Fully Developed Free Convection Flow in a Vertical Slot with Open to Capped Ends: D’Alembert’s Approach

Basant Kumar Jha; Michael Oluwakayode Oni

doi:doi:10.11648/j.mma.20170205.12

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Fully Developed Free Convection Flow in a Vertical Slot with Open to Capped Ends: D’Alembert’s Approach

Basant Kumar Jha, Michael Oluwakayode Oni

Published in Mathematical Modelling and Applications (Volume 2, Issue 5)

Received: 26 September 2017 Accepted: 27 October 2017 Published: 20 November 2017

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Abstract

The fully developed free convection flow in a vertical slot with open to capped ends discussed by Weidman [5] and Magyari [6] is scrutinized in this present work. Exact solution of momentum and energy equations under relevant boundary conditions as discussed in [5, 6] is obtained using the D’Alembert’s method. Numerical comparison of this present work is made with previous result of [6] and the results were justified using the well-known implicit finite difference method (IFDM); this gives an excellent comparison. During the course of numerical investigation, it is found that D’Alembert’s approach is a simpler, reliable and accurate tool for solving coupled equations.

Published in	Mathematical Modelling and Applications (Volume 2, Issue 5)
DOI	10.11648/j.mma.20170205.12
Page(s)	52-56
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

Fully Developed, Free Convection, Vertical Slot, Capped Ends, D’Alembert’s Approach

References

[1]	Batchelor G. K. (1964). Heat transfer by free convection across a closed cavity between vertical boundaries at different temperature. Quart Appl Math. 12:209-233
[2]	Elder J. W. (1965). Laminar free convection in a vertical slot. J Fluid Mech 23:77-98
[3]	Daniels P. G. (1987). Convection in a vertical slot. J Fluid Mech 176:419-441
[4]	Bu ̈hler K. (2003). Special solutions of Boussinesq-equations for free convection flows in a vertical gap. Heat Mass Transfer 39:631-638
[5]	Weidman P. D. (2006). Convection regime flow in a vertical slot: continuum solutions from capped to open ends. Heat Mass Transfer 43:103-109
[6]	Magyari E. (2006). Normal mode analysis of the fully developed free convection flow in a vertical slot with open to capped ends. Heat Mass Transfer 43:827-832
[7]	Jha, B. K., Oni, M. O., and Aina, B.: Steady fully developed mixed convection flow in a vertical micro-concentric-annulus with heat generating/absorbing fluid: an exact solution. Ain Shams Engineering Journal (2016) DOI: 10.1016/j.asej.2016.08.005
[8]	Jha, B. K., M. O. Oni, Natural convection flow in a vertical tube inspired by time-periodic heating, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/j.aej.2016.08.025
[9]	M. O. Oni, Combined effect of heat source, porosity and thermal radiation on mixed convection flow in a vertical annulus: An exact solution, Eng. Sci. Tech., Int. J. (2017), 20 (2017) 518–527, http://dx.doi.org/10.1016/j.jestch.2016.12.009
[10]	B. K. Jha, C. A. Apere, (2013). Unsteady MHD two-phase Couette flow of fluid–particle suspension. Applied Mathematical Modelling 37:1920-1931
[11]	Jha, B. K., M. O. Oni, Laminar Convection in a Uniformly Heated Vertical Porous Channel Revisited, Advances in Applied Sciences 2017; 2(3): 28-32

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APA Style

Basant Kumar Jha, Michael Oluwakayode Oni. (2017). Fully Developed Free Convection Flow in a Vertical Slot with Open to Capped Ends: D’Alembert’s Approach. Mathematical Modelling and Applications, 2(5), 52-56. https://doi.org/10.11648/j.mma.20170205.12

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ACS Style

Basant Kumar Jha; Michael Oluwakayode Oni. Fully Developed Free Convection Flow in a Vertical Slot with Open to Capped Ends: D’Alembert’s Approach. Math. Model. Appl. 2017, 2(5), 52-56. doi: 10.11648/j.mma.20170205.12

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AMA Style

Basant Kumar Jha, Michael Oluwakayode Oni. Fully Developed Free Convection Flow in a Vertical Slot with Open to Capped Ends: D’Alembert’s Approach. Math Model Appl. 2017;2(5):52-56. doi: 10.11648/j.mma.20170205.12

