Homework 1 MAE 502 Homework #1 Instructions/Notes: 1 Show all details! These are individual assignments and absolutely no group collaboration is permitted. Copying MATLAB codes and scripts from any source, including online mediums, is considered plagiarism and will not be tolerated. Submission Deadline in Beachboard: 09/22 (Tuesday, 11:59 pm) In the figure below, heat is added to the oven as shown through the heating element and is simultaneously lost to the environment due to temperature drop across the oven walls. Oven Heating coil The variable x denotes the temperature inside the oven, which is assumed to be uniform, while T denotes the ambient temperature of the air outside to oven. Both are expressed in degrees K . The rate of change of oven temperature x is proportional to the rate of heat entering the oven from the heating element minus the rate of heat leaving the oven due to convection and radiation. Empirically, a following non-linear relationship is observed: dx 4 4 2 =α (T −x ) + β ( T −x ) + γ u dt Here α , β ,∧γ are positive constants that depend on the thermal capacity of the oven. The term α (T −x ) represents heat loss due to convection and β ( T 4 −x 4 ) represents heat loss due to radiation. The input variable u denotes the current in the heating element. For many manufacturing processes, such as annealing, the temperature of the oven must be carefully controlled. If the current in the heating element is kept constant to a range of values, determine the corresponding range of steady state temperatures ( dx /dt=0 ) that would be maintained inside the oven. Use the following data: Parameter u α β γ - Values 10 A , 15 A , 20 A , 25 A , 30 A , 35 A −1 50 min −7 −1 −3 2 ×10 min ° K −1 −2 800 ° K min A Use Bisection method, Newton method and Secant method to determine the steady state temperature x for each value of current to the heating elementu as specified. Plot u vs . x Homework 1 MAE 502 - Comment on your results and discuss your observations.