Comparison between two common collocation approaches based on radial basis functions for the case of heat transfer equations arising in porous medium

Communications in Nonlinear Science and Numerical Simulation

Volumn 16, Issue 3, 2011, Pages 1396-1407

  Parand, K ^a   Abbasbandy, S ^b   Kazem, S ^b   Rezaei, A R ^a  

^a SHAHID BEHESHTI UNIVERSITY   (Iran)

^b IMAM KHOMEINI INTERNATIONAL UNIVERSITY   (Iran)

Author keywords

Collocation method; Direct inverse multiquadric; Indirect multiquadric; Nonlinear ODE; Porous media; Radial basis functions

Indexed keywords

FUNCTIONS; HEAT CONDUCTION; HEAT CONVECTION; HEAT TRANSFER COEFFICIENTS; INVERSE PROBLEMS; RADIAL BASIS FUNCTION NETWORKS; WASTE DISPOSAL;

BASE FUNCTION; COLLOCATION METHOD; DIRECT INVERSE MULTIQUADRIC; INDIRECT MULTIQUADRIC; INVERSE MULTIQUADRIC; MULTIQUADRICS; NONLINEAR ODES; POROUS MEDIUM; RADIAL BASE FUNCTION; RADIAL BASIS;

POROUS MATERIALS;

EID: 77957361317     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2010.07.011     Document Type: Article

References (47)

