The universal Blasius problem: New results by Duan–Rach Adomian Decomposition Method with Jafarimoghaddam contraction mapping theorem and numerical solutions

Abstract

In the present work, Blasius problem subject to a moving and permeable wall (as a universal scheme) is tackled analytically and numerically in a comprehensive manner. In the analytic part, it is initially employed perturbation technique to develop some new asymptotic solutions; then, a modified scheme of Adomian Decomposition Method (namely, Duan–Rach ADM) combined with Jafarimoghaddam contraction mapping theorem, 2019 is brought into account to provide some new insights to the nonlinearity. Particularly, this combination led to an accurate analytic estimation of the critical points within the nonlinearity as well as an excellent improvement of the series solution presumably for the 1st time in the state of art. In the numerical part, the nonlinearity underwent Runge–Kutta–Fehlberg (RKF45) algorithm and the dual-nature solutions were confirmed. As a new finding in this part, it is mentioned to a critical injection rate of Scr.≈−0.873 for the existence of duality in the solution. In other words, for Scr.<−0.873 dual-nature solutions transform into single-nature ones.