Nonisothermal Shrinking Unreacted-Core Systems

It is seen that conversion is given as a function of reduced time, 4D tjL with kLjD as a parameter. This is analogous to Eq. (3.3.33) except that the relationship is more complicated. The values of the sum in Eq. (3.5.8) are tabulated as a function of kLjlD and (4D tlL ) in the literature [31]. 

Although Landler and Komarek determined the diffusivity of iron using Eq. (3.5.8) and experimental conversion data, a more valid use of this equation would be in predicting the conversion from separately obtained information on surface reaction and diffusion. The solid state diffusion can be studied independently, as shown by Edstroem and Bitsianes [30] and Himmel and coworkers [32]. 

1 Temperature Rises in a Diffusion-Controlled Shrinking Unreacted-Core System 

For a system that undergoes an exothermic reaction and is controlled by the diffusion through the product layer, Luss and Amundson [33] have calculated the maximum temperature rise in the solid as affected by the various parameters. 

The solution for a spherical particle is given in the following. The reader is referred to the original article of Luss and Amundson for detailed mathematics. The temperature at any position in the pellet when the reaction front is at 

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