Question $1$: A spherical pellet containing pure solid $A$ is suspended in a flowing liquid stream at $20C.$ The initial diameter of the pellet is $1\mathrm{.}0cm,$ and the bulk liquid velocity is $5c\frac{m}{s}.$ Component $A$ is soluble in the liquid, and as time progresses, the diameter of the pellet decreases. The flowing liquid effectively serves as an "infinite sink" for the solute, so that the dissolved solute concentration in the bulk liquid is essentially zero. This process represents a "pseudo steady state" convective mass transfer system. All relevant physical properties of the system are provided below

${}_A,$ the density of solid $A,=2\mathrm{.}0\frac{g}{c}{m}^3$

$M_A,$ the molecular weight of solute $A=110\frac{g}{g}$mol $c_A^{**},$ the equilibrium solubility of solute $A,$ at liquid$-$solid interface, $=7{10}^{-4}g$ mole $\frac{?}{c{m}^3}$; $n,$ the kinematic viscosity of the bulk fluid at $20C=9\mathrm{.}95{10}^{-3}c\frac{m^2}{s}$; $D_{AB},$ the diffusion coefficient of solute $A$ in the liquid at ${20}^{0}C=1\mathrm{.}2{10}^{-5}c\frac{m^2}{s}.$

a$.$ Estimate the film transfer coefficient at the initial pellet $1\mathrm{.}0cm$ diameter.

b$.$ Estimate the rate of pellet shrinkage, $d\frac{R}{d}t,$ in $c\frac{m}{h},$ when the pellet diameter is $1\mathrm{.}0cm.$

c$.$ If the pellet diameter decreases from $1\mathrm{.}0$ to $0\mathrm{.}5cm,$ the total mass transfer rate, $W_A,$ will change by what factor?