6. Suppose that a solid sphere of unit radius is held at a uniform temperature, 1 = 1, when, at 1 =0, it is plunged into a bath of freezing water. Use separation of variables to determine the solution a (assumed to be spherically symmetric for all time) that satisfies the heat equation, 2 Du + r Or with the initial condition, "(r, 0) = 1 and the boundary condition u(1,() =0. From this solution deduce the dominant behaviour of the temperature at the centre of the sphere at large times