Exact and asymptotic solutions to magnetohydrodynamic flow over a nonlinear stretching sheet with a power-law velocity by the homotopy renormalization method

Abstract

We apply an asymptotic analysis to a nonlinear magnetohydrodynamic boundary-layer flow over a nonlinear stretching sheet with two types of boundary conditions: slip and no-slip. The original partial differential equations governing the flow regime are first transformed into a nonlinear ordinary equation by using a special type of similarity transformation. Asymptotic solutions are then obtained in simple explicit form via the homotopy renormalization method. These solutions satisfy the boundary conditions, and, for special values of the parameters, the asymptotic solutions are just the exact solutions. In addition, the impacts of the magnetic energy effect, the electrical conductivity, and the slip boundary are shown graphically. The validity of the asymptotic solutions is evaluated by comparison with numerical solutions. The results show that the explicit solutions, with finite numbers of terms, perform very well over the whole domain, indicating that our solutions are almost exact.

Exact dynamical behavior for a dual Kaup–Boussinesq system by symmetry reduction and coupled trial equations method

“…These methods have been extensively developed and applied to a lot of nonlinear problems [26][27][28][29][30][31][32][33][34][35][36][37]. Liu's renormalization method and its applications can be found in [38][39][40][41][42][43][44][45]. Some new methods and results on fractional differential equations can be seen in [46][47][48][49][50][51][52][53][54][55][56][57] and the references therein.…”