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Meher R. K. and Mehta M. N. Meher S. K., Instability phenomenon arising in double phase flow through porous media with capillary pressure., Int. J. of Appl. Math and Mech. 7 (15): 97-112, 2011.

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Article

Application of Homotopy Analysis Method in One-Dimensional Instability Phenomenon Arising in Inclined Porous Media

1Department of Applied Mathematics & Humanities, S. V. National Institute of Technology, Surat, India


American Journal of Applied Mathematics and Statistics. 2014, Vol. 2 No. 3, 106-114
DOI: 10.12691/ajams-2-3-4
Copyright © 2014 Science and Education Publishing

Cite this paper:
Kajal K. Patel, M. N. Mehta, Twinkle R. Singh. Application of Homotopy Analysis Method in One-Dimensional Instability Phenomenon Arising in Inclined Porous Media. American Journal of Applied Mathematics and Statistics. 2014; 2(3):106-114. doi: 10.12691/ajams-2-3-4.

Correspondence to: Kajal  K. Patel, Department of Applied Mathematics & Humanities, S. V. National Institute of Technology, Surat, India. Email: kajal11@gmail.com

Abstract

During secondary oil recovery process when water is injected in inclined oil formatted area then phenomenon of instability occurs due to viscosity difference of water and oil. The non-linear partial differential equation for this instability phenomenon have been obtained. The Homotopy analysis method has been applied to this governing equation by using appropriate initial and boundary conditions. The guess value of saturation of injected water has been satisfying its initial and boundary conditions. The numerical value and graphical presentation are given by using Maple software and it is concluded that the saturation of injected water is increasing during instability phenomenon in inclined porous media when length of fingers and time increases.

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