Application of a New Hybrid Method for Solving System of Nonlinear BVPs Arising in Fluid Mechanics

Abstract

This article is aimed to introduce a new hybrid analytical-digital technique for solving a wide range of problems in fluid mechanics. This method is according to the Different Transform Method (DTM) and Newton's Iterative Method (NIM). In the Boundary Value Problems (BVP), the system and the boundary conditions converted to an algebraic equation set, and the Taylor series of the solution are subsequently calculated. By finding Jacobian matrix, the unknown parameters of the solution may be calculated using the multi-variable iterative Newton's method. The techniques are employed to determine a proximate solution for the problem. To expound upon the application of the new hybrid method illustratively, two nonlinear problems in fluid mechanics are considered: condensation film on the inclined rotating disk and the rotating MHD flow on a porous shrinking sheet. Using comparing the present results obtained with the numerical solutions and results presented in the literature, an excellent accuracy is observed. Quick convergence of the solution is another important merit of the proposed method.