In hydraulic analysis, one of the most popular viscosity models for non-Newtonian fluids is the Power Law model. In shear-thinning and shear-thickening, the governing system of partial differential equations is transformed into a system of coupled highly non-linear ordinary differential equations. The effects of emerging parameters on velocities, temperature, and concentration as well as the engineering quantities (friction factor, Nusselt number, and Sherwood number) are presented in tables, graphs, and discussed. Most previous studies do not care about studying the effect of different parameters on stream velocity, and this is one of the advantages of our current study, which can be used by researchers in the future to make comparisons and verify the validity of the solutions. The higher accuracy of fifth-order FDM is tested by comparing it (in the Newtonian case) with previously published works and the results are in excellent agreement with these analytical and numerical works.