eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2333-4576 2014-04-24 2 3 106 114 10.12691/ajams-2-3-4 AJAMS2014234 article Kajal K. Patel kajal11@gmail.com 1 M. N. Mehta 1 Twinkle R. Singh 1 Department of Applied Mathematics & Humanities, S. V. National Institute of Technology, Surat, India 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. http://pubs.sciepub.com/ajams/2/3/4/ajams-2-3-4.pdf instability phenomenon homotopy analysis method porous matrix secondary oil recovery process