Consider a metallic spherical shell in three spatial dimensions of inner radius r=1 and outerradius r=2, and let u(r,t) denote the temperature inside it. The inner and outer surfaces of theshell are placed on ice so that the temperature atr=1 and r=2is always equal to zero:u(1,t)=u(2,t)=0for all t0.Att=0 the temperature inside the shell is given byu(r,0)=-sinr,1r2Solve the heat equation in spherical polar coordinates to work out the temperature inside the shellatt>0.