Science and Education Publishing American Journal of Applied Mathematics and Statistics 2333-4576 2 3 2014 04 24 Application of Homotopy Analysis Method in One-Dimensional Instability Phenomenon Arising in Inclined Porous Media 106 114 EN Kajal K. Patel Department of Applied Mathematics & Humanities, S. V. National Institute of Technology, Surat, India M. N. Mehta Twinkle R. Singh AJAMS2014234 10.12691/ajams-2-3-4 2014 -1 21 2014 03 06 2014 04 24 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.