A circular fin is made of pure copper with a thermal conductivity of k = 400 W/(m C), h = 150 W/(m2 C), mass density r = 8900 kg/m3, and specific heat c = 375 J/(kg C). The initial temperature of the fin is 25 C. The fin length is 2 cm and the diameter is 0.4 cm. The right tip of the fin is insulated. See Figure P16–18. The base of the fin is then suddenly increased to a temperature of 85 C and maintained at this temperature. Use the lumped form of the capacitance matrix, a time step of 0.1 s, and b =2 3. Use two elements of equal length.

Determine the temperature distribution up to 3 s. Compare your results with Example 16.7, which used the consistent form of the capacitance matrix.