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 100C and the ends
u(x=0, t) = 30C and u(x=0, t) = 60C.
(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.
(d) Discuss the effect of material on the temperature distribution.
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