must solve ALL, and must SHOW WORK for a like. if not ill dislike

(Continuation of Recitation #6) You have been told of a mysterious stone wall 0.1 m thick with an unknown source of internal heat generation "=120,000 W/m2. The wall material has the properties: k=70 W/m-K, p= 8,000 kg/m and Cp = 500 J/kg-K. The wall has been at 20C, but in an effort to understand the nature of the heat generation, the temperature on one side of the wall was quickly raised to 150C and the other side was raised to 300C. As the new engineer on the team, you haven't been told of the reasoning for inducing this temperature change on the walls, but you have been asked to determine the temperature profile in the wall over time. You have been told that it will be adequate for the initial evaluation of the wall to define nodes 0.02 m apart and a time step of 30 seconds. Parts a and b from recitation #6 do not need to be redone here but you need the results to complete c and d. a) Set up the system of equations for an implicit solution. Develop the matrices needed to solve at each time step. b) Solve for two forward time steps of 30 seconds each using matrix algebra (e.g., solve for the temperature profiles at 30 seconds and at 60 seconds). c) For this assignment, calculate at least four additional time steps and plot the temperature vs distance at the various time steps and plot the temperature for the different positions as a function of time. About how long does it take to reach steady state? d) Explain briefly if the trends in your plots match the trends you would have expected for heat conduction in a wall with internal heat generation before you made the calculations. Note anything that may have been unexpected at first glance