Abstracts of Paper's Published in 2004


  1. M.I. Nelson and H.S. Sidhu. Bifurcation phenomena for an oxidation reaction in a continuously stirred tank reactor. II Diabatic operation. The Anziam Journal, 45, 303-326, 2004.

    The DOI (Digital Object Identifier) link for this article is http://dx.doi.org/10.1017/S1446181100013389.

  2. M.I. Nelson and H.S. Sidhu. Flammability limits of an oxidation reaction in a batch reactor. II The Rychlý mechanism. Journal of Mathematical Chemistry, 35(2), 119-129, February 2004.

    The DOI (Digital Object Identifier) link for this article is http://dx.doi.org/10.1023/B:JOMC.0000014308.66514.e7.

  3. T.R. Marchant and M.I. Nelson. Semi-analytical solutions for one and two-dimensional pellet problems. Proceedings of the Royal Society of London A, 460, 2381-2394, 2004.

Bifurcation phenomena for an oxidation reaction in a continuously stirred tank reactor. II Diabatic operation

Abstract

We extend an investigation into the bifurcation phenomena exhibited by an oxidation reaction in an adiabatic reactor to the case of a diabatic reactor. The primary bifurcation parameter is the fuel fraction, the inflow pressure and inflow temperature are the secondary bifurcation parameters. The inclusion of heat loss in the model does not change the static steady-state bifurcation diagram; the organising centre is a pitchfork singularity for both the adiabatic and diabatic reactors. However, unlike the adiabatic reactor, Hopf bifurcations may occur in the diabatic reactor. We construct the degenerate Hopf bifurcation curve by determining the double-Hopf locus. When the steady-state and degenerate Hopf bifurcation diagrams are combined it is found that there are 23 generic steady-state diagrams over the parameter region of interest. The implications of these structures from the perspective of flammability in the CSTR are discussed.

M.I. Nelson and H.S. Sidhu. Bifurcation phenomena for an oxidation reaction in a continuously stirred tank reactor. II Diabatic operation. The Anziam Journal, 45, 303-326, 2004. http://dx.doi.org/10.1017/S1446181100013389.


Flammability limits of an oxidation reaction in a batch reactor. II The Rychlý mechanism

Abstract
It is often numerically convenient to reduce models in two-dimensions to one-dimension. This can be done formally through the use of centre manifold techniques, or informally using physical reasoning. We investigate the extent to which flammability limits in a two-dimensional slab are accurately represented by the values in the corresponding one-dimensional slab. We use a simple chemical mechanism containing exothermic and endothermic reactions that has been used to model the combustion of hydrocarbon fragments produced by polymer pyrolysis.

Keywords: Flammability limits. .

M.I. Nelson and H.S. Sidhu. Flammability limits of an oxidation reaction in a batch reactor. II The Rychlý mechanism. Journal of Mathematical Chemistry, 35(2), 119-129, February 2004.

The DOI (Digital Object Identifier) link for this article is http://dx.doi.org/10.1023/B:JOMC.0000014308.66514.e7.


Semi-analytical solutions for one and two-dimensional pellet problems

Abstract

The problem of heat and mass transfer within a porous catalytic pellet in which an irreversible first-order exothermic reaction occurs is a much studied problem in chemical reactor engineering. The system is described by two coupled reaction-diffusion equations for the temperature and the degree of reactant conversion. The Galerkin method is used to obtain a semi-analytical model for the pellet problem with both one and two-dimensional slab geometries. This involves approximating the spatial structure of the temperature and reactant conversion profiles in the pellet using trial functions. The semi-analytical model is obtained by averaging the governing partial differential equations. As the Arrhenius law cannot be integrated explicitly, the semi-analytical model is given by a system of integro-differential equations. The semi-analytical model allows both steady-state temperature and conversion profiles and steady-state diagrams to be obtained as the solution to sets of transcendental equations (the integrals are evaluated using quadrature rules). Both the static and dynamic multiplicity of the semi-analytical model is investigated using singularity theory and a local stability anlaysis. An example of a stable limit-cycle is also considered in detail. Comparison with numerical solutions of the governing reaction-diffusion equations and with other results in the literature shows that the semi-analytical solutions are extremely accurate.

Keywords: reaction-diffusion equations, catalytic pellet, singularity theory, Hopf bifurcation, semi-analytical solutions, Arrhenius law.

T.R. Marchant and M.I. Nelson. Semi-analytical solutions for one and two-dimensional pellet problems. Proceedings of the Royal Society of London A, 460, 2381-2394, 2004.


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