Register to reply

General homogeneous shrinking core problem

Share this thread:
Jan1-14, 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 non-catalytic 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,

Phys.Org News Partner Engineering news on
Greater safety and security at Europe's train stations
Fingerprints for freight items
On the way to a safe and secure smart home
Jan2-14, 06:04 AM
P: 2
Problem solved. Thanks for anyone who had a look.

Register to reply

Related Discussions
What direction is a shrinking cube going + logical problem General Physics 7
Shrinking core model Differential Equations 1
Why is general solution of homogeneous equation linear Differential Equations 4
Magnetic Field Outside of Finite Solenoid Greater for Air-Core or Ferrite-Core? General Physics 6
General solution for homogeneous equation Calculus & Beyond Homework 2