and cast iron (α = 0.12 cm2 /s), each with initial temperature of 100C and

Consider the PDE: 2 2 x u t u       where u is the temperature in degree Celsius, α is thermal diffusivity in cm2 /s, t is in seconds and x is in cm. It is required to compare the temperature profile of the 10 cm long rods of silver (α = 1.71 cm2 /s) and cast iron (α = 0.12 cm2 /s), each with initial temperature of 100C and the ends u(x=0, t) = 30C and u(x=0, t) = 60C. (a) Write down the Difference equation for u(x, t) using fully implicit scheme with h = 1 cm. (b) Solve the temperature at all unknown nodes from t = 0 to 10 s for both materials using 1 s time step. (c) Plot the temperature distribution for both materials at every 2 s.