An analytical solution for the Marangoni mixed convection boundary layer flow

• Published in: Proceedings of the Institution of Mechanical Engineers. Part C, Journal of mechanical engineering science Vol. 224; no. 6; pp. 1193 - 1202
• Main Authors: Moghimi, M A, Kimiaeifar, A, Rahimpour, M, Bagheri, G H
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01.06.2010; SAGE PUBLICATIONS, INC
• Subjects: Acceptability; Accuracy; Boundary layer; Boundary layer flow; Computational fluid dynamics; Convection; Convergence; Differential equations; Fluid flow; Fluid mechanics; Ham; Mathematical analysis; Mathematical models; Navier-Stokes equations; Nonlinear equations; Nonlinearity; Ordinary differential equations; Similarity; Stability; Surface tension; mixed convection; analytical solution; Marangoni boundary layer; homotopy analysis method
• ISSN: 0954-4062; 2041-2983
• DOI: 10.1243/09544062JMES1945

Abstract In this article, an analytical solution for a Marangoni mixed convection boundary layer flow is presented. A similarity transform reduces the Navier—Stokes equations to a set of non-linear ordinary differential equations, which are solved analytically by means of the homotopy analysis method (HAM). The results obtained in this study are compared with the numerical results released in the literature. A close agreement of the two sets of results indicates the accuracy of the HAM. The method can obtain an expression that is acceptable for all values of effective parameters and is also able to control the convergence of the solution. The numerical solution of the similarity equations is developed and the results are in good agreement with the analytical results based on the HAM.