A thin metal plate is a 15cm25cm rectangle. If one of the 15cm edges is held at 100C and the other three edges are held at 0C, what are the steady state temperatures at interior points? Assume that the temperature only changes in x and y direction, and the top and the bottom surface of the plate are isolated along the z direction. Assume that k/Cp=1 where k is the thermal conductivity, is density, and Cp is specific heat capacity of the metal plate. a). Write the PDE governing the heat transport in this problem. You can use the general heat transport equation developed in the class and simplify the terms to generate the final PDE. Identify the boundary conditions and classify the PDE as parabolic, elliptic and hyperbolic. (10) b). Solve the PDE using Central Finite Difference Method with step size h=5cm for both x and y domains. Plot the nodes and solutions. (20)