A revised model for the effect of nanoparticle mass flux on the thermal instability of a nanofluid layer

• Autorzy: Alharbi Ozwah S. , Abdullah Abdullah A.

Identyfikatory

DOI

10.1515/dema-2021-0045

• Języki publikacji: EN

Abstrakty

EN

A revised model of the nanoparticle mass flux is introduced and used to study the thermal instability of the Rayleigh-Benard problem for a horizontal layer of nanofluid heated from below. The motion of nanoparticles is characterized by the effects of thermophoresis and Brownian diffusion. The nanofluid layer is confined between two rigid boundaries. Both boundaries are assumed to be impenetrable to nanoparticles with their distribution being determined from a conservation condition. The material properties of the nanofluid are allowed to depend on the local volume fraction of nanoparticles and are modelled by non-constant constitutive expressions developed by Kanafer and Vafai based on experimental data. The results show that the profile of the nanoparticle volume fraction is of exponential type in the steady-state solution. The resulting equations of the problem constitute an eigenvalue problem which is solved using the Chebyshev tau method. The critical values of the thermal Rayleigh number are calculated for several values of the parameters of the problem. Moreover, the critical eigenvalues obtained were real-valued, which indicates that the mode of instability is via a stationary mode.

Słowa kluczowe

EN

linear stability; Rayleigh-Benard convection; nanofluid; thermophoresis; Brownian; Chebyshev tau method

PL

stabilność liniowa; konwekcja Rayleigha-Benarda; nanociecze; termoforeza; metoda Czebyszewa

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2021
• Tom: Vol. 54, nr 1
• Strony: 488--499
• Opis fizyczny: Bibliogr. 25 poz., rys., tab.

Twórcy

autor

Alharbi Ozwah S.

• Department of Mathematical Sciences, Umm Al-Qura University, Makkah, Saudi Arabia

autor

Abdullah Abdullah A.

• Department of Mathematical Sciences, Umm Al-Qura University, Makkah, Saudi Arabia

