MA2102 - Problem Sheet on the Heat Equation March 13, 2022 Consider a thin aluminum rod of length L=20cm and thermal diffusivity 2= 0.86cm2s1. The lateral surface of the rod, as well as the two ends x=0 and x=L, are thermally insulated, so there is no heat flux across these surfaces: xu(0,t)=xu(L,t)=0 The initial distribution of temperature of the rod is described by the function u(x,0)=f(x)=100Lx Answer the following questions: i) is the initial distribution of temperature u(x,0) thermally balanced? Why? ii) for all t0, find the distribution of temperature u(x,t) in the rod. ii) after very long time, what will be the equilibrium temperature in the rod