Problem 1 (Total: 30 pts) With reference to the figure on the right,
(1) (10 pts) applying the first law of thermodynamics over a
differential volume, derive the governing heat conduction
equation for 1-D steady state, heat conduction in a slab with
a heat generation of $\dot{e}_{gen}$,
(2) (5 pts) write the boundary conditions,
(3) (10 pts) solve the equation with boundary conditions to
obtain the linear distribution of temperature distribution in
the slab
(4) (5 pts) obtain the heat flow rate $\dot{Q}$ in the slab.
