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

Abdul-Sattar Jaber Ali Al-Saif

doi:doi:10.11648/j.acm.20150404.16

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

Abdul-Sattar Jaber Ali Al-Saif

Published in Applied and Computational Mathematics (Volume 4, Issue 4)

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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TY  - JOUR
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
PY  - 2015
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
SP  - 275
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

Abdul-Sattar Jaber Ali Al-Saif

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

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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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
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
PY  - 2015
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
SP  - 275
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  -

Copy | Download