Rigorous Bounds and Relations among Spatial and Temporal Approximations
نویسندگان
چکیده
AbslraclRigorous bounds on temperature and concentration are obtained for a model reacting system incorporating spatial variation, reactant consumption, and Arrhenius kinetics. Similar bounds are obtained for the Semenov (spatially uniform) approximation. Temperatures predicted by the FrankKamenetskii (stationaryl approximation are shown to be upper bounds on the temperature of the complete time-dependent system. The latter supports numerical and approximate analytic arguments that the critical value of the Frank Kamenetskii heat generation parameter in the stationary approximation is a lower bound on analogously defined ctitical parameter values in the complete system. The fundamental mathematical tool is a comparison result for svstems of parabolic partial differential equations.
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