Many applications require us to know the temperature distribution in an object. For example, this information is important for controlling the material properties, such as hardness, when cooling an object formed from molten metal. In a heat transfer course, the following description of the temperature distribution in a flat, rectangular metal plate is often derived. The temperature is held constant at T1 on three sides and at T2 on the fourth side as shown in the figure below. y T2 W T1 T(x,y) T1 T1 The temperature T(x,y) as a function of the xy coordinates shown is given by T(x,y) = (T2-T1)w(x,y) + TI where sinh плу w(x,y) = == 22sin nлx L Π n odd n L nлW sinh Use the following data: T1 = 70 F, T2 = 200 F, and W = L = 2 ft. a. The terms in the preceding series become smaller in magnitude as n increases. Write a MATLAB program to verify this fact for n=1,3,..., 19 for the center of the plate (x = y = 1). b. Modify the program from part a to compute the temperatures in the plate; use a spacing of 0.2 for both x and y. (That is, you should get an mxn matrix containing the values of T(x,y)). c. Using a spacing of 0.2 for both x and y, generate a surface mesh plot and a contour plot of the temperature distribution in the plate. d. Write a MATLAB program to animate the surface plot, to see how the precision of the temperature distribution changes when n increases from 1 to 19. (learn how to animate over n yourself in Matlab using the Matlab help and online resources)