Problem 2 A slab of thickness L is initially at a uniform temperature To. Then, the boundary at x = 0 is brought to a temperature T1, and the boundary at x = L is exposed to a radiative heat source that pumps in a constant heat flux of magnitude qo into the slab. The two boundaries are then kept at these conditions. The slab is made of a material with thermal conductivity k, heat capacity Cp, and density p. a) Find an expression for how the temperature profile within the slab varies with time. b) Find an expression for how the average temperature in the slab varies with time. c) Find an expression for how the heat flux at x = 0 varies with time. d) Approximately how long will it take for the slab to reach a new steady state after the changes are applied at the boundaries