The analysis of the nature of flow structure in a slowly varying channel is presented. The solution procedure, proposed and implemented, is valid for any smooth geometry. The expansion of the stream function in terms of l = Re , R the Reynolds number ande the slope (small) parameter is considered. The coefficients generated in the expansion are universal (valid for any smooth geometry). This is accomplished using novel semi numerical schemes based on combinatorial concepts, as well as Mathematica. The converging Pade’ sums of the series, for sufficiently largel , gives analytic continuation of the series solution of non-linear partial differential equation for a variety of slowly varying geometries and shed useful light on flow structure. Comparison of predicted values of shear stress based on numerical and experimental findings are given and in the present analysis these are valid for much larger values of l .