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An Efficient Scheme of Differential Quadrature Based on Upwind Difference for Solving Two-dimensional Heat Transfer Problems
Applied and Computational Mathematics
Volume 4, Issue 4, August 2015, Pages: 275-285
Received: May 29, 2015; Accepted: Jun. 16, 2015; Published: Jul. 2, 2015
Author
Abdul-Sattar Jaber Ali Al-Saif, Department of Mathematics, College of Education for Pure Science, University of Basrah, Basrah, Iraq
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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.
Keywords
Upwind Difference Scheme, Differential Quadrature Method, Two-dimensional Convection-diffusion, Accuracy, Convergence
Abdul-Sattar Jaber Ali Al-Saif, An Efficient Scheme of Differential Quadrature Based on Upwind Difference for Solving Two-dimensional Heat Transfer Problems, Applied and Computational Mathematics. Vol. 4, No. 4, 2015, pp. 275-285. doi: 10.11648/j.acm.20150404.16
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