Convective Transport of Nanofluid Saturated with Porous Layer

Jada Prathap Kumar; Jawali Channabasappa Umavathi; Channakeshava Murthy

doi:doi:10.11648/j.ajam.20170501.11

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Convective Transport of Nanofluid Saturated with Porous Layer

Jada Prathap Kumar, Jawali Channabasappa Umavathi, Channakeshava Murthy

Published in American Journal of Applied Mathematics (Volume 5, Issue 1)

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

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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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TY  - JOUR
T1  - Convective Transport of Nanofluid Saturated with Porous Layer
AU  - Jada Prathap Kumar
AU  - Jawali Channabasappa Umavathi
AU  - Channakeshava Murthy
Y1  - 2017/01/18
PY  - 2017
N1  - https://doi.org/10.11648/j.ajam.20170501.11
DO  - 10.11648/j.ajam.20170501.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 1
EP  - 13
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
ER  -

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Author Information

Jada Prathap Kumar

Department of Mathematics, Gulbarga University, Kalaburagi, Karnataka, India
Jawali Channabasappa Umavathi

Department of Mathematics, Gulbarga University, Kalaburagi, Karnataka, India
Channakeshava Murthy

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

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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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - Convective Transport of Nanofluid Saturated with Porous Layer
AU  - Jada Prathap Kumar
AU  - Jawali Channabasappa Umavathi
AU  - Channakeshava Murthy
Y1  - 2017/01/18
PY  - 2017
N1  - https://doi.org/10.11648/j.ajam.20170501.11
DO  - 10.11648/j.ajam.20170501.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 1
EP  - 13
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
ER  -

Copy | Download