On steady flow of a reactive variable viscosity fluid in a cylindrical pipe with an isothermal wall

Abstract

Purpose

This paper aims to demonstrate an application of a novel approximation technique, for a function whose partial series is known, to a problem in thermal ignition in a combustible variable viscosity fluid.

Design/methodology/approach

Analytical solutions are constructed for the governing non‐linear boundary‐value problem using regular perturbation technique (RPT) coupled with computer‐extended series solution (CESS) and a special type of Hermite‐Padé approximant.

Findings

The steady state thermal ignition criticality conditions and their dependent on both Frank‐Kamenetskii and viscous heating parameters are accurately obtained. The results also revealed the rapid convergence of the approximation procedure with gradual increase in the number of series coefficients utilized in the approximants.

Originality/value

The analytical and computational procedures utilized in this paper are advocated as an effective tool for investigating several other parameter dependent nonlinear boundary‐value problems.

Citation

Makinde, O.D. (2007), "On steady flow of a reactive variable viscosity fluid in a cylindrical pipe with an isothermal wall", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 17 No. 2, pp. 187-194. https://doi.org/10.1108/09615530710723957