| The shrinking core model, including the effect of transient diffusion, non-linear kinetics and non-isothermal effects was solved using finite elements in space and finite differences in time. The method of solution proposed by Murray and Carey was used with some modification to include an adjustable time step.;The solution for the first order isothermal case agreed well with the well-known pseudo steady state solution, within the conditions defined by Bischoff. At high dimensionless bulk concentration, the solution differed from the pseudo steady state especially at high Damkohler number (Da $>$ 10) where diffusion was dominating.;In the non-linear kinetics case, the effect of reaction order was minimal at high values of the Damkohler number, where diffusion limitations minimized the effect of reaction order. The critical parameters such as the dimensionless heat of reaction above which non-isothermal kinetics effects dominate were also determined. |
