$450kgmi{n}^{-1}$ of wet particulate material containing $60\%\frac{w}{w}$ of water is fed into a rotary counter current dryer at a temperature of $15\mathrm{.}5C.$ The solids leave the dryer at $38\mathrm{.}0C$ with a moisture content of $5\%\frac{w}{w}.$ The air enters the dryer at $120C$ with an losses from the dryer are $35\mathrm{.}0kJk{g}^{-1}$ of dry air which passes through the system.

a$)$ Draw a schematic diagram of the process.

$[2$ marks$]$

b$)$ Calculate the amount of dried particulate matter and water leaving the dryer per in $kgmi{n}^{-1}.$

$[3$ marks$]$

c$)$ Write the energy balance around the dryer, stating any assumptions clearly.

$[2$ marks$]$

d$)$ Calculate the enthalpies of all streams and the humidity of the exit air. $[8$ marks$]$

Additional data:

Latent heat of vaporization of water at $15\mathrm{.}5C=2460kJk{g}^{-1}$

Specific heats $($assume constant in $0-100C$ range$)$

Specific heat of water vapour $=2\mathrm{.}010kJk{g}^{-1}{K}^{-1}$

Specific heat of dry air

$=1\mathrm{.}005kJk{g}^{-1}{K}^{-1}$

Specific heat of solids material

Specific heat of water

$=1\mathrm{.}260kJK{g}^{-1}{K}^{-1}$

$=4\mathrm{.}18kJk{g}^{-1}{K}^{-1}$