Q2

Use Crank-Nicolson method to solve for the temperature distribution in a long, thin rod

with a length of 12 cm and following values: k' = 0.49 cal/(s.cm.ºC) and At = 0.25 sec. At t =

0 sec (initial condition), the inner temperature of the entire rod is 25°C. The left Boundary is

initially at 90°C and the right boundary condition is 41°C. However, the left boundary

temperature increases by an amount of 2°C after every time step considered. The right

boundary condition is fixed at 41°C for all time steps. Note that the rod is aluminum with C

= 0.2174 cal/(g.°C) and p = 2.7 g/cm³. Find the temperature values on the inner grid nodes

for t = 0.5 sec. Use Thomas Algorithm to solve for the matrix form of the system of equations

for the unknown inner temperatures of the rod. The rod is shown below.

Grid nodes

T(x,0) = 25°C

Initial

BC = 90°C

(0)

(1)

(2)

12 cm

(3)

(4) 41°C

(Note: Show all the steps in detail. Use and show appropriate units throughout the solution.

It is optional to develop a code for the Crank Nicolson problem, Q2)