TY  - JOUR
VL  - 52
Y1  - 1992/10//
AV  - public
TI  - Weakly Nonuniform Thermal Effects in a Porous Catalyst: Asymptotic Models and Local Nonlinear Stability of the Steady States.
SP  - 1238
KW  - porous catalysts
KW  -  weakly nonlinear stability
KW  -  normal form
N2  - This paper considers a first-order, irreversible exothermic reaction in a bounded porous catalyst, with smooth boundary, in one, two, and three space dimensions. It is assumed that the characteristic reaction time is sufficiently small for the chemical reaction to be confined to a thin layer near the boundary of the catalyst, and that the thermal diffusivity is large enough for the temperature to be uniform in the reaction layer, but that it is not so large as to avoid significant thermal gradients inside the catalyst. For appropriate realistic limiting values of the several nondimensional parameters of the problem, several time-dependent asymptotic models are derived that account for the chemical reaction at the boundary (that becomes essentially impervious to the reactant), heat conduction inside the catalyst, and exchange of heat and reactant with the surrounding unreacted fluid. These models possess asymmetrical steady states for symmetric shapes of the catalyst, and some of them exhibit a rich dynamic behavior that includes quasi-periodic phenomena. In one case, the linear stability of the steady states, and also the local bifurcation to quasi-periodic solutions via center manifold theory and normal form reduction, are analyzed.
UR  - http://www.jstor.org/stable/view/2102307
SN  - 0036-1399
ID  - upm5799
IS  - 5
A1  - Mancebo, Francisco J.
A1  - Vega de Prada, José Manuel
PB  - SIAM - Society for Industrial and Applied Mathematics
EP  - 1259
JF  - SIAM Journal on Applied Mathematics
ER  -