Q.1

Use the explicit method to solve for the temperature distribution of a long, thin rod with a

length of 2 cm and the following values: Ax = 0.5 cm. At t=0, the inner temperature of the

rod is 15ºC and the boundary conditions are fixed for all times at T (0) = 100°C and T (2) =

50°C. The value of k = 0.835 cm²/sec. Apply the condition At ≤ 14 to determine At. Put the

given values of Ax and k in the condition for At given above. Time step At should be less

than half of the value obtained from the above condition. Obtain the temperature values of

the inner nodes of the rod at the end of two selected times steps At.

100°C (0)

Grid nodes

(1)

T(x, 0) = 15°C

(2)

2 cm

(3)

(4) 50°C

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

Value of A can be calculated by using the relation λ =

ΚΔΕ

(Ax)2/