A long square duct (outside: 0.2 mx0.2 m; inside: 0.1 m 0.1 m) is Alr Toh filled with a heat-generating material that provides for a uniform volumetric generation rate of 9 = 2 x 10 W/m. The square duct is exposed to air at Tair = 300 K with the convection coefficient h=100 W/mK. Both the duct wall and heat-generating material have the same thermo-physical properties: p = 1000 kg/m': Cp=3000 J/kg-K; k = 30 W/m-K. Initially the entire square duct including its content is at a uniform temperature T; = 300 K. We are interested to find the temperature distribution in the square duct (both within the duct wall 0.2 m and inside the duct) at time t and at steady state. To solve this problem, you will have to use the finite difference method. Let us make a grid size Ar = Ay = 0.05 m and label the temperatures T1, T2, T3, T4, Ts, To at 6 different locations as shown in the diagram. a) Use energy balance to derive the finite difference equations for T1, T2, ..., T.. (25 points) b) Specify an appropriate At for use to determine these temperatures. Briefly discuss your reasons for the specified At. (5 points) c) Find the temperatures T1, T2,..., T. at time t = 1 h and at steady state. (10 points) d) Find the heat transfer rate q' per unit length from the square duct to air at time t=1 h (5 points) e) Find the maximum temperature in the square duct and the time to reach the maximum temperature. (5 points)