$(25$ points$)$ Suppose you are designing a refrigeration system in a fruit juice plant to cool oranges. The oranges which have an average mass of $100g$ are to be cooled from $32C$ to $10C$ using air at $2C.$ You can assume that the specific heat of an orange is $3\mathrm{.}81\frac{kJ}{kg.K}.$ If

the cooling section is well$-$insulated, and the oranges enter the cooling section at a rate of $8000$ oranges$/$h$,$ determine

a$)$ the rate of heat removal from the oranges,

b$)$ the required volumetric air flow rate, if the temperature rise of air is not to exceed $5C,$

c$)$ the rate of entropy generation in $\frac{kW}{K}$ during this process.

You can take the specific heat of air as $1\mathrm{.}005\frac{kJ}{kg.K}$