Solve the following questions about drying process.

$($a$)$ A perforated tray $($dimension: $0\mathrm{.}80m0\mathrm{.}60m0\mathrm{.}10m$;$40\%$ porosity$)$ is filled with

$50kg($wet solid mass$)$ of spherical silica particles which are about to be dried by

through$-$circulation of hot air with superficial velocity of $2\frac{m}{s}.$ The initial and the

critical moisture contents $($dry basis, total moisture contents for both$)$ are $20\%$ and $5\%,$

respectively. The specific external surface area of dried silica particle was measured to

be $0\mathrm{.}32\frac{m^2}{k}$gSiO$2.$ Calculate the drying time for the constant$-$rate period, $t_c,$ using the

conditions below if the preheat period is neglected. Assume no$-$shrinkage for the silica

particle.

$(15$ Marks$)$

$T_d=80C$;$T_w=41C$; Enthalpy of vaporization $=2404k\frac{J}{k}g$; Viscosity of air $()=$

$2\mathrm{.}00{10}^{-5}k\frac{g}{m}-s$