1. Nield D.A., Bejan A. Convection in porous media 2006, Springer-Verlag, New York. 3rd ed.
2. Merkin J.H. Free convection boundary layers in a saturated porous medium with lateral mass flux. Int J Heat Mass Transfer 1978, 21:1499-1504.
3. Merkin J.H. Free convection boundary layers on axisymmetric and two dimensional bodies of arbitrary shape in a saturated porous medium. Int J Heat Mass Transfer 1979, 22:1461-1462.
4. Minkowycz W.J., Cheng P. Local non-similar solutions for free convective flow with uniform lateral mass flux in a porous medium. Lett Heat Mass Transfer 1982, 9:159-168.
5. Minkowycz W.J., Cheng P., Moalem F. The effect of surface mass transfer on buoyancy induced Darcian flow adjacent to a horizontal heated surface. Int Commun Heat Mass Transfer 1985, 12:55-65.
6. Cheng P., Le T.T., Pop I. Natural convection of a Darcian fluid about a cone. Int Commun Heat Mass Transfer 1985, 12:705-717.
7. Pop I., Cheng P. An integral solution for free convection of a Darcian fluid about a cone with curvature effects. Int Commun Heat Mass Transfer 1986, 13:433-438.
8. Ingham D.B., Pop I. Natural convection about a heated horizontal cylinder in a porous medium. J Fluid Mech 1987, 184:157-181.
9. Pop I., Ingham D.B. Convective heat transfer: mathematical and computational modeling of viscous fluids and porous media 2001, Pergamon Press, Oxford.
10. Vafai K. Handbook of porous media 2000, Marcel Dekker, New York.
11. Bejan A., Khair K.R. Heat and mass transfer by natural convection in a porous medium. Int J Heat Mass Transfer 1985, 28:909-918.
12. Nakayama A., Hossain M.A. An integral treatment for combined heat and mass transfer by natural convection in a porous medium. Int J Heat Mass Transfer 1995, 38:761-765.
13. Yih K.A. Coupled heat and mass transfer by free convection over a truncated cone in porous media: VWT/VWC or VHF/VMF. Acta Mech 1999, 137:83-97.
14. Yih K.A. Uniform transpiration effect on coupled heat and mass transfer in mixed convection about inclined surfaces in porous media: the entire regime. Acta Mech 1999, 132:229-240.
15. Cheng C.Y. An integral approach for heat and mass transfer by natural convection from truncated cones in porous media with variable wall temperature and concentration. Int Commun Heat Mass Transfer 2000, 27:437-548.
16. Cheng C.Y. Soret and Dufour effects on natural convection heat and mass transfer from a vertical cone in a porous medium. Int Commun Heat Mass Transfer 2009, 36:1020-1024.
17. Rahman S.U., Mahgoub K., Nafees A. Natural convective mass transfer from upward pointing conical surfaces in porous media. Chem Eng Commun 2007, 194:280-290.
18. Pop I., Na T.Y. Natural convection of a Darcian fluid about a wavy cone. Int Commun Heat Mass Transfer 1994, 21:891-899.
19. Pop I., Na T.Y. Natural convection over a frustum of a wavy cone in a porous medium. Mech Res Commun 1995, 22:181-190.
20. Lai F.C., Kulacki F.A. Coupled heat and mass transfer by natural convection from vertical surfaces in porous media. Int J Heat Mass Transfer 1991, 34(4-5):1189-1194.
21. Sohouli A.R., Famouri M., Kimiaeifar A., Domairry G. Application of homotopy analysis method for natural convection of Darcian fluid about a vertical full cone embedded in pours media prescribed surface heat flux. Commun Nonlinear Sci Numer Simul 2010, 15(7):1691-1699.
22. Abbasbandy S., Hayat T. Solution of the MHD Falkner-Skan flow by homotopy analysis method. Commun Nonlinear Sci Numer Simul 2009, 14(9-10):3591-3598.
23. Abbasbandy S. Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by means of the homotopy analysis method. Chem Eng J 2008, 136:144-150.
24. Parand K., Razzaghi M. Rational Legendre approximation for solving some physical problems on semi-infinite intervals. Phys Scr 2004, 69:353-357.
25. Parand K., Dehghan M., Pirkhedri A. Sinc-collocation method for solving the Blasius equation. Phys Lett A 2009, 373(44):4060-4065.
26. Parand K., Dehghan M., Rezaei A.R., Ghaderi S.M. An approximational algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method. Comput Phys Commun 2010, 10.1016/j.cpc.2010.02.018.
27. Parand K., Rezaei A.R., Ghaderi S.M. An approximate solution of the MHD Falkner-Skan flow by Hermite functions pseudospectral method. Commun Nonlinear Sci Numer Simul 2011, 16(1):274-283.
28. Abbasbandy S., Shivanian E. Exact analytical solution of a nonlinear equation arising in heat transfer. Phys Lett A 2010, 374(4):567-574.
29. Mai-Duy N. Solving high order ordinary differential equations with radial basis function networks. Int J Numer Meth Eng 2005, 62(6):824-852.
30. Kansa E.J. Multiquadrics - a scattered data approximation scheme with applications to computational fluid dynamics II. Solutions to parabolic, hyperbolic and elliptic partial differential equations. Comput Math Appl 1990, 19(8-9):147-161.
31. Zerroukat M., Power H., Chen C.S. A numerical method for heat transfer problems using collocation and radial basis functions. Int J Numer Meth Eng 1998, 42:1263-1278.
32. Mai-Duy N., Tran-Cong T. Numerical solution of differential equations using multiquadric radial basis function networks. Neural Netw 2001, 14(2):185-199.
33. Mai-Duy N., Tran-Cong T. Numerical solution of Navier-Stokes equations using multiquadric radial basis function networks. Int J Numer Meth Fluids 2001, 37:65-86.
34. Fornberg B. Comparisons between pseudospectral and radial basis function derivative approximations. IMA J Numer Anal 2008, 30(1):149-172.
35. Mai-Duy N., Tran-Cong T. Approximation of function and its derivatives using radial basis function network methods. Appl Math Model 2003, 27:197-220.
36. Golberg M.A., Chen C.S., Bowman H. Some recent results and proposals for the use of radial basis functions in the BEM. Eng Anal Bound Elem 1999, 23(4):285-296.
37. Buhmann M.D. Radial basis functions 2003, Cambridge University Press, Cambridge.
38. Fasshauer G.E. Meshfree approximation methods with matlab 2007, World Scientific Publishing, Singapore.
39. Powell M.J.D. The theory of radial basis function approximation in 1990. Advances in numerical analysis 1992, Clarendon, Oxford.
40. Dehghan M., Shokri A. A meshless method for numerical solution of the one-dimensional wave equation with an integral condition using radial basis functions. Numer Algorithms 2009, 52(3):461-477.
41. 2 in multiquadric interpolation. Comput Math Appl 1991, 21(9):29-42.
42. Rippa S. An algorithm for selecting a good parameter c in radial basis function interpolation. Adv Comput Math 1999, 11:193-210.
43. Fornberg B., Dirscol T., Wright G., Charles R. Observations on the behavior of radial basis function approximations near boundaries. Comput Math Appl 2002, 43:473-490.
44. Sarra S.A. Adaptive radial basis function method for time dependent partial differential equations. Appl Numer Math 2005, 54:79-94.
45. Wu Z.M. Radial basis function scattered data interpolation and the meshless method of numerical solution of PDEs. J Eng Math 2002, 19(2):112. (in Chinese).
46. Wu Z.M., Schaback R. Local error estimates for radial basis function interpolation of scattered data. IMA J Numer Anal 1993, 13:13-27.
47. Fornberg B., Wright G. Stable computation of multiquadric interpolants for all values of the shape parameter. Comput Math Appl 2004, 48(5/6):853-867.