The non-isothermal catalyst pellet smouldering combustion

A classic chemical engineering problem of the form under consideration here is that of a non-isothermal reaction occurring in a catalytic particle or packed bed into which a single gaseous participant diffuses from a surrounding reservoir (Hatfield and Aris 1969 Luss and Lee 1970 Aris 1975 Burnell et al. 1983). This scenario is also appropriate to the technologically important problem of spontaneous combustion of stockpiled, often cellulosic, material in air (Bowes 1984). If we represent the concentration of the gaseous species as c, the mass- and heat-balance equations for reaction in an infinite slab are 

Here Cp is a heat capacity, k the thermal conductivity, and Q the reaction exothermicity. The term A exp [ — E/RT is simply the Arrhenius form of the reaction rate constant. 

The dimensionless temperature excess and activation energy have the same forms as those used in chapter 4 6 = (T — TJE/RT2 and y = RTJE, where Ta is the ambient (reservoir) temperature. The dimensionless concentration X is simply c/c , where c0 is the reservoir concentration of the gaseous reactant. The group 3 is given by 

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