Laminar Convection in a Uniformly Heated Vertical Porous Channel Revisited

Basant K. Jha; Michael O. Oni

doi:doi:10.11648/j.aas.20170203.11

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Laminar Convection in a Uniformly Heated Vertical Porous Channel Revisited

Basant K. Jha, Michael O. Oni

Published in Advances in Applied Sciences (Volume 2, Issue 3)

Received: 2 March 2017 Accepted: 25 April 2017 Published: 5 July 2017

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Abstract

This work revisited the mixed convection flow formation in a uniformly heated vertical porous channel filled with porous material as discussed by Chandrasekhara and Nayrayanan [11]. Using perturbation method as well as numerical solution, Chandrasekhara and Nayrayanan [11] discussed the behavior of the fluid as well as rate of heat transfer. This methods are known not to be exact solution. In this work, we derived an exact solution using D’Alembert’s method and corrected some results obtained in [11]. To justify the accuracy of the present method, we used the implicit finite difference method (IFDM). Result shows that D’Alembert’s method is more efficient, effective and thus a promising tool for finding exact solution for coupled equations.

Published in	Advances in Applied Sciences (Volume 2, Issue 3)
DOI	10.11648/j.aas.20170203.11
Page(s)	28-32
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

Laminar, Uniform Heating, Vertical Porous Channel, D’Alembert Approach

References

[1]	W. Elenbaas, Heat Dissipation of Parallel Plates by Free convection,Physica, vol. 9, n° 1, pp.1-28, 1942.
[2]	J. R. Bodoia and J. F. Osterle, The Development of Free ConvectionBetween Heated Vertical Plates, J. of Heat Transfer, Trans. ASME,Series C, vol. 84, n°1, pp. 40-44, 1962.
[3]	S. J. Kim, S. W. Lee, Air Cooling Technology for Electronic Equipment,CRC Press, Boca Raton, FL, 1996.
[4]	A. Bejan, Shape and Structure from Engineering to Nature, CambridgeUniversity Press, New York, 2000.
[5]	G. A. Ledezma, A. Bejan, Optimal geometric arrangement of staggeredvertical plates in natural convection, ASME J. Heat Transfer 119; pp. 700–708, 1997.
[6]	S. Sathe, B. Sammakia, A review of recent developments in somepractical aspects of air-cooled electronic packages, ASME J. HeatTransfer 120; pp. 830–839, 1998.
[7]	A. Bejan, A. K. da Silva, S. Lorente, Maximal heat transfer density invertical morphing channels with natural convection, Numer. HeatTransfer A 45; pp. 135–152, 2004.
[8]	A. Auletta, O. Manca, B. Morrone, V. Naso, Heat transfer enhancementby the chimney effect in a vertical isoflux channel, Int. J. Heat MassTransfer 44 pp. 4345–4357, 2001.
[9]	A. K. da Silva, L. Gosselin, Optimal geometry of L- and C-shapedchannels for maximum heat transfer rate in natural convection, Int. J. Heat Mass Transfer 48 pp. 609–620, 2005.
[10]	Mishra, A., Paul, T., and Singh, A.; Mixed convection flow in a porous medium bounded by two vertical walls, ForschungimIngenieurwesen, V.67, pp. 198–205 (2002).
[11]	Chandrasekhara BC., Radha N.; Laminar convection in a uniformly heated vertical porous channel, Indian Journal of Technology, 27 pp. 371-376 (1989).
[12]	B. K. Jha, C. A. Apere, (2013) Unsteady MHD two-phase Couette flow of fluid–particle suspension. Applied Mathematical Modelling 37:1920-1931.
[13]	Z. Recebli, H. Kurt, Two-phase steady flow along a horizontal glass pipe in the presence of magnetic and electric field, Int. J. Heat Fluid Flow, 29; 263-268 (2008).

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APA Style

Basant K. Jha, Michael O. Oni. (2017). Laminar Convection in a Uniformly Heated Vertical Porous Channel Revisited. Advances in Applied Sciences, 2(3), 28-32. https://doi.org/10.11648/j.aas.20170203.11

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ACS Style

Basant K. Jha; Michael O. Oni. Laminar Convection in a Uniformly Heated Vertical Porous Channel Revisited. Adv. Appl. Sci. 2017, 2(3), 28-32. doi: 10.11648/j.aas.20170203.11

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AMA Style

Basant K. Jha, Michael O. Oni. Laminar Convection in a Uniformly Heated Vertical Porous Channel Revisited. Adv Appl Sci. 2017;2(3):28-32. doi: 10.11648/j.aas.20170203.11

