Consider a 1D slab (0 SXSL) with uniform heat generation. Initially the slab is at a constant temperature f(x). Suddenly, at 1 = 0. the boundary surface at x = 0 started varying as g) and the surface at x = L started varying as h(t), where g and h are functions of time alone. Write down the unsteady state heat conduction equation along with the boundary and initial conditions, and prove that the solution of this equation is unique. [8]