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Effective Calculation of Multiple Solutions of Mixed Convection in a Porous Medium | ||
| AUT Journal of Modeling and Simulation | ||
| مقاله 1، دوره 44، شماره 1، تیر 2012، صفحه 1-6 اصل مقاله (227.38 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22060/miscj.2012.20 | ||
| نویسندگان | ||
| S. Abbasbandy* 1؛ E. Shivanian2 | ||
| 1Corresponding Author, S. Abbasbandy is with the Department of Mathematics, Imam Khomeini International University, Qazvin, Iran (e-mail: abbasbandy@yahoo.com). | ||
| 2E. Shivanian is with the Department of Mathematics, Imam Khomeini International University, Qazvin, Iran (e-mail: shivanian@ikiu.ac.ir). | ||
| چکیده | ||
| This paper considers an important model of boundary value problem with a condition at infinity namely combined free and forced convection over a plane of arbitrary shape embedded in a fluid-saturated porous medium; this model admits dual solutions, and uses a technique, which is to some extent modification of homotopy analysis method (HAM), in order to obtain dual solutions analytically with high accuracy. | ||
| کلیدواژه‌ها | ||
| Homotopy analysis method؛ rule of multiplicity of solutions؛ prescribed parameter؛ convergence-controller parameter | ||
| عنوان مقاله [English] | ||
| Effective Calculation of Multiple Solutions of Mixed Convection in a Porous Medium | ||
| نویسندگان [English] | ||
| عباس بندی1؛ | ||
| 1Corresponding Author, S. Abbasbandy is with the Department of Mathematics, Imam Khomeini International University, Qazvin, Iran (e-mail: abbasbandy@yahoo.com). | ||
| 2E. Shivanian is with the Department of Mathematics, Imam Khomeini International University, Qazvin, Iran (e-mail: shivanian@ikiu.ac.ir). | ||
| چکیده [English] | ||
| This paper considers an important model of boundary value problem with a condition at infinity namely combined free and forced convection over a plane of arbitrary shape embedded in a fluid-saturated porous medium; this model admits dual solutions, and uses a technique, which is to some extent modification of homotopy analysis method (HAM), in order to obtain dual solutions analytically with high accuracy. | ||
| کلیدواژه‌ها [English] | ||
| Homotopy analysis method, rule of multiplicity of solutions, prescribed parameter, convergence-controller parameter | ||
| مراجع | ||
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[1] S. J. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method, Chapman Hall CRC/Press, Boca Raton, 2003.
[2] T. Hayat, N. Ahmed, M. Sajid, S. Asghar, “On the MHD flow of a second grade fluid in a porous channel,” Comput Math Appl,vol. 3, pp. 549-557, Apr. 1988. 2007;54:14-40.
[3] S. Abbasbandy, “Soliton solutions for the 5th-order KdV equation with the homotopy analysis method,” Nonlinear Dyn,vol. 51, pp. 83-87, Apr. 2008.
[4] S. Abbasbandy, “The application of the homotopy analysis method to solve a generalized Hirota-Satsuma coupled KdV equation,” Phys Lett A, vol. 361, pp. 478-483, Apr. 2007.
[5] S. Abbasbandy , “The application of the homotopy analysis method to nonlinear equations arising in heat transfer,” Phys Lett A, vol. 360, pp. 109-113, Apr. 2006.
[6] S. P. Zhu, “An exact and explicit solution for the valuation of American put options,” Quant Fin, vol. 6, pp. 229-242, Apr.2006.
[7] M. Yamashita, K. Yabushita, K. Tsuboi, “An analytic solution of projectile motion with the quadratic resistance law using the homotopy analysis method,” J Phys A, vol. 40, pp. 8403-8416,Apr. 2007.
[8] Y. Bouremel, “Explicit series solution for the Glauert-jet problem by means of the homotopy analysis method,” Commun Nonlinear Sci Numer Simulat, vol. 12(5), pp. 714-724, Apr.2007.
[9] L. Tao, H. Song, S. Chakrabarti, “Nonlinear progressive waves in water of finite depth-an analytic approximation,” vol. 54, pp.549825-834, Apr. 2007.
[10] H. Song H, L. Tao, “Homotopy analysis of 1D unsteady,nonlinear groundwater flow through porous media,” J Coastal Res, vol. 50, pp. 292-305, Apr. 2007.
[11] A. S. Bataineh, M. S. M. Noorani, I. Hashim, “Solutions of timedependent Emden–Fowler type equations by homotopy analysis method,” Phys Lett A, vol. 371, pp. 72-82, Apr. 2007.
[12] Z. Wang, L. Zou, H. Zhang, “Applying homotopy analysis method for solving differential-difference equation,” Phys Lett A, vol. 369, pp. 77-84, Apr. 2007.
[13] Inc. Mustafa, “On exact solution of Laplace equation with Dirichlet and Neumann boundary conditions by the homotopy analysis method,” Phys Lett A, vol. 365, pp. 412-415, Apr. 2007.
[14] S. Abbasbandy, E. Magyari, E. Shivanian, “The homotopy analysis method for multiple solutions of nonlinear boundary value problems,” Commun Nonlinear Sci Numer Simulat, vol.14, pp. 3530-3536, Apr. 2009.
[15] S. Abbasbandy, E. Shivanian, “Prediction of multiplicity of solutions of nonlinear boundary value problems: novel application of homotopy analysis method,” Commun Nonlinear Sci Numer Simulat, vol. 15, pp. 3830-3846, Apr. 2010.
[16] A. Nakayama, H. Koyama, “A general similarity transformation for combined free and forced-convection flows within a fluidsaturated
porous medium,” ASME J. Heat Trans, vol. 109, pp. 1041-1045, Apr. 1987.
[17] E. Magyari, I. Pop, B. Keller, “Exact dual solutions occurring in Darcy mixed convection flow,” Int Journal Heat Mass Transf, vol. 44, pp. 4563-4566, Apr. 2001. | ||
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