The temperature of a cylindrical solid bar $($diameter $D,$ length, $L)$ changes in the axial direction at dynamic conditions $($unsteady state$)$

a$)(4$p$)$ Draw the volume element

b$)(20$p$)$ Derive an equation to express the change in the temperature in the bar.

c$)(3$p$)$ Define the equation you obtained

$($ordinary$?$ partial? variable coefficient? oxder?etce$)$

d$)(3$p$)$ How many boundary conditions do you need? Explain.