A long rectangular bar with a height of H = 0.2 m and a width of W = 0.15 m and having a thermal conductivity of k = 70 W/m.K, density of p = 1.0 g/cm, and heat capacity of Cp = 4.18 J/gK is subjected to heating followed by cooling. Before heating, the temperature of this bronze bar is at equilibrium with the room temperature (25C). At time t = 0, hot air (Tair = 100C) is blown onto the surface of this bar to heat it up for 3 minutes. The heated bar is then immediately immersed in cold water (Twater = 10C) for 2 minutes to cool it down. The convection heat transfer coefficients for air and water hair and hwater are in the range of 100 750 W/m.K. You are asked to determine the temperature distribution and history of the bar throughout the heating- cooling process. Your report should include: a) A section that outlines your analysis and assumptions used in your calculations. (10%) b) Derivations and approach to numerical solution on a separate sheet. Include a schematic of the physical system and use it to explain your finite difference method. [You need to specify the grid size (Ar= Ay) and time step (At) and justify them] (10%) c) A Matlab program for determining the temperature distributions and history. In your program, use as many comment statements as you feel necessary to explain your logic and procedure in various sections. (Submit your program and results in the same computer output with your name and mailbox on the first page.) (40%) d) A plot of temperature vs. time at three points inside the rectangular bar: 1) center point, 2) a point which is 4 cm from the surface of the short side (width) and 5 cm from the surface of the long side (height), and 3) a point which is 0.5 cm from the surface on both sides. (15%) e) Tables showing the temperature distribution in the bar at 1 minute interval (e.g., 60, 120, 180, 240, and 300 seconds). Each table should be arranged so that the positions of the entries in the table correspond to the positions of the temperatures in the bar. (10%) f) Discussion on the accuracy of your results. You should compare your numerical solutions with analytical solutions whenever it is possible. (15%) Note: For the convection heat transfer coefficients, choose values for hair and hwater in the range of 100 750 W/mK, with hwater = 3 hair