$4.$ Derive the radial temperature distribution in an artery $($of radius $5$ mm and length $10$ inches$)$ under steady$-$state conditions $($following the steps below$).$ The temperature at the center of the artery is $34$ C and the ambient temperature outside the artery is $33$ C$.$ The thermal conductivity of the artery is $0\mathrm{.}1$ kcal$/$hr$-$m$-0$C$.($Points: $25)$

a$.$ Draw the physical system and show the direction of transport, and fluxes, along with the coordinate system.

b$.$ Identify your differential volume and the IN$,$ OUT, ACCUMALATION, SOURCE, SINK terms.

c$.$ Perform your molecular transport balance, assuming a one$-$dimensional flow direction.

d$.$ Derive the radial temperature distribution in the artery, stating your boundary conditions.

e$.$ Plot the temperature at radius varying from $0-5$ mm$,$ at increments of $0\mathrm{.}1$ mm$.$