A previous numerical solution method to the strong nonlinear T-φS-CL coupling for a Scheil-type binary solidification process was extended and modified for single-phase dendrite solidifications of any nominal alloy composition(in a composition range of single-phase or eutectic solidification) and with any solid-back diffusion extents. Numerical sample computations were performed on Al-Cu system with different nominal compositions from almost pure Al to nearly eutectic and with different solid diffusion coefficients, which are factitiously enlarged or decreased in eight orders of magnitude. The calculation results exhibit the feasibility, capability and efficiency of the proposed numerical scheme in modeling an arbitrary binary dendrite solidification problem.