Problem \#1: Consider a thin and infinitely long rectangular plate that is free of heat sources as illustrated in the figure below (like Fig. 17-12 of your book). Assume L=1m. Answer the following questions: a) If the heat transfer occurs steadily and in x-direction, then find the temperature profile analytically and compare that with a numerical analysis (use MATLAB) based on finite difference. Show the results from both analysis in a graph of T vs. x. For numerical results use 10 nodes in the x-direction. Hint: in this part ignore the temperature gradient in the y-direction. b) If the heat transfer occurs steadily and in x and y directions, then find the temperature profile numerically based on finite difference. Compare your results with analytical solution provided in your textbook (eq. 17-57 in your book). Show the results from both analysis in a graph of T vs. x and T vs. y. For numerical part use 10 nodes in the x and y directions. Please attach MATLAB code to your answers on Canvas