Homework Assignment Finite Difference Methods Consider a 1-dimensional bar with length of 4 cm. The bar is allowed to rest at room temperature (T=20C) such that it is a uniform temperature along its entire length. At time t=0s, the left end of the bar is cooled and held at T=0C while the right end is heated to T=100C. The bar has properties of =1500 kg/m^3, k=500 W/m-C, and cp=1000 J/kg-C. You are asked to use the finite difference method to model the temperature change in the bar for x=1cm (therefore 5 nodes exist) and for a time step of t=0.1 s. Specifically, determine: (a) The temperature at each node after 0.1 second has elapsed using an explicit model, calculated by hand. (b) The temperature at each node after 0.1 second has elapsed using an implicit model, calculated by hand. (You are allowed to invert your stiffness matrix using Matlab) (c) Write code to calculate the temperature at each node in the bar for the first 1 second of the process using an explicit method. Plot the temperature profile at each 0.2 seconds. (d) Write code to calculate the temperature at each node in the bar for the first 1 second of the process using an implicit method. Plot the temperature profile at each 0.2 seconds.