Q1

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.°C) 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

12 cm

(4) 41°C