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@article{10.11648/j.aas.20170203.11,
  author = {Basant K. Jha and Michael O. Oni},
  title = {Laminar Convection in a Uniformly Heated Vertical Porous Channel Revisited},
  journal = {Advances in Applied Sciences},
  volume = {2},
  number = {3},
  pages = {28-32},
  doi = {10.11648/j.aas.20170203.11},
  url = {https://doi.org/10.11648/j.aas.20170203.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.aas.20170203.11},
  abstract = {This work revisited the mixed convection flow formation in a uniformly heated vertical porous channel filled with porous material as discussed by Chandrasekhara and Nayrayanan [11]. Using perturbation method as well as numerical solution, Chandrasekhara and Nayrayanan [11] discussed the behavior of the fluid as well as rate of heat transfer. This methods are known not to be exact solution. In this work, we derived an exact solution using D’Alembert’s method and corrected some results obtained in [11]. To justify the accuracy of the present method, we used the implicit finite difference method (IFDM). Result shows that D’Alembert’s method is more efficient, effective and thus a promising tool for finding exact solution for coupled equations.},
 year = {2017}
}

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TY  - JOUR
T1  - Laminar Convection in a Uniformly Heated Vertical Porous Channel Revisited
AU  - Basant K. Jha
AU  - Michael O. Oni
Y1  - 2017/07/05
PY  - 2017
N1  - https://doi.org/10.11648/j.aas.20170203.11
DO  - 10.11648/j.aas.20170203.11
T2  - Advances in Applied Sciences
JF  - Advances in Applied Sciences
JO  - Advances in Applied Sciences
SP  - 28
EP  - 32
PB  - Science Publishing Group
SN  - 2575-1514
UR  - https://doi.org/10.11648/j.aas.20170203.11
AB  - This work revisited the mixed convection flow formation in a uniformly heated vertical porous channel filled with porous material as discussed by Chandrasekhara and Nayrayanan [11]. Using perturbation method as well as numerical solution, Chandrasekhara and Nayrayanan [11] discussed the behavior of the fluid as well as rate of heat transfer. This methods are known not to be exact solution. In this work, we derived an exact solution using D’Alembert’s method and corrected some results obtained in [11]. To justify the accuracy of the present method, we used the implicit finite difference method (IFDM). Result shows that D’Alembert’s method is more efficient, effective and thus a promising tool for finding exact solution for coupled equations.
VL  - 2
IS  - 3
ER  -

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Author Information

Basant K. Jha

Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria
Michael O. Oni

Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria

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APA Style

Basant K. Jha, Michael O. Oni. (2017). Laminar Convection in a Uniformly Heated Vertical Porous Channel Revisited. Advances in Applied Sciences, 2(3), 28-32. https://doi.org/10.11648/j.aas.20170203.11

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ACS Style

Basant K. Jha; Michael O. Oni. Laminar Convection in a Uniformly Heated Vertical Porous Channel Revisited. Adv. Appl. Sci. 2017, 2(3), 28-32. doi: 10.11648/j.aas.20170203.11

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AMA Style

Basant K. Jha, Michael O. Oni. Laminar Convection in a Uniformly Heated Vertical Porous Channel Revisited. Adv Appl Sci. 2017;2(3):28-32. doi: 10.11648/j.aas.20170203.11

Copy | Download

@article{10.11648/j.aas.20170203.11,
  author = {Basant K. Jha and Michael O. Oni},
  title = {Laminar Convection in a Uniformly Heated Vertical Porous Channel Revisited},
  journal = {Advances in Applied Sciences},
  volume = {2},
  number = {3},
  pages = {28-32},
  doi = {10.11648/j.aas.20170203.11},
  url = {https://doi.org/10.11648/j.aas.20170203.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.aas.20170203.11},
  abstract = {This work revisited the mixed convection flow formation in a uniformly heated vertical porous channel filled with porous material as discussed by Chandrasekhara and Nayrayanan [11]. Using perturbation method as well as numerical solution, Chandrasekhara and Nayrayanan [11] discussed the behavior of the fluid as well as rate of heat transfer. This methods are known not to be exact solution. In this work, we derived an exact solution using D’Alembert’s method and corrected some results obtained in [11]. To justify the accuracy of the present method, we used the implicit finite difference method (IFDM). Result shows that D’Alembert’s method is more efficient, effective and thus a promising tool for finding exact solution for coupled equations.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Laminar Convection in a Uniformly Heated Vertical Porous Channel Revisited
AU  - Basant K. Jha
AU  - Michael O. Oni
Y1  - 2017/07/05
PY  - 2017
N1  - https://doi.org/10.11648/j.aas.20170203.11
DO  - 10.11648/j.aas.20170203.11
T2  - Advances in Applied Sciences
JF  - Advances in Applied Sciences
JO  - Advances in Applied Sciences
SP  - 28
EP  - 32
PB  - Science Publishing Group
SN  - 2575-1514
UR  - https://doi.org/10.11648/j.aas.20170203.11
AB  - This work revisited the mixed convection flow formation in a uniformly heated vertical porous channel filled with porous material as discussed by Chandrasekhara and Nayrayanan [11]. Using perturbation method as well as numerical solution, Chandrasekhara and Nayrayanan [11] discussed the behavior of the fluid as well as rate of heat transfer. This methods are known not to be exact solution. In this work, we derived an exact solution using D’Alembert’s method and corrected some results obtained in [11]. To justify the accuracy of the present method, we used the implicit finite difference method (IFDM). Result shows that D’Alembert’s method is more efficient, effective and thus a promising tool for finding exact solution for coupled equations.
VL  - 2
IS  - 3
ER  -

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