A long copper rod of thermal diffusivity is heated at one end with a flame passing

Question:

A long copper rod of thermal diffusivity λ is heated at one end with a flame passing underneath it periodically, while the other end is located so far away that it remains at room temperature T₀. Consider the rod as a one-dimensional system with a periodic temperature variation of amplitude ΔT at x = 0, given by,where x is the spatial coordinate along the wire. Once the rod has reached a regime at which every point of the rod has a periodic temperature variation, show that the temperature profile is given by,The temperature oscillation at position x is dephased by an angle −x/d with respect to the oscillation at position x = 0. The amplitude of oscillation is attenuated by a factor exp (−x/d).