| Peer-Reviewed

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

Received: 26 September 2017     Accepted: 27 October 2017     Published: 20 November 2017
Views:       Downloads:
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
Cite This Article
  • 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

    Copy | Download

    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

    Copy | Download

    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

    Copy | Download

  • @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

Author Information
  • Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria

  • Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria

  • Sections