Draw a 4x4 grid of nodes. a. How many interior nodes are there? b. Mark node (2,3) on your grid with a star. If x=2 cm and Ay = 3 cm, what is (x,y) at the node (2.3)? 2. Consider this PDE: a? a? arz +...

Draw a 4x4 grid of nodes. a. How many interior nodes are there? b. Mark node (2,3) on your grid with a star. If x=2 cm and Ay = 3 cm, what is (x,y) at the node (2.3)? 2. Consider this PDE: a? a? arz + ayz = 0. a. Convert this to a system of linear equations using the central difference approximation for the interior nodes of your 4x4 grid. Use the notation Tlus.TRNS. Tror, Trop for the temperature on the edges of the grid. Complete this table. The first row has been done for you. il Equation 721 - 271,1 + TMS Ax2 11.2-271,1 + Tror Ay? 3. Express your answer to Question 2 in the form of Where x= -12. Leave Ax, Ay, and the temperatures on the boundaries as symbolic terms. The first row of A and b has been done for you. b = 4. Set up an Excel spreadsheet to solve steady state heat conduction problems on a 4x4 grid. Your Excel spreadsheet should: . TRNS, Thor, Trop on a. Have cells where your user enters Ax, Ay, and the temperatures T the boundaries. b. Compute the elements of A and b. c. Solve the system of linear equations (you can use any technique you like for this) d. Report the temperatures on the 4x4 grid in matrix form. 5. Use your answer to question 4 to solve the following problems: Right Edge Temp., °C Left Edge Temp., °C Problem # 1 25 Problem 21000 Problem #3 25 Problem #4 10 25 Bottom Edge Temp., °C 25 125 1000 20 Top Edge Temp., °C 25 125 25 30 100