Find: $($a$)$ Sketch a control volume consisting of a tube section of length $z$ showing

convective inputs and outputs of $P$ and $G,$ absorption of $G$ at the tube wall and internal

chemical reaction.

$($b$)$ Using this control volume, derive the dynamic molar balances for glucose and

polysaccharide to describe the concentrations $C_P(z,t)$ and $C_G(z,t).$ Start with $\frac{(C_{i}Az)}{dt}=$cdots

$0(i=G,P).$

$($c$)$ By taking the limit of an infinitesimal control volume, derive the differential

concentration equations for polysaccharide and glucose. Under what conditions are the

same final equations obtained directly from Eq$.2\mathrm{.}4-25$ in the textbook?