A timed-release drug is dissolving in the intestine of a modern humanoid. As a steady-state approximation, we may assume that the drug is a rod of overall radius \(r_{o}(\mathrm{~m})\) and length of \(L(\mathrm{~m})\). The timed-release action is accomplished by putting an inert coating on the drug through which the drug diffuses with a diffusivity \(D_{a b}\). At the inner edge of the coating, \(\left(r_{i}\right)\) the composition (mole fraction) of the drug is \(x_{a p}\). On the outer surface, the digestive juices provide for mass transfer with a mass transfer coefficient of \(k_{a c}(\mathrm{~m} / \mathrm{s})\). The amount of drug within the intestine can be approximated as \(x_{a \infty} \approx 0\). Derive an expression for the steady-state, mole fraction profile of the drug through the coating. You may assume the total concentration of all species within the coating is \(c_{t}\) and that the partition coefficient between the drug in the coating and the fluid is 1 .