Thermal criticality for a reactive gravity driven thin film flow of a third-grade fluid with adiabatic free surface down an inclined plane
type: Item
instance of: scholarly article
title: Thermal criticality for a reactive gravity driven thin film flow of a third-grade fluid with adiabatic free surface down an inclined plane
zbMATH Open document ID: 1172.80003
author: O. D. Makinde
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 2009-05-04T00:00:00Z
review text: The author considers the flow of a hydrodynamically and thermally developed reactive liquid film on an inclined heated plate. The fluid is supposed to be of third-grade type. The author assumes that a lubrication theory may be used for this model. Writing the balances of momentum and of energy, and using a change of variables, the author obtains a system of two nonlinear and coupled ordinary differential equations of second-order with respect to the variable \(y\) orthogonal to the plate. The unknowns are the velocity field and the temperature. In the energy balance, a Arrhenius kinetic term is introduced which corresponds to an exothermic reaction in the fluid. These equations involve the Frank-Kamenetskii parameter \(\lambda \) and a non-newtonian \(\gamma \) among other parameters. Boundary conditions are imposed at \(y=0\) (the plate) and at \(y=1\) (the adiabatic free surface). The author uses power-series expansions in terms of \(\gamma \) (for the velocity field) or of \(\lambda \) (for the temperature) for the resolution of this problem. Using the MAPLE software, he computes the first terms of this solution. The main part of the paper describes the thermal criticality of this problem. A theoretical analysis shows that a special kind of Hermite-Padé approximation may be obtained. This theoretical analysis is then completed using the MAPLE software. The last part of the paper describes some qualitative properties of this criticality situation (study of the influence of the parameters).
reviewed by: Alain Brillard
Mathematics Subject Classification ID: 80A20
Mathematics Subject Classification ID: 76A05
zbMATH DE Number: 5550604
zbMATH Keywords: third-grade fluid
zbMATH Keywords: isothermal inclined plate
zbMATH Keywords: adiabatic free surface
zbMATH Keywords: power-series expansion
zbMATH Keywords: thermal criticality
zbMATH Keywords: Hermite-Padé approximation
zbMATH Keywords: MAPLE software
describes a project that uses: Maple
MaRDI profile type: Publication
full work available at URL: s10483-009-0311-6
OpenAlex ID: W2002743896
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DOI: 10.1007/S10483-009-0311-6
description: scientific article; zbMATH DE number 5550604