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Convective Transport of Nanofluid Saturated with Porous Layer

Received: 10 November 2016     Accepted: 26 November 2016     Published: 18 January 2017
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Abstract

In the present article, the onset of convection in a horizontal layer of porous medium saturated by ananofluid is investigated analytically using linear and weakly nonlinear analysis. The model used for the nanofluid incorporates the effect of Brownian motion and thermophoresis. The effect of Raleigh-Darcy number, Lewis number, modified diffusivity ratio, on the stability of the system is investigated. Stationary and Oscillatory modes of convections has been studied. The linear stability analysis is based on normal mode technique, while then on linear theory is based on the truncated representation of Fourier series method. A weekly nonlinear analysis is used to obtain the concentration and thermal Nusselt number. The behavior of the concentration and thermal Nusselt number is investigated by solving the finite amplitude equations. Obtained results have been presented graphically and discussed in details.

Published in American Journal of Applied Mathematics (Volume 5, Issue 1)
DOI 10.11648/j.ajam.20170501.11
Page(s) 1-13
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Nanofluid, Porous Medium, Instability, Natural Convection

References
[1] Choi, S.: Enhancing thermal conductivity of fluids with nanoparticles. In: Signier, D. A., Wang, H. P. (eds.) Development and application of Non-Newtonian flows, ASME FED, Vol.231/MD Vol.66, pp.99-105 (1995).
[2] Masuda, H., Ebata, A., Teramae, K., Hishinuma, N.: Alteration of thermal conductivity and viscosity of liquid by dispersing ultra fine particles. Netsu Bussei 7, 227-233 (1993).
[3] Eastman, J. A., Choi, S. U. S., Tu, W., Thosmpson, L. J.: Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles. Appl. Phys. Lett. 78, 718-720(2001).
[4] Das, S. K., Putra, N., Thiesen, P., Roetzel, W.: Temperature dependence of thermal conductivity enhancement for nanofulids. ASME J. Heat Transf. 125, 567-574 (2003).
[5] Buongiorno, J.: Convective transport in nanofluids. ASME J. Heat Transer. 128, 240-250 (2006)
[6] Pearlstein, A. J: Effect of rotation on the stability of a doubly diffusive fluid layer. J. Fluid Mech. 103, 389-412(1981).
[7] Chakrabarti, A, Gupta, A. S.: Nonlinear thermo- haline convection in a rotating porous medium. Mech. Res. Commun. 8, 9-22(1981).
[8] Patil, P. R., Vidyanathan, G.: On setting up of convective currents in a ratoting porous medium under the influence of variable viscosity. Int. J. Eng. Sci. 21,123-130(1983).
[9] Vadasz, P: Free Convection in Rotating Porous Media, Transport Phenomena in Porous Media. pp. 285-312. Elsevier, Amsterdam (1998).
[10] Horton, W., Rogers, F. T.: Convection currents in a porous medium. J. Appl. Phys. 16, 367-370(1945).
[11] Lapwood, E. R.: Convection of a fluid in a porous medium. Proc. Camb. Phil. Soc. 44,508-521(1948).
[12] Neild, D. A.: Onset of thermohaline convection in a porous medium. Water Resour. Res. 4, 553-560(1968).
[13] Rudraiah, N., Malashetty, M. S.: The influence of couple molecular diffusion on the double diffusive convection in a porous medium. ASME J. Heat Transf. 108, 872-876(1986).
[14] Murray, B. T., Chen, C. F.: Double diffusive convection in a porous medium. J. Fluid Mech. 201, 147-166 (1989).
[15] Bhadauria, B. S.: Double diffusive convection in a porous medium with modulated temperature on the boundaries. Transp. Porous Med. 70, 191-211 (2007a).
[16] Vafai, K.: Handbook of Porous Media. Taylor and Francis, London (2005).
[17] Neild, D. A., Bejan, A.: Convection in Porous Media. 3rd edn. Springer, New York (2006).
[18] Neild, D. A., Kuznetsov, A. V.: Thermal instability in aporous medium layer saturated by nonofluid. Int. J. Heat Mass Transf. 52, 5796-5801(2009a).
[19] Neild, D. A., Kuznetsov, A. V.: The cheng-Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid. Int J. Heat Mass Transf. 52, 5792-5795(2009b).
[20] Neild, D. A., Kuznetsov, A. V.: The onset of convection in a horizontal nanofluid layer of finite dept. Eur. J. Mech. B 29, 217-223 (2010).
[21] Agarwal, S., Bhadauria, B. S., Siddheshwar, P. G.: Thermal instability of a nanofluid saturating a rotating anisotropic porous medium. Spec. Top. Rev. Porous Media Begell House Publ. 2(1), 53-64 (2001).
[22] Bhadauria, B. S., Agarwal, S., Kumar, A.: Non-linear two-dimensional convection in a nanofluid saturated porous medium. Transp. Porous Media 90(2), 605-625(2011).
[23] Umavathi, J. C.: Rayleigh Benard convection subject to time dependent wall temperature in a porous medium layer saturated by a nanofluid. Meccanica. 50,981-984(2015)
[24] Umavathi, J. C. and Monica B Mohite.: Convective transport in a porous medium layer satuated with a Maxwell nanofluid. Jour of King Saud University-Engineering sciences. 28,56-68(2016).
[25] Umavathi, J. C. and Prathap Kumar, J.: Onset of Convection in a porous medium layer saturated with an Oldoyd nanofluid, ASME J. Heat Transf. 139, 012401-0124014(2016).
[26] Nield, D. A., Bejan, A.: Convection in porous Medial, third ed., Springer, New York, 2006.
[27] Kuznetsov, A. V., Avramenko, A. A.: Effect of small particles on the stability of bioconvection in a suspension of gyrotactic microorganisms in a layerof finite length, Int. Commun. Heat Mass Transfer 31, 1-10 (2004).
[28] Buongiorno, J. and Hu, L. W. “Nanofluid Coolants for Advanced Nuclear Power Plants”, Paper 5705, Proceedings of ICAPP ’05, Seoul, May 15-19. (2005).
[29] Bhadauria B. S, Agarwal S: Natural convection in a nanofluid saturated rotating porous layer, a nonlinear study. Transp Porous Media 87(2), 585-602(2011).
[30] Tiwari R. K, Das M. K: Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluid. Int. J Heat Mass Transf, 50, 2002-2018(2007).
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  • APA Style

