Find the temperature distribution in the wall

Question

The project requires hand calculations and coding using the program, Matlab.

A flue passing hot exhaust gases has a square cross section, 300 mm to a side. The walls are constructed of refractory brick 150 mm thick with a thermal conductivity of 0.85 W/mK. Initially with no flue gases flowing, the walk (α = 5.5 x 10^-7 m²/s) are at a uniform temperature of 25 °C. The interior surface is exposed to hot gases at 350 °C with a convection coefficient of 100 W/m²K, while the exterior surface experiences convection with air at 25 °C and a convection coefficient of 5 W/m²K. Use a grid spacing of 50 mm. Using the implicit, finite-difference method with a time increment of I h, find the temperature distribution in the wall 5, 10. 50, and 100 h after introduction of the flue gases.

The project should be reported in the following format:

1. Given Conditions.

2. Assumptions.

3. Properties.

4. Analysis

a. Show formulae for all the nodes.

b. Show the 1-DEs (finite-difference equations) represented in matrix notation, [A][T] = [C].

c. Tabulate the temperatures of all nodes for the time at 5, 10, 50, and 100 h.

d. Show and justify the time to reach steady state.

e. Show the temperatures after reaching steady state in terms of coordinate system, y and x.

f. Plot the isothermal lines at steady state

g. Show computer lines of codes.

5. Conlusions/Discussions

a. Discussions.
b. Conclusions.