A circular fin is made of pure copper with a thermal conductivity of k = 400 W / (m ( oC), h = 150 W / (m2 ( oC), mass density ( = 8900 kg / m3, and specific heat c = 375 J / (kg ( oC). The initial temperature of the fin is 25oC. The fin length is 2 cm and the diameter is 0.4 cm. The right tip of the fin is insulated. See Figure P16 -19. The base of the fin is then suddenly increased to a temperature of 85oC and maintained at this temperature. Use the lumped form of the capacitance matrix, a time step of 0.1 s, and β = 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.
Figure P16-19

25C Insulated tip 2 cm 85C