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@article{10.11648/j.mma.20170205.12,
  author = {Basant Kumar Jha and Michael Oluwakayode Oni},
  title = {Fully Developed Free Convection Flow in a Vertical Slot with Open to Capped Ends: D’Alembert’s Approach},
  journal = {Mathematical Modelling and Applications},
  volume = {2},
  number = {5},
  pages = {52-56},
  doi = {10.11648/j.mma.20170205.12},
  url = {https://doi.org/10.11648/j.mma.20170205.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20170205.12},
  abstract = {The fully developed free convection flow in a vertical slot with open to capped ends discussed by Weidman [5] and Magyari [6] is scrutinized in this present work. Exact solution of momentum and energy equations under relevant boundary conditions as discussed in [5, 6] is obtained using the D’Alembert’s method. Numerical comparison of this present work is made with previous result of [6] and the results were justified using the well-known implicit finite difference method (IFDM); this gives an excellent comparison. During the course of numerical investigation, it is found that D’Alembert’s approach is a simpler, reliable and accurate tool for solving coupled equations.},
 year = {2017}
}

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TY  - JOUR
T1  - Fully Developed Free Convection Flow in a Vertical Slot with Open to Capped Ends: D’Alembert’s Approach
AU  - Basant Kumar Jha
AU  - Michael Oluwakayode Oni
Y1  - 2017/11/20
PY  - 2017
N1  - https://doi.org/10.11648/j.mma.20170205.12
DO  - 10.11648/j.mma.20170205.12
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 52
EP  - 56
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20170205.12
AB  - The fully developed free convection flow in a vertical slot with open to capped ends discussed by Weidman [5] and Magyari [6] is scrutinized in this present work. Exact solution of momentum and energy equations under relevant boundary conditions as discussed in [5, 6] is obtained using the D’Alembert’s method. Numerical comparison of this present work is made with previous result of [6] and the results were justified using the well-known implicit finite difference method (IFDM); this gives an excellent comparison. During the course of numerical investigation, it is found that D’Alembert’s approach is a simpler, reliable and accurate tool for solving coupled equations.
VL  - 2
IS  - 5
ER  -

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Author Information

Basant Kumar Jha

Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria
Michael Oluwakayode Oni

Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria

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APA Style

Basant Kumar Jha, Michael Oluwakayode Oni. (2017). Fully Developed Free Convection Flow in a Vertical Slot with Open to Capped Ends: D’Alembert’s Approach. Mathematical Modelling and Applications, 2(5), 52-56. https://doi.org/10.11648/j.mma.20170205.12

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ACS Style

Basant Kumar Jha; Michael Oluwakayode Oni. Fully Developed Free Convection Flow in a Vertical Slot with Open to Capped Ends: D’Alembert’s Approach. Math. Model. Appl. 2017, 2(5), 52-56. doi: 10.11648/j.mma.20170205.12

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AMA Style

Basant Kumar Jha, Michael Oluwakayode Oni. Fully Developed Free Convection Flow in a Vertical Slot with Open to Capped Ends: D’Alembert’s Approach. Math Model Appl. 2017;2(5):52-56. doi: 10.11648/j.mma.20170205.12

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@article{10.11648/j.mma.20170205.12,
  author = {Basant Kumar Jha and Michael Oluwakayode Oni},
  title = {Fully Developed Free Convection Flow in a Vertical Slot with Open to Capped Ends: D’Alembert’s Approach},
  journal = {Mathematical Modelling and Applications},
  volume = {2},
  number = {5},
  pages = {52-56},
  doi = {10.11648/j.mma.20170205.12},
  url = {https://doi.org/10.11648/j.mma.20170205.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20170205.12},
  abstract = {The fully developed free convection flow in a vertical slot with open to capped ends discussed by Weidman [5] and Magyari [6] is scrutinized in this present work. Exact solution of momentum and energy equations under relevant boundary conditions as discussed in [5, 6] is obtained using the D’Alembert’s method. Numerical comparison of this present work is made with previous result of [6] and the results were justified using the well-known implicit finite difference method (IFDM); this gives an excellent comparison. During the course of numerical investigation, it is found that D’Alembert’s approach is a simpler, reliable and accurate tool for solving coupled equations.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Fully Developed Free Convection Flow in a Vertical Slot with Open to Capped Ends: D’Alembert’s Approach
AU  - Basant Kumar Jha
AU  - Michael Oluwakayode Oni
Y1  - 2017/11/20
PY  - 2017
N1  - https://doi.org/10.11648/j.mma.20170205.12
DO  - 10.11648/j.mma.20170205.12
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 52
EP  - 56
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20170205.12
AB  - The fully developed free convection flow in a vertical slot with open to capped ends discussed by Weidman [5] and Magyari [6] is scrutinized in this present work. Exact solution of momentum and energy equations under relevant boundary conditions as discussed in [5, 6] is obtained using the D’Alembert’s method. Numerical comparison of this present work is made with previous result of [6] and the results were justified using the well-known implicit finite difference method (IFDM); this gives an excellent comparison. During the course of numerical investigation, it is found that D’Alembert’s approach is a simpler, reliable and accurate tool for solving coupled equations.
VL  - 2
IS  - 5
ER  -

Copy | Download