hi want to compare for practise exam Question $4$

A confectionery product contains an aroma volatile as part of its formulation to provide flavour. The product is spherical with diameter $10mm.$ There are concerns over the shelflife of the product which is determined by the loss of flavour.

The diffusivity of the aroma volatile in the product matrix is $1\mathrm{.}3{10}^{-12}{m}^2.s^{-1}$ at ambient conditions.

a$)$ The worst case scenario for shelf life is when there is no volatile retention in the packaging $($meaning the concentration in the air is negligibly small$).$ For this scenario and assuming there is no external mass transfer resistance, calculate the fraction of the volatile that is lost after $6$ weeks.

$[7$ marks$]$

b$)$ The shelf life is defined as the time it takes for $75\%$ of the volatile to be lost. Calculate the shelf life of the product.

$[8$ marks$]$

The manufacturer is considering coating the external surface of the product with an edible material. Research suggests that the mass transfer coefficient achieved after application of the coating is $1\mathrm{.}82{10}^{-10}m.s^{-1}.$

c$)$ Show the mass transfer Biot number for the system $=0\mathrm{.}7.$ You will need to adapt the definition or Biot number for heat transfer considering what it represents. You should check the units to ensure the answer is dimensionless.

$[2$ marks$]$

d$)$ Based on this Biot number, adapt and apply the analytical solution for heat transfer to this mass transfer problem and use it to predict the fraction of the volatile that is lost from the product after $6$ weeks with the coating present.

$[8$ marks$]$

$[$Total $25$ marks$]$