MESHLESS LOCAL RBF-DQ FOR 2-D HEAT CONDUCTION: A COMPARATIVE STUDY

Abstract

Meshless local radial basis function-based differential quadrature method is applied to 2-D conduction problem. Numerical results are compared with those gained by homotopy perturbation method. Outcomes are presented through graphs which prove the accuracy of homotopy perturbation method and its applicability in heat transfer problems.

Dates

  • Submission Date2010-07-04
  • Revision Date2010-09-16
  • Acceptance Date2010-11-11

DOI Reference

10.2298/TSCI11S1117S

References

  1. Soleimani, S., et al., Local RBF-DQ Method for Two-Dimensional Heat Conduction Problems, Int. commun. Heat. Mass Trans. doi:10.1016/j.icheatmasstransfer.2010.06.033
  2. Bararnia, H., et al., Numerical Simulation of Joule Heating Phenomenon Using Meshless RBF-DQ Method. Int. J. Therm. Sci. doi:10.1016/j.ijthermalsci.2010.06.008
  3. Shu, C., Ding, H., Yeo, K. S., Local Radial Basis Function-Based Differential Quadrature Method and its Application to Solve Two-Dimensional Incompressible Navier-Stokes Equations, Comput. Methods. Appl. Mech. Eng., 192 (2003), 7-8, pp. 941-954
  4. He, J.-H., Homotopy Perturbation Method for Bifurcation on Nonlinear Problems, Int. J. Nonlinea. Sci. Numer. Simul., 6 (2005), 2, pp. 207-208
  5. Yildirim, A., Exact Solutions of Nonlinear Differential-Difference Equations by He's Homotopy Perturbation Method, International Journal of Nonlinear Sciences and Numerical Simulation, 9 (2008), 2, pp. 111-114
  6. He, J.-H., A Review on Some New Recently Developed Nonlinear Analytical Techniques, Int. J. Nonlinea. Sci. Numer. Simul., 1 (2000), 1, pp. 51-70
  7. He, J.-H., Book Keeping Parameter in Perturbation Methods, Int. J. Nonlinea. Sci. Numer. Simul., 2 (2001), 3, pp. 257-264
  8. Ganji, D. D., Sadighi, A., Application of He's Homotopy-Perturbation Method to Nonlinear Coupled Systems of Reaction-Diffusion Equations, Int. J. Nonlinea. Sci. Numer. Simul., 7 (2006), 4, pp. 411-418
  9. Ganji, Z. Z., Ganji, D. D., Approximate Solutions of Thermal Boundary-Layer Problems in a Semi-Infinite Flat Plate by Using He's Homotopy Perturbation Method, Int. J. Nonlinea. Sci. Numer. Simul., 9 (2008), 4, pp. 415-422
  10. Bararnia, H., et al., HPM-Pade' Method on Natural Convection of Darcian Fluid about a Vertical Full Cone Embedded in Porous Media Prescribed Wall Temperature, Journal of Porous Media, In press
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