductance of nanofluids: is the controversy over? J. Nanopart. Res. 10, 1089–1097.CrossRefGoogle Scholar
Kleinstreuer, C. & Feng, Y. 2011 Experimental and theoretical studies of nanofluid thermal conductivity enhancement: a review. Nanoscale Res. Lett. 6 (1), 229.CrossRefGoogle ScholarPubMed
Kumar, R., Sharma, J. & Sood, J. 2020 Rayleigh–Bénard cell formation of green synthesized nano-particles of silver and selenium. Mater. Today: Proc. 28, 1781–1787.Google Scholar
Kuznetsov, A.V. & Nield, D.A. 2010 Thermal instability in a porous medium layer saturated by a nanofluid: Brinkman model. Transp. Porous Med. 81, 409–422.CrossRefGoogle Scholar
Lee, J.-H., Hwang, K.-S., Jang, S.-P., Lee, B.-H., Kim, J.-H., Choi, S.U.S. & Choi, C.J. 2008 Effective viscosities and thermal conductivities of aqueous nanofluids containing low volume concentrations of Al2O3 nanoparticles. Intl J. Heat Mass Transfer 51, 2651–2656.CrossRefGoogle Scholar
Lekkerkerker, H. N. W. 1982 The physical mechanism of oscillatory and finite amplitude instabilities in systems with competing effects. In: Nonlinear Phenomena at Phase Transitions and Instabilities (ed. Riste, T.), NATO Advanced Study Institutes Series, vol. 77. Springer.Google Scholar
Lhost, O. & Platten, J.K. 1989 Large-scale convection induced by the Soret effect. Phys. Rev. A 40 (11), 6415–6420.CrossRefGoogle ScholarPubMed
Mahian, O., Kianifari, A., Kalogirou, S.A., Pop, I. & Wongwises, S. 2013 A review of the applications of nanofluids in solar energy. Intl J. Heat Mass Transfer 57, 582–594.CrossRefGoogle Scholar
Mahian, O., Kolsi, L., Amani, M., Estellé, P., Ahmadi, G., Kleinstreuer, C., Marshall, J.S., Siavashi, M., Taylor, R.A., Niazmand, H., Wongwises, S., Hayat, T., Kolanjiyil, A., Kasaeian, A. & Pop, I. 2019 Recent advances in modeling and simulation of nanofluid flows – Part I: fundamentals and theory. Phys. Rep. 790, 1–48.CrossRefGoogle Scholar
Maiga, S., Nguyen, C.T., Galanis, N. & Roy, G. 2004 Heat transfer behaviors of nanofluids in a uniformly heated tube. Superlattices Microstruct. 35, 543–557.CrossRefGoogle Scholar
Malvandi, A., Moshizi, S.A., Soltani, E.G. & Ganji, D.D. 2014 Modified Buongiorno's model for fully developed mixed convection flow of nanofluids in a vertical annular pipe. Comput. Fluids 89, 124–132.CrossRefGoogle Scholar
Masuda, H., Ebata, A., Teramae, K. & Hishinuma, N. 1993 Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles. Netsu Bussei 7 (4), 227–233.CrossRefGoogle Scholar
Murshed, S.M.S. & Estellé, P. 2017 A state of the art review on viscosity of nanofluids. Renew. Sustain. Energy Rev. 76, 1134–1152.CrossRefGoogle Scholar
Namburu, P.K., Kulkarni, D.P., Dandekar, A. & Das, D.A. 2007 Experimental investigation of viscosity and specific heat of silicon dioxide nanofluids. Micro Nano Lett. 2, 67–71.CrossRefGoogle Scholar
Nguyen, C.T., Desgranges, F., Roy, G., Galanis, N., Maré, T., Boucher, S. & Angue Mintsa, H. 2007 Temperature and particle-size dependent viscosity data for water-based nanofluids - hysteresis phenomenon. Intl J. Heat Fluid Flow 28, 1492–1506.CrossRefGoogle Scholar
Nield, D.A. & Kuznetsov, A.V. 2010 The onset of convection in a horizontal nanofluid layer of finite depth. Eur. J. Mech. B/Fluids 29, 217–223.CrossRefGoogle Scholar
Nield, D.A. & Kuznetsov, A.V. 2014 The onset of convection in a horizontal nanofluid layer of finite depth: a revised model. Intl J. Heat Mass Transfer 77, 915–918.CrossRefGoogle Scholar
Özerinç, S. & Kakaç, S. 2010 Enhanced thermal conductivity of nanofluids: a state-of-the-art review. Microfluid. Nanofluid. 8, 145–170.CrossRefGoogle Scholar
Pak, B.C. & Cho, Y. 1998 Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles. Exp. Heat Transfer 11, 151–170.CrossRefGoogle Scholar
Ruo, A.-C., Yan, W.-M. & Chang, M.-H. 2021 The onset of natural convection in a horizontal nanofluid layer heated from below. Heat Transfer 50 (8), 7764–7783.CrossRefGoogle Scholar
Saidur, R., Leong, K.Y. & Mohammad, H.A. 2011 A review on applications and challenges of nanofluids. Renew. Sustain. Energy Rev. 15, 1646–1668.CrossRefGoogle Scholar
Sheremet, M.A. & Pop, I. 2014 Conjugate natural convection in a square porous cavity filled by a nanofluid using Buongiorno's mathematical model. Intl J. Heat Mass Transfer 79, 137–145.CrossRefGoogle Scholar
Tzou, D.Y. 2008 a Instability of nanofluids in natural convection. ASME J. Heat Transfer 130, 072401.CrossRefGoogle Scholar
Tzou, D.Y. 2008 b Thermal instability of nanofluids in natural convection. Intl J. Heat Mass Transfer 51, 2967–2979.CrossRefGoogle Scholar
Vajjha, R.S. & Das, D.K. 2009 Specific heat measurement of three nanofluids and development of new correlations. Trans ASME J. Heat Transfer 131, 071601.CrossRefGoogle Scholar
Wang, X.-Q. & Mujumdar, A.S. 2007 Heat transfer characteristics of nanofluids: a review. Intl J. Therm. Sci. 46, 1–19.CrossRefGoogle Scholar
Xuan, Y. & Li, Q. 2003 Investigation on convective heat transfer and flow features of nanofluids. J. Heat Transfer 125, 151–155.CrossRefGoogle Scholar
Yazida, M.N.A.W.M., Sidik, N.A.C. & Yahya, W.J. 2017 Heat and mass transfer characteristics of carbon nanotube nanofluids: a review. Renew. Sustain. Energy Rev. 80, 914–941.CrossRefGoogle Scholar
Zhou, S.-Q. & Ni, R. 2008 Measurement of the specific heat capacity of water-based Al2O3 nanofluid. Appl. Phys. Lett. 92, 093123.CrossRefGoogle Scholar