Bibliografia

• [1] H. Masuda, A. Ebata, K. Teramae, and N. Hishinuma, Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles, Netsu. Bussei. 7 (1993), 227–233, DOI: https://doi.org/10.2963/jjtp.7.227.
• [2] S. Choi and J. Eastman, Enhancing thermal conductivity of fluids with nanoparticles, in: International Mechanical Engineering Congress & Exposition, ASME, San Francisco, 1995.
• [3] J. Eastman, S. Choi, S. Li, W. Yu, and L. Thompson, Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles, Appl. Phys. Lett. 78 (2001), 718–720, DOI: https://doi.org/10.1063/1.1341218.
• [4] S. Das, N. Putra, and W. Roetzel, Pool boiling characteristics of nano-fluids, Int. J. Heat Mass Trans. 46 (2003), no. 5, 851–862, DOI: https://doi.org/10.1016/S0017-9310(02)00348-4.
• [5] S. Jain, H. Patel, and S. Das, Brownian dynamic simulation for the prediction of effective thermal conductivity of nanofluid, J. Nanopart. Res. 11 (2009), 767, DOI: https://doi.org/10.1007/s11051-008-9454-4.
• [6] J. Kim, Y. Kang, and C. Choi, Analysis of convective instability and heat transfer characteristics of nanofluids, Phys. Fluids 16 (2004), no. 7, 2395–2401, DOI: https://doi.org/10.1063/1.1739247.
• [7] J. Buongiorno, Convective transport in nanofluids, J. Heat Trans. ASME 128 (2006), 240–250, DOI: https://doi.org/10.1115/1.2150834.
• [8] D. Tzou, Thermal instability of nanofluids in natural convection, Int. J. Heat Mass Trans. 51 (2008), 2967–2979, DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2007.09.014.
• [9] D. Tzou, Instability of nanofluids in natural convection, ASME J. Heat Trans. 130 (2008), no. 7, 072401, DOI: https://doi.org/10.1115/1.2908427.
• [10] A. V. Kuznetsov and D. A. Nield, Thermal instability in a porous medium layer saturated by a nanofluid, Int. J. Heat Mass Trans. 52 (2009), 5796–5801, DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2009.07.023.
• [11] D. A. Nield and A. V. Kuznetsov, The onset of convection in a horizontal nanofluid layer of finite depth, Eur. J. Mech. B/ Fluids 29 (2010), 217–223, DOI: https://doi.org/10.1016/j.euromechflu.2010.02.003.
• [12] D. Yadav, G. S. Agrawal, and R. Bhargava, Thermal instability of rotating nanofluid layer, Int. J. Eng. Sci. 49 (2011), 1171–1184, DOI: https://doi.org/10.1016/j.asej.2015.05.005.
• [13] D. Yadav, R. Bhargava, and G. S. Agrawal, Thermal instability in a nanofluid layer with a vertical magnetic field, J. Eng. Math. 80 (2013), 147–164, DOI: https://doi.org/10.1007/s10665-012-9598-1.
• [14] A. Mahajan and M. Arora, Convection in rotating magnetic nanofluids, Appl. Math. Comput. 219 (2013), 3284–6296, DOI: https://doi.org/10.1016/j.amc.2012.12.012.
• [15] D. A. Nield and A. V. Kuznestov, The onset of convection in a horizontal nanofluid layer of finite depth: a revised model, Int. J. Heat Mass Trans. 77 (2014), 915–918, DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2014.06.020.
• [16] S. Agarwal, P. Rana, and B. S. Bhadauria, Rayleigh-Benard convection in a nanofluid layer using a thermal nonequilibrium model, ASME J. Heat Trans. 136 (2014), no. 12, 122501, DOI: https://doi.org/10.1115/1.4028491.
• [17] D. Yadav, C. Kim, J. Lee, and H. H. Cho, Influence of magnetic field on the onset of nanofluid convection induced by purely internal heating, Comput. Fluids 121 (2015), 26–36, DOI: https://doi.org/10.1016/j.compfluid.2015.07.024.
• [18] S. Agarwal and P. Rana, Convective heat transport by longitudinal rolls in dilute nanoliquid layer of finite depth, Int. J. Therm. Sci. 108 (2016), 235–243, DOI: https://doi.org/10.1016/j.ijthermalsci.2016.05.013.
• [19] A. Abdullah and K. Lindsay, Marangoni convection in a layer of nanofluid, Int. J. Heat Mass Trans. 104 (2017), 693–702, DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2016.08.099.
• [20] A. Abdullah, S. Althobaiti, and K. Lindsay, Marangoni convection in water-alumina nanofluids: Dependence on the nanoparticle size, Eur. J. Mech. B/Fluids 67 (2018), 259–268, DOI: https://doi.org/10.1016/j.euromechflu.2017.09.015.
• [21] G. Rana, P. Gautam, and H. Saxena, Electrohydrodynamic thermal instability in a walters (MODEL B) rotating nanofluid saturating a porous medium, J. Serb. Soc. Comput. Mech. 13 (2019), 19–35, DOI: https://doi.org/10.24874/jsscm.2019.13.02.03.
• [22] J. Ahuja and U. Gupta, Magneto convection in rotating nanofluid layer: Local thermal non-equilibrium model, J. Nanofluids 8 (2019), no. 2, 430–438, DOI: https://doi.org/10.1166/jon.2019.1585.
• [23] K. Khanafer and K. Vafai, A critical synthesis of thermophysical characteristics of nanofluids, Int. J. Heat Mass Trans. 4 (2011), 4410–4428, DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2011.04.048.
• [24] H. C. Brinkman, The viscosity of concentrated suspensions and solutions, J. Chem. Phys. 20 (1952), no. 4, 571, DOI: https://doi.org/10.1063/1.1700493.
• [25] R. Hamilton and O. K. Crosser, Thermal conductivity of heterogeneous two-component systems, Ind. Eng. Chem. Fundamen. 1 (1962), no. 3, 187–191, DOI: https://doi.org/10.1021/i160003a005.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).