Effectiveness factors for thin disks $($Fig$.18$B$\mathrm{.}14).$ Consider porous catalyst particles in the

shape of thin disks, such that the surface area of the edge of the disk is small in comparison

with that of the two circular faces. Apply the method of $518\mathrm{.}7$ to show that the steady$-$state

concentration profile is

where z and b are described in the figure. Show that the total mass transfer rate at the surfaces

z $=+$bis

$1$ WAI $=21$rR$*$c$,,91$~h tanh hb $(18$B$\mathrm{.}14-2)$

in which h $=$ m$.$ Show that, if the disk is sliced parallel to the xy$-$plane into n slices, the

total mass transfer rate becomes

Obtain the expression for the effectiveness factor by taking the limit

Express this result in terms of the parameter A defined in $518\mathrm{.}6.$