    Jada Prathap Kumar, Jawali Channabasappa Umavathi, Channakeshava Murthy. (2017). Convective Transport of Nanofluid Saturated with Porous Layer. American Journal of Applied Mathematics, 5(1), 1-13. https://doi.org/10.11648/j.ajam.20170501.11

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    ACS Style

    Jada Prathap Kumar; Jawali Channabasappa Umavathi; Channakeshava Murthy. Convective Transport of Nanofluid Saturated with Porous Layer. Am. J. Appl. Math. 2017, 5(1), 1-13. doi: 10.11648/j.ajam.20170501.11

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    AMA Style

    Jada Prathap Kumar, Jawali Channabasappa Umavathi, Channakeshava Murthy. Convective Transport of Nanofluid Saturated with Porous Layer. Am J Appl Math. 2017;5(1):1-13. doi: 10.11648/j.ajam.20170501.11

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  • @article{10.11648/j.ajam.20170501.11,
      author = {Jada Prathap Kumar and Jawali Channabasappa Umavathi and Channakeshava Murthy},
      title = {Convective Transport of Nanofluid Saturated with Porous Layer},
      journal = {American Journal of Applied Mathematics},
      volume = {5},
      number = {1},
      pages = {1-13},
      doi = {10.11648/j.ajam.20170501.11},
      url = {https://doi.org/10.11648/j.ajam.20170501.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20170501.11},
      abstract = {In the present article, the onset of convection in a horizontal layer of porous medium saturated by ananofluid is investigated analytically using linear and weakly nonlinear analysis. The model used for the nanofluid incorporates the effect of Brownian motion and thermophoresis. The effect of Raleigh-Darcy number, Lewis number, modified diffusivity ratio, on the stability of the system is investigated. Stationary and Oscillatory modes of convections has been studied. The linear stability analysis is based on normal mode technique, while then on linear theory is based on the truncated representation of Fourier series method. A weekly nonlinear analysis is used to obtain the concentration and thermal Nusselt number. The behavior of the concentration and thermal Nusselt number is investigated by solving the finite amplitude equations. Obtained results have been presented graphically and discussed in details.},
     year = {2017}
    }
    

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    T1  - Convective Transport of Nanofluid Saturated with Porous Layer
    AU  - Jada Prathap Kumar
    AU  - Jawali Channabasappa Umavathi
    AU  - Channakeshava Murthy
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    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
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    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.20170501.11
    AB  - In the present article, the onset of convection in a horizontal layer of porous medium saturated by ananofluid is investigated analytically using linear and weakly nonlinear analysis. The model used for the nanofluid incorporates the effect of Brownian motion and thermophoresis. The effect of Raleigh-Darcy number, Lewis number, modified diffusivity ratio, on the stability of the system is investigated. Stationary and Oscillatory modes of convections has been studied. The linear stability analysis is based on normal mode technique, while then on linear theory is based on the truncated representation of Fourier series method. A weekly nonlinear analysis is used to obtain the concentration and thermal Nusselt number. The behavior of the concentration and thermal Nusselt number is investigated by solving the finite amplitude equations. Obtained results have been presented graphically and discussed in details.
    VL  - 5
    IS  - 1
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Author Information
  • Department of Mathematics, Gulbarga University, Kalaburagi, Karnataka, India

  • Department of Mathematics, Gulbarga University, Kalaburagi, Karnataka, India

  • Department of Mathematics, Gulbarga University, Kalaburagi, Karnataka, India

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