Effect of Buoyancy Force on the Flow Field in a Square Cavity with Heated from Below

Md. Noor-A-Alam Siddiki; Ferjana Habiba; Raju Chowdhury

doi:doi:10.11648/j.dmath.20170202.13

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Effect of Buoyancy Force on the Flow Field in a Square Cavity with Heated from Below

Md. Noor-A-Alam Siddiki, Ferjana Habiba, Raju Chowdhury

Published in International Journal of Discrete Mathematics (Volume 2, Issue 2)

Received: 25 January 2017 Accepted: 8 February 2017 Published: 1 March 2017

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Abstract

In this paper, the effect of buoyancy force in a square enclosure is studied numerically. The coupled equations of continuity, momentum and energy are solved by a finite difference method. The SIMPLE algorithm is used to solve iteratively the pressure-velocities coupling. The numerical investigations in this analysis are made over a wide range of parameters, Rayleigh number and dimensionless heater lengths. Results are presented graphically in the form of streamlines, isotherms and also with a velocity profiles and average Nusselt numbers.

Published in	International Journal of Discrete Mathematics (Volume 2, Issue 2)
DOI	10.11648/j.dmath.20170202.13
Page(s)	43-47
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

Natural Convection, Nusselt Number, Square Cavity, Numerical Simulation, Finite Difference Method, Heat Source, Streamline, Isotherm, Average Nusselt Numbers

References

[1]	G. de Vahl Davis and I. P. Jones, “Natural convection in a square cavity: a comparison exercise”, Int. J. Num. Methods Fluid, vol. 3, pp. 227-249, 1983.
[2]	S. Ostrach, “Natural convection in enclosures”, J. Heat Transfer, vol. 110, pp. 1175-1190, 1988.
[3]	F. A. Kulacki and R. J. Goldstein, “Thermal convection in a horizontal fluid layer with uniform volumetric energy sources”, J. Fluid Mech., vol. 55, pp. 271-287, 1972.
[4]	F. A. Kulacki and M. E. Nagle, “Natural convection in a horizontal fluid layer with volumetric energy sources”, J. Heat Transfer, vol. 97, pp. 204-211, 1975.
[5]	S. Acharya and R. J. Goldstein, “Natural convection in an externally heated vertical or inclined square box containing internal energy sources”, J. Heat Transfer, vol. 107, pp. 855-866, 1985.
[6]	J. H. Lee and R. J. Goldstein, “An experimental study on natural convection heat transfer in an inclined square enclosure containing internal energy sources”, J. Heat Transfer, vol. 110, pp. 345-349, 1988.
[7]	Hakan F. Oztop, Eiyad Abu-Nada, Yasin Varol and Ali Chakma, “Natural convection in wavy enclosures with volumetric heat sources”, Int. J. Thermal sciences, vol. 50, pp. 502-514, 2011.
[8]	D. a. Neild and A. Bejan, Convection in porous Media, Springer, New York, 1998.
[9]	D. B. Ingham and I. Pop, Transport phenomena in porous media, Elsevier, Amsterdam, 1998.
[10]	S. Ostrach, Natural convection in enclosures, J. Heat Transfer 110 (1998), 1175-1190.
[11]	R. Anderson and G Lauriat, The horizontal Natural convection boundary layer regime in a closed cavity, proceedings of the eight international Heat transfer conference, Vol. 4, San Francisco, CA, 1986, pp, 1453-1458.
[12]	Delavar, M. A. and Sedighi, K. [2011] Effect of discrete heater at the vertical wall of the cavity over the heat transfer and entropy generation using Lattice Boltzmann method, Thermal Science, Vol. 15, N, 2, 423-435.
[13]	Radhwan, M. and Zaki, G. M. [2000] Laminar natural convection in a square enclosure with discrete heating of vertical walls, JKAU, Eng. Sci., Vol. 12, N°. 2, 83-99.
[14]	Varol, Y., Oztop, H. F., Koca, A. and Ozgen, F. [2009] Natural convection and fluid flow in inclined enclosure with a corner heater, Applied Thermal Engineering, 29, 340–350.
[15]	Che Sidik, N. A. [2009] Prediction of natural convection in a square cavity with partially heated from below and cooling from SSN -216X Vol. 35 N°3, 347-354. The manuscript number is 147012010.

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APA Style

Md. Noor-A-Alam Siddiki, Ferjana Habiba, Raju Chowdhury. (2017). Effect of Buoyancy Force on the Flow Field in a Square Cavity with Heated from Below. International Journal of Discrete Mathematics, 2(2), 43-47. https://doi.org/10.11648/j.dmath.20170202.13

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ACS Style

Md. Noor-A-Alam Siddiki; Ferjana Habiba; Raju Chowdhury. Effect of Buoyancy Force on the Flow Field in a Square Cavity with Heated from Below. Int. J. Discrete Math. 2017, 2(2), 43-47. doi: 10.11648/j.dmath.20170202.13

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AMA Style

Md. Noor-A-Alam Siddiki, Ferjana Habiba, Raju Chowdhury. Effect of Buoyancy Force on the Flow Field in a Square Cavity with Heated from Below. Int J Discrete Math. 2017;2(2):43-47. doi: 10.11648/j.dmath.20170202.13

