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General homogeneous shrinking core problem 
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#1
Jan114, 11:39 PM

P: 2

Hi Guys,
First post here. I'm just wondering if anyone could lend a helping hand in the following derivation. It is taken from Ishida AIChE J 14 (1968) 311 (also very similar to that derived by Ausman Chem Eng Sci 17 (1962) 323) and concerns the derivation of the general noncatalytic shrinking core model. The step which is confusing me concerns the derivation of the transient behavior of the retreating interface. This is achieved through setting [tex]a' = a[/tex] and [tex]X = 0[/tex] and differentiating with respect to [tex]c[/tex] within the following equation [itex]X = 1  \frac{{\sinh \left( {ab} \right)}}{{a\sinh \left( b \right)}}  \frac{{\sinh \left( {ab} \right)}}{a}\int_{c1}^{c} {\frac{{{{a'} \mathord{\left/ {\vphantom {{a'} {\sinh \left( {a'b} \right)}}} \right. \kern\nulldelimiterspace} {\sinh \left( {a'b} \right)}}}}{{1 + d\left[ {1  a + \frac{a}{{Sh}}} \right]\left[ {a'b\coth \left( {a'b} \right)  1} \right]}}} dc[/itex] The solution given by Ishida is [tex]\frac{{dc}}{{da'}} =  \frac{1}{{a'}}\left[ {a'b\coth\left( {a'b} \right)  1} \right]\left[ {1 + d\left[ {1  a + \frac{a}{{Sh}}} \right]\left[ {a'b\coth\left( {a'b} \right)  1} \right]} \right][/tex] however, no matter how hard I try, I can't seem to arrive at their answer. I know I'm missing something simple, but I just can't see it. Any help on a way forward with this problem would be greatly appreciated. Thanks and kind regards, Jason 


#2
Jan214, 06:04 AM

P: 2

Problem solved. Thanks for anyone who had a look.



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