Q2. Use the Alternating Direction Implicit (ADI) method to solve for the temperature

distribution in the plate, shown in the figure below, at time t = 2 sec. Initially, the plate

surface is at 5°C with the given boundary conditions shown in the figure. The dimensions

and the nodes to find the temperatures on are also shown in the figure below. The time

interval At is 1 sec. The plate is made of a material with thermal diffusivity k = 0.745 cm²/sec.

Find T1².1, T2².1, T1²,2, and T 2².2. The nodes are equally spaced in x- and y-directions. After the

obtaining the tri-diagonal coefficient matrix, use the Thomas Algorithm to solve for the

unknown temperatures for each time step. Indicate the temperature values on the inner

nodes in a separate diagram.

12 cm

68°C

(1,2)

(1,1)

110°C

(2,2)

(2,1)

45°C