When a fluid with low species concentration is injected through a permeable membrane into a high species concentration fluid then the concentration difference inside the fluid creates a motion pressure which drives an indirect natural convection boundary layer on the horizontal surface. Understanding such boundary layers are important because they abound in industrial processes such as catalysis,seperation by membranes,drying,burning of fuel films etc.We present a new formulation for such boundary layers. We first find the characteristic scales of horizontal velocity,velocity boundary layer thickness,species boundary layer thickness by doing an order of magnitude analysis of integral boundary layer equations . We then use these to define similarity variable(ƞ).These scales and the similarity variable include constant through flow Vi at the surface which is the source of the non-similarity of this problem.However using a single similarity variable also does not give a similarity solution and leading us to introduce one non-similarty variable ξ (=〖〖Re〗_x〗^(5/4)⁄〖〖Gr〗_x〗^(1/4) ) . We then transform the all boundary layer equations and the boundary conditions into ƞ,ξ coordinates to obtain two coupled , non-linear , integro partial differential equations.These equations have are then solved numerically by local non-similarity method to obtain dimensionless profiles horizontal velocities concentration for the range of 2≤Sc≤20 and 0