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The present paper represents an analytical solution of fingering phonomenon arising in double phase flow through homogeneous media under certain initial & boundary condition using techniques of calculus of variation and similarity theory. The numerical and graphical representation of solution has been given the graph of saturatin F(?) of injected liquid, is increasing after ? = 0.5 for t > 0, which indicates that when injected liquid entries into native liquid at common-interface, then suddenly the native liquid enters into injected liquid due to difference in wettability. Hence initial saturation will decrease and then after ? > 0.5 the saturation uniformly increases parabolically which is physically consistent with the available theory

journal of mathematics research

An Analytic Soluion of Fingering Phoenomenon Arising in Fluid Flow through Porous Media by Using Techniques of Calculus of Variation and Similarity Theory