APPLICATION OF THE HOMOTOPY ANALYSIS METHOD (HAM) TO THIN FILM FLOW OF A GENERALIZED SECOND-GRADE FLUID ON A VERTICALLY MOVING BELT

Abstract

We formulate and apply the homotopy analysis method (HAM) to determine the solution of the nonlinear differential equation governing thin film flow of a generalized second-grade fluid on a vertically moving belt. This problem is also known as the Landau–Levich or drag-out problem, which is the problem of withdrawal of a plate or fiber from a liquid bath. We make use of a modified model that has shear-dependent viscosity and that can predict normal stress differences. The results obtained exhibit the effectiveness and reliability of HAM.

Keywords:

• Generalized second-grade fluid
• Homotopy analysis method (HAM)
• Moving belt
• Thin film flow

Acknowledgments

SA is grateful to the University of the Witwatersrand, Johannesburg and the NRF, Pretoria, South Africa for financial support. SNN thanks the University of the Witwatersrand, Johannesburg and the NRF, Pretoria, South Africa for research funding. The comments made by Professor Tasawar Hayat on the first draft of the manuscript are highly valued. We thank the anonymous referees for their constructive comments and suggestions, which have led to a significantly improved article.