Abstract

In this paper a uniqueness theorem for classical solutions is proved in the case of the evolution of a nanofluid filling a bounded domain under the Boussinesq approximation. The mass density of the nanofluid depends on the temperature and on the nanoparticle volume fraction. A decay in time of a suitable energy is achieved assuming that the material parameters satisfy some conditions. These results are then generalized in the presence of a magnetic field.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 32
Issue: 4
Year: 2019

DOI: 10.12732/ijam.v32i4.2

Download Section

Download the full text of article from here.

You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.

References

1. [1] R. Azizian, E. Dorooduchi, T. McKrell, J. Buongiorno, L.W. Hu, B. Moghtaderi, Effect of magnetic field on laminar convective heat transfer of magnetite nanofluids, Int. J. Heat Mass Transfer, 68 (2014), 94-109.
2. [2] J. Buongiorno et al., A benchmark study on the thermal conductivity of nanofluids, J. Appl. Phys., 106 (2009), 1-14.
3. [3] A. Borrelli, G. Giantesio, M.C. Patria, A.V. Rosca, N.C. Rosca, I. Pop, Influence of temperature and magnetic field on the oblique stagnation-point flow for a nanofluid past a vertical stretching/shrinking sheet, Intern. J. of Numerical Methods for Heat & Fluid Flow, 28 (2018), 2874-2894.
4. [4] J. Buongiorno, Convective transport in nanofluids, ASME J. Heat Transfer, 128 (2006), 240-250.
5. [5] S.U.S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, In: Proc. of the 1995 ASME Intern. Mechanical Engineering Congress and Exposition 66, ASME, San Francisco, CA, 99-105.
6. [6] S.K. Das, S.U.S. Choi, W. Yu, Y. Pradeep, Nanofluids: Science and Technology, Wiley, New Jersey (2008).
7. [7] J. Fan, L. Wang, Review of heat conduction in nanofluids, ASME J. Heat Transfer, 133 (2011), 1-14.
8. [8] D.H. Fontes, D. Dall’Onder dos Santos, E.L. Mart`ınez Padilla, E.P. Bandarra Filh, Two numerical modelings of free convection heat transfer using nanofluids inside a square enclosure, Mech. Res. Comm., 66 (2015), 34-43.
9. [9] S. Kaka¸c, A. Pramuanjaroenkij, Review of convective heat transfer enhancement with nanofluids, Int. J. Heat Mass Transfer, 52 (2009), 31873196.
10. [10] A.U. Khan, S. Nadeem, S.T. Hussain, Phase flow study of MHD nanofluid with slip effects on oscillatory oblique stagnation point flow in view of inclined magnetic field, J. of Molecular Liquids, 224 (2016), 1210-1219.
11. [11] D. Khurana, R. Choudhary, S. Subudhi, A critical review of forced convection heat transfer and pressure drop of and CuO nanofluids, Heat Mass Transfer, 53 (2017), 343-361.
12. [12] A.V. Kuznetsov, D.A. Nield, Natural convective boundary-layer flow of a nanofluid past a vertical plate: A revised model, Int. J. Thermal Sci., 77 (2014), 126-129.
13. [13] O. Mahian, A. Kianifar, S.A. Kalogirou, I. Pop, S. Wongwises, A review of the applications of nanofluids in solar energy, Int. J. Heat Mass Transfer, 57 (2013), 582-594.
14. [14] O. Manca, Y. Jaluria, D. Poulikakos, Heat transfer in nanofluids, Adv. Mechanical Engng., (2010), # 380826.
15. [15] A.A. Minea, A study on Brinkman number variation on water based nanofluid heat transfer in partially heated tubes, Mech. Res. Comm., 73 (2016), 7-11.
16. [16] W.J. Minkowycz, E.M. Sparrow, J.P. Abraham (Eds.), Nanoparticle Heat Transfer and Fluid Flow, CRC Press, Taylor & Fracis Group, New York (2013).
17. [17] T.G. Myers, H. Ribera, V. Cregan, Does mathematics contribute to the nanofluid debate?, Int. J. Heat Mass Transfer, 111 (2017), 279-288.
18. [18] M.M. Rahman, T. Grosan, I. Pop. Oblique stagnation-point flow of a nanofluid past a shrinking sheet, Int. J. Numer Methods Heat Fluid Flow, 26 (2016), 189-213.
19. [19] N.C. Ro¸sca, I. Pop, Axisymmetric rotational stagnation point flow impinging radially a permeable stretching/shrinking surface in a nanofluid using Tiwari and Das model, Scientific Reports, 7 (2017), # 40299; DOI: 10.1038/srep40299.
20. [20] M. Sheikholesslami, D.D. Ganji, Applications of Nanofluid for Heat Transfer and Enhancemen, Elsevier, 2017.
21. [21] M. Sheikholeslami, H. B. Rokni, Nanofluid two phase model analysis in existence of induced magnetic field, Int. J. of Heat and Mass Transfer, 107 (2017), 288-299.
22. [22] A. Shenoy, M. Sheremet, I. Pop, Convective Flow and Heat Transfer from Wavy Surfaces: Viscous Fluids, Porous Media and Nanofluids, CRC Press, Taylor & Francis Group, New York, 2016.
23. [23] R.K. Tiwari, M.K. Das, Heat transfer augmentation in a two-sided liddriven differentially heated square cavity utilizing nanofluids, Int. J. Heat Mass Transfer, 50 (2007), 2002-2018.
24. [24] D. Y. Tzou, Thermal instability of nanofluids in natural convection, Int. J. Heat Mass Transfer, 51 (2008), 2967-2979.
25. [25] N.A.Yacob, A. Ishak, I. Pop, K. Vajravelu, Boundary layer flow past a stretching/shrinking surface beneath an external uniform shear flow with a convective surface boundary condition in a nanofluid. Nanoscale Res. Lett., 6 (2011), 1-7.