The following information must be included:

• A short description of the problem

• A sketch of the problem

• Derivation of difference equation (D.E.)

• Results in tabular and plot forms

• Discussions and conclusions

• Computer program and its output

Make any necessary assumptions.

Consider the PDE:

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 ends held at 0C.

(a) Write down the Difference equation for u(x, t) using explicit scheme with h = 1 cm.

(b) What is the maximum value of t for each material using the explicit scheme?

(c) Solve the temperature at all unknown nodes from t = 0 to 10 s for both materials using the maximum time step from Part (b).

(d) Plot the temperature distribution for both materials at every 2 s.

(e) Discuss the effect of material on the temperature distribution.