18. Let a metallic rod 20 cm long be heated to a uniform temperature of 100°C. Suppose that at t = 0 the ends of the rod are plunged into an ice bath at 0°C, and thereafter main- tained at this temperature, but that no heat is allowed to es- cape through the lateral surface. Find an expression for the temperature at any point in the rod at any later time. Deter- mine the temperature at the center of the rod at time t = 30 s if the rod is made of (a) silver, (b) aluminum, or (c) cast iron.