Part II [40 Points] Problem 29.20 (page 885) of the textbook for the course. Use the numerical procedure discussed in class to calculate the temperatures, and Eqns. 29.14 and 29.15 to calculate the heat flux. Of course, the governing equation to be solved is given by aT k' x2 aT +k' ay+0=0, where T is the temperature in C, k' is the thermal conductivity of aluminum, in cal/(s.cm. C).and Q is the heat input in cal/s. Use a mesh of 7 x7 grid points in (x, y). Use MATLAB for this problem. Textbook: Numerical Methods for Engineers, Steven C. Chapra and Raymond P. Canale, McGraw-Hill, Eighth Edition (2021). 29.20 Determine the temperature distribution and fluxes for the plate depicted in Fig. P29.20. The plate is 60 60 1 cm, is made out of aluminum [k' = 0.49 cal/(s cm C)], with an input of 10 cal/s into the middle node. 75C 100C 0C 50C FIGURE P29.20 For the heated plate, a secondary variable is the rate of heat flux across the plate's surface. This quantity can be computed from Fourier's law. Centered finite-difference approximations for the first derivatives (recall Fig. 23.3) can be substituted into Eq. (29.4) to give the following values for heat flux in the x and y dimensions: Ti+1,j Ti-1,j 9x=-k'- 2 Ax and Tij+1 - Ti,j-1 9y=-k' 2 Ay (29.14) (29.15)