Vemuri Balakotaiah | PubMed Health

PubMed2003

Low-dimensional models for vertically falling viscous films.

Long wave evolution on free falling viscous films is described using a new evolution equation. The scaling proposed here brings in the viscous and pressure correction terms that are missing in the existing long-wave equations. Small amplitude expansion of the equation gives a dissipative form of the Kuromoto-Sivashinsky equation. Improved accuracy of the new equation over existing equations is demonstrated by comparison of neutral curves with Orr-Sommerfeld equations and experimental data.

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PubMed1999

Bifurcation analysis of chemical reactors and reacting flows.

In this work we review the local bifurcation techniques for analyzing and classifying the steady-state and dynamic behavior of chemical reactor models described by partial differential equations (PDEs). First, we summarize the formulas for determining the derivatives of the branching equation and the coefficients in the amplitude equations for the most common singularities. We also illustrate the procedure for the numerical computation of these coefficients. Next, the application of these local results to various reactor models described by PDEs is discussed. Specifically, we review the recent literature on the bifurcation features of convection-reaction and convection-diffusion-reaction models in one and more spatial dimensions, with emphasis on the features introduced due to coupling between the flow, heat and mass diffusion and chemical reaction. Finally, we illustrate the use of dynamical systems concepts in developing low dimensional (effective or pseudohomogeneous) models of reactors and reacting flows, and discuss some problems of current interest. (c) 1999 American Institute of Physics.

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