Abstract
We present an efficient iterative power series method for nonlinear boundary-value problems that treats the typical divergence problem and increases arbitrarily the radius of convergence. This method is based on expanding the solution around an iterative initial point. We employ this method to study the unsteady, viscous, and incompressible laminar flow and heat transfer over a shrinking permeable cylinder. More precisely, we solve the unsteady nonlinear Navier–Stokes and energy equations after reducing them to a system of nonlinear boundary-value problems of ordinary differential equations. The present method successfully captures dual solutions for both the flow and heat transfer fields and a unique solution at a specific critical unsteadiness parameter. Comparisons with previous numerical methods and an exact solution verify the validity, accuracy, and efficiency of the present method.
Highlights
Numerous phenomena in engineering and applied science fields are governed by nonlinear boundary-value problems (BVPs)
We presented a numerical technique for solving nonlinear BVPs based on iterative power series solutions
We have demonstrated its efficiency and accuracy through validation against the numerical ERK4
Summary
Numerous phenomena in engineering and applied science fields are governed by nonlinear boundary-value problems (BVPs). Many numerical techniques have been developed to solve such type of problems These methods include Adomian’s decomposition method, homotopy perturbation method, variational iteration method, optimal homotopy asymptotic method, operational matrices techniques based on various orthogonal polynomials and wavelets, finite difference method, and spectral methods; the reader is referred to [1,2,3,4,5,6] and references therein. The fluid dynamics and heat transfer of a viscous incompressible fluid flowing past stretching surfaces, such as a sheet or tube, have attracted considerable interests of many researchers because of their importance in many industrial applications such as the quality of certain products. The literature reveals numerous research papers discussing the flow over a stretching sheet and moving plate [18,19,20,21,22,23,24,25,26], there are only few studies focusing on the problem of flowing past a stretching cylinder or tube; see [8,9,10] and references therein
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