Name
Abstract | ||
|---|---|---|
A coupled system of partial differential equations that describes the evolution of solid and gas temperatures and gas concentration inside a catalytic converter is derived and examined. The use of a reaction term, which is a discontinuous function of the solid temperature and gas concentration, implies that two types of nontrivial solutions may occur. These are characterised by the manner in which the reaction switches off: either the solid temperature becomes too low (U-solutions) or the gaseous concentration is exhausted (G-solutions). This reaction term differs from the usual combustion term because the reaction is modeled as two-stage, with the large activation-energy limit then justifying the step-function approach adopted.First, steady solutions for which the gas and solid are in thermal equilibrium are studied, and a constraint relating the system's parameters is derived as a necessary condition for the existence of such solutions. Explicit solutions are presented for a particular class of reaction rates, with a linear stability analysis of one case indicating that G-solutions are stable while U-solutions are not.Steady solutions for which the solid and gas are no longer in thermal equilibrium are then considered. For a particular asymptotic limit (and choice of the reaction term), the construction of asymptotic power series expansions shows that the gas temperature exceeds the solid temperature at all points inside the converter. The analysis indicates that separate treatment of the solid and gaseous temperatures has no effect on the qualitative nature of the steady solutions, that is, their existence, stability, and parameter dependence. |
Year | DOI | Venue |
|---|---|---|
1994 | 10.1137/S0036139991217872 | SIAM Journal of Applied Mathematics |
Keywords | Field | DocType |
stable solution,catalytic converter,reaction kinetics,mathematical model,combustion,thermodynamics,activation energy,partial differential equation,power series expansion,chemical reaction,reaction rate,kinetics | Combustion,Continuous function,Catalytic converter,Thermodynamics,Thermal equilibrium,Gas concentration,Mathematical model,Kinetics,Partial differential equation,Mathematics | Journal |
Volume | Issue | ISSN |
54 | 3 | 0036-1399 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Helen Byrne | 1 | 0 | 1.01 |
| John Norbury | 2 | 10 | 4.41 |