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@article{10.11648/j.dmath.20170202.13,
  author = {Md. Noor-A-Alam Siddiki and Ferjana Habiba and Raju Chowdhury},
  title = {Effect of Buoyancy Force on the Flow Field in a Square Cavity with Heated from Below},
  journal = {International Journal of Discrete Mathematics},
  volume = {2},
  number = {2},
  pages = {43-47},
  doi = {10.11648/j.dmath.20170202.13},
  url = {https://doi.org/10.11648/j.dmath.20170202.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20170202.13},
  abstract = {In this paper, the effect of buoyancy force in a square enclosure is studied numerically. The coupled equations of continuity, momentum and energy are solved by a finite difference method. The SIMPLE algorithm is used to solve iteratively the pressure-velocities coupling. The numerical investigations in this analysis are made over a wide range of parameters, Rayleigh number and dimensionless heater lengths. Results are presented graphically in the form of streamlines, isotherms and also with a velocity profiles and average Nusselt numbers.},
 year = {2017}
}

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TY  - JOUR
T1  - Effect of Buoyancy Force on the Flow Field in a Square Cavity with Heated from Below
AU  - Md. Noor-A-Alam Siddiki
AU  - Ferjana Habiba
AU  - Raju Chowdhury
Y1  - 2017/03/01
PY  - 2017
N1  - https://doi.org/10.11648/j.dmath.20170202.13
DO  - 10.11648/j.dmath.20170202.13
T2  - International Journal of Discrete Mathematics
JF  - International Journal of Discrete Mathematics
JO  - International Journal of Discrete Mathematics
SP  - 43
EP  - 47
PB  - Science Publishing Group
SN  - 2578-9252
UR  - https://doi.org/10.11648/j.dmath.20170202.13
AB  - In this paper, the effect of buoyancy force in a square enclosure is studied numerically. The coupled equations of continuity, momentum and energy are solved by a finite difference method. The SIMPLE algorithm is used to solve iteratively the pressure-velocities coupling. The numerical investigations in this analysis are made over a wide range of parameters, Rayleigh number and dimensionless heater lengths. Results are presented graphically in the form of streamlines, isotherms and also with a velocity profiles and average Nusselt numbers.
VL  - 2
IS  - 2
ER  -

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Author Information

Md. Noor-A-Alam Siddiki

Department of Natural Science, Stamford University Bangladesh, Dhaka, Bangladesh
Ferjana Habiba

Department of Natural Science, Stamford University Bangladesh, Dhaka, Bangladesh
Raju Chowdhury

Department of Natural Science, Stamford University Bangladesh, Dhaka, Bangladesh

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APA Style

Md. Noor-A-Alam Siddiki, Ferjana Habiba, Raju Chowdhury. (2017). Effect of Buoyancy Force on the Flow Field in a Square Cavity with Heated from Below. International Journal of Discrete Mathematics, 2(2), 43-47. https://doi.org/10.11648/j.dmath.20170202.13

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ACS Style

Md. Noor-A-Alam Siddiki; Ferjana Habiba; Raju Chowdhury. Effect of Buoyancy Force on the Flow Field in a Square Cavity with Heated from Below. Int. J. Discrete Math. 2017, 2(2), 43-47. doi: 10.11648/j.dmath.20170202.13

Copy | Download

AMA Style

Md. Noor-A-Alam Siddiki, Ferjana Habiba, Raju Chowdhury. Effect of Buoyancy Force on the Flow Field in a Square Cavity with Heated from Below. Int J Discrete Math. 2017;2(2):43-47. doi: 10.11648/j.dmath.20170202.13

Copy | Download

@article{10.11648/j.dmath.20170202.13,
  author = {Md. Noor-A-Alam Siddiki and Ferjana Habiba and Raju Chowdhury},
  title = {Effect of Buoyancy Force on the Flow Field in a Square Cavity with Heated from Below},
  journal = {International Journal of Discrete Mathematics},
  volume = {2},
  number = {2},
  pages = {43-47},
  doi = {10.11648/j.dmath.20170202.13},
  url = {https://doi.org/10.11648/j.dmath.20170202.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20170202.13},
  abstract = {In this paper, the effect of buoyancy force in a square enclosure is studied numerically. The coupled equations of continuity, momentum and energy are solved by a finite difference method. The SIMPLE algorithm is used to solve iteratively the pressure-velocities coupling. The numerical investigations in this analysis are made over a wide range of parameters, Rayleigh number and dimensionless heater lengths. Results are presented graphically in the form of streamlines, isotherms and also with a velocity profiles and average Nusselt numbers.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Effect of Buoyancy Force on the Flow Field in a Square Cavity with Heated from Below
AU  - Md. Noor-A-Alam Siddiki
AU  - Ferjana Habiba
AU  - Raju Chowdhury
Y1  - 2017/03/01
PY  - 2017
N1  - https://doi.org/10.11648/j.dmath.20170202.13
DO  - 10.11648/j.dmath.20170202.13
T2  - International Journal of Discrete Mathematics
JF  - International Journal of Discrete Mathematics
JO  - International Journal of Discrete Mathematics
SP  - 43
EP  - 47
PB  - Science Publishing Group
SN  - 2578-9252
UR  - https://doi.org/10.11648/j.dmath.20170202.13
AB  - In this paper, the effect of buoyancy force in a square enclosure is studied numerically. The coupled equations of continuity, momentum and energy are solved by a finite difference method. The SIMPLE algorithm is used to solve iteratively the pressure-velocities coupling. The numerical investigations in this analysis are made over a wide range of parameters, Rayleigh number and dimensionless heater lengths. Results are presented graphically in the form of streamlines, isotherms and also with a velocity profiles and average Nusselt numbers.
VL  - 2
IS  - 2
ER  -

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