Applied Mathematics and Mechanics

, Volume 30, Issue 3, pp 373–380 | Cite as

Thermal criticality for a reactive gravity driven thin film flow of a third-grade fluid with adiabatic free surface down an inclined plane

  • Oluwole Daniel MakindeEmail author


This study is devoted to the investigation of thermal criticality for a reactive gravity driven thin film flow of a third-grade fluid with adiabatic free surface down an inclined isothermal plane. It is assumed that the reaction is exothermic under Arrhenius kinetics, neglecting the consumption of the material. The governing non-linear equations for conservation of momentum and energy are obtained and solved by using a new computational approach based on a special type of Hermite-Padé approximation technique implemented in MAPLE. This semi-numerical scheme offers some advantages over solutions obtained with traditional methods such as finite differences, spectral method, and shooting method. It reveals the analytical structure of the solution function. Important properties of overall flow structure including velocity field, temperature field, thermal criticality, and bifurcations are discussed.

Key words

isothermal inclined plate third-grade fluid Hermite-Padé approximation thermal criticality 

Chinese Library Classification


2000 Mathematics Subject Classification



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Copyright information

© Shanghai University and Springer-Verlag GmbH 2009

Authors and Affiliations

  1. 1.Faculty of EngineeringCape Peninsula University of TechnologyBellvilleSouth Africa

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