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An Efficient Scheme of Differential Quadrature Based on Upwind Difference for Solving Two-dimensional Heat Transfer Problems

Received: 29 May 2015     Accepted: 16 June 2015     Published: 2 July 2015
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Abstract

In this paper, a new technique of differential quadature method called the upwind difference - differential quadature method (UDDQM) for solving two-dimensional heat transfer (convection-diffusion) problems is proposed. Also, investigated the effects of physical quantities on behavior of flow problems, and combined effects of upwind difference mechanism together with differential quadrature method to modified the numerical solutions of heat transfer problems are presented. To validate our proposed UDDQM, two convection-diffusion problems ((i) Steady-state incompressible flow problem has exact solution and (ii) Natural convection motion of the incompressible fluid flow problem hasn't exact solution) are solving numerically. Graphical results on the effects of parameter variation on velocity, temperature, Peclet number, Grashof number, and Prandtl number are presented and discussed. Numerical experiments are conducted to test its accuracy and convergence and compare it with the standard DQM and other numerical methods that are available in literature. The numerical results show the efficiency of the proposed method to handle the problems, and it is more accurate and convergent than other methods.

Published in Applied and Computational Mathematics (Volume 4, Issue 4)
DOI 10.11648/j.acm.20150404.16
Page(s) 275-285
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), 2015. Published by Science Publishing Group

Keywords

Upwind Difference Scheme, Differential Quadrature Method, Two-dimensional Convection-diffusion, Accuracy, Convergence

References
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    Abdul-Sattar Jaber Ali Al-Saif. (2015). An Efficient Scheme of Differential Quadrature Based on Upwind Difference for Solving Two-dimensional Heat Transfer Problems. Applied and Computational Mathematics, 4(4), 275-285. https://doi.org/10.11648/j.acm.20150404.16

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    ACS Style

    Abdul-Sattar Jaber Ali Al-Saif. An Efficient Scheme of Differential Quadrature Based on Upwind Difference for Solving Two-dimensional Heat Transfer Problems. Appl. Comput. Math. 2015, 4(4), 275-285. doi: 10.11648/j.acm.20150404.16

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    AMA Style

    Abdul-Sattar Jaber Ali Al-Saif. An Efficient Scheme of Differential Quadrature Based on Upwind Difference for Solving Two-dimensional Heat Transfer Problems. Appl Comput Math. 2015;4(4):275-285. doi: 10.11648/j.acm.20150404.16

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  • @article{10.11648/j.acm.20150404.16,
      author = {Abdul-Sattar Jaber Ali Al-Saif},
      title = {An Efficient Scheme of Differential Quadrature Based on Upwind Difference for Solving Two-dimensional Heat Transfer Problems},
      journal = {Applied and Computational Mathematics},
      volume = {4},
      number = {4},
      pages = {275-285},
      doi = {10.11648/j.acm.20150404.16},
      url = {https://doi.org/10.11648/j.acm.20150404.16},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150404.16},
      abstract = {In this paper, a new technique of differential quadature method called the upwind difference - differential quadature method (UDDQM) for solving two-dimensional heat transfer (convection-diffusion) problems is proposed. Also, investigated the effects of physical quantities on behavior of flow problems, and combined effects of upwind difference mechanism together with differential quadrature method to modified the numerical solutions of heat transfer problems are presented. To validate our proposed UDDQM, two convection-diffusion problems ((i) Steady-state incompressible flow problem has exact solution and (ii) Natural convection motion of the incompressible fluid flow problem hasn't exact solution) are solving numerically. Graphical results on the effects of parameter variation on velocity, temperature, Peclet number, Grashof number, and Prandtl number are presented and discussed. Numerical experiments are conducted to test its accuracy and convergence and compare it with the standard DQM and other numerical methods that are available in literature. The numerical results show the efficiency of the proposed method to handle the problems, and it is more accurate and convergent than other methods.},
     year = {2015}
    }
    

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    T1  - An Efficient Scheme of Differential Quadrature Based on Upwind Difference for Solving Two-dimensional Heat Transfer Problems
    AU  - Abdul-Sattar Jaber Ali Al-Saif
    Y1  - 2015/07/02
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    N1  - https://doi.org/10.11648/j.acm.20150404.16
    DO  - 10.11648/j.acm.20150404.16
    T2  - Applied and Computational Mathematics
    JF  - Applied and Computational Mathematics
    JO  - Applied and Computational Mathematics
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    EP  - 285
    PB  - Science Publishing Group
    SN  - 2328-5613
    UR  - https://doi.org/10.11648/j.acm.20150404.16
    AB  - In this paper, a new technique of differential quadature method called the upwind difference - differential quadature method (UDDQM) for solving two-dimensional heat transfer (convection-diffusion) problems is proposed. Also, investigated the effects of physical quantities on behavior of flow problems, and combined effects of upwind difference mechanism together with differential quadrature method to modified the numerical solutions of heat transfer problems are presented. To validate our proposed UDDQM, two convection-diffusion problems ((i) Steady-state incompressible flow problem has exact solution and (ii) Natural convection motion of the incompressible fluid flow problem hasn't exact solution) are solving numerically. Graphical results on the effects of parameter variation on velocity, temperature, Peclet number, Grashof number, and Prandtl number are presented and discussed. Numerical experiments are conducted to test its accuracy and convergence and compare it with the standard DQM and other numerical methods that are available in literature. The numerical results show the efficiency of the proposed method to handle the problems, and it is more accurate and convergent than other methods.
    VL  - 4
    IS  - 4
    ER  - 

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Author Information
  • Department of Mathematics, College of Education for Pure Science, University of Basrah, Basrah, Iraq

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