GIVE B-D SOLUTION AS MATLAB SCRIPT

Problem 6. ( 35 points) A thin stainless-steel plate is to be heat-treated for a period of time in a high-temperature vacuum fumace. The stainless-steel plate is 0.5m0.5m with a thickness of 0.0015m. The initial temperature of the plate is 20C, and the furnace temperature is 1000C. The plate is to be suspended in the furnace so that radiation from the furnace walls provides rapid heating to both surfaces of the plate. The interior of the furnace and the surfaces of the plate can be considered to radiate as black bodies. Thermal conduction is assumed to be very rapid so that the temperature is uniform throughout the plate. The heat flux Q to the plate in W/m2(=J/m2s) is given by Q=F12(TF4T4) where is the Stefan-Boltzmann constant with a value of 5.676108W/m2K4F12 is the view factor that can be assumed to be unity (=1.0), and TF is the temperature of the furnace in K. Thermal energy changes E in the plate can be represented by E=mcpT where m is mass of the plate, cp is the heat capacity of the plate with a value of 0.468kJ/kgK for stainless-steel. The density of stainless-steel is 8238kg/m3. (a) Write the energy balance for the metal plate. Rearrange the energy balance with respect to dT/d. (Write your answer on paper, separated from a MATLAB script.) (b) What is the steady-state temperature with two correct decimal places? Use the ode 45 function. (c) Plot the temperature of the plate as a function of time to steady-state. On the same plot, plot the heat flux to the plate as a function of time to steady-state with the second y-axis. (d) What time is required for I to reach 99% of the possible temperature change? Read the results in part (b) and find the corresponding temperature and time