A novel Laplace decomposition method for non-linear stretching sheet problem in the presence of MHD and slip condition

• Published in: International journal of numerical methods for heat & fluid flow Vol. 24; no. 1; pp. 73 - 85
• Main Author: Khan, Yasir
• Format: Journal Article
• Language: English
• Published: Bradford Emerald Group Publishing Limited 01.01.2014
• Subjects: Algorithms; Approximation; Boundary layers; Computational fluid dynamics; Cooling; Decomposition; Differential equations; Engineering; Fluid flow; Fluid mechanics; Laplace transforms; Lie groups; Magnetic fields; Magnetohydrodynamics; Mathematical models; Mechanical engineering; Methods; MHD; Nonlinearity; Ordinary differential equations; Polynomials; Power; Problems; Slip; Stretching; Viscosity; Pade approximants; Slip condition; Stretching sheet; He's polynomials; Laplace decomposition method; Convergence
• ISSN: 0961-5539; 1758-6585
• DOI: 10.1108/HFF-02-2012-0048

Purpose – This paper aims to suggest a novel modified Laplace decomposition method (MLDM) for MHD flow over a non-linear stretching sheet with slip condition by suitable choice of an initial solution. Design/methodology/approach – The governing partial differential equations are converted into dimensionless non-linear ordinary differential equation by similarity transformation, which is solved by MLDM. The method is based on the application of Laplace transform to boundary layers in fluid mechanics. The non-linear term can be easily handled by the use of He's polynomials. Findings – The series solution of the MHD flow of an incompressible viscous fluid over a non-linear stretching sheet subject to slip condition is obtained. An excellent agreement between the MLDM and HPM is achieved. Convergence of the obtained series solution is properly checked by using the ratio test. Practical implications – Stretching surface is an important type of flow occurring in a number of engineering processes such as heat-treated materials travelling between a feed roll and a wind up roll, aerodynamic extrusion of plastic sheets, glass fiber and paper production, cooling of an infinite metallic plate in a cooling path, manufacturing of polymeric sheets are few examples of flow due to stretching surfaces. This work provides a very useful source of information for researchers on this subject. Originality/value – Such flow analysis is even not available yet for the hydrodynamic fluid. The series solution for MHD boundary layer problem with slip condition by means of MLDM is yet not available in the literature.