3. (6 pt) Numerical analysis with MATLAB A hot pipe carrying steam runs horizontally through an empty room that has an air temperature of 25°C. The cylindrical pipe is made of
oxidized cast iron, is 3 m long, and has an outer diameter of 0.47 m. The pipe is wrapped in 3 cm of insulation that lowers the thermal emissivity to 0.5. The heat flux due to free convection is 60 W/m² greater than the heat flux due to thermal radiation. You may assume the following properties of air: Ideal gas kf= 0.025 W/m.K 1 Pr = 0.7 v 1.5 x 10-5 m²/s A. Using Newton's Method with a tolerance of 10-5, find the temperature of the outside of the pipe. Write out all equations that you use and include your MATLAB script. For full credit, your MATLAB code must be turned in and include: . Your name commented in the file(s) • At least 3 commented lines in the Newton function explaining what the step on that line is doing in the calculation • Labels and include units (where applicable) on all variables in your script B. Compare the temperature that you found using Newton's method in part A and the temperature that you find using the fsolve function in MATLAB. (Hint: use your answer from part A to inform your initial point). C. What is the heat transfer coefficient for free convection? D. Is the thermal boundary layer greater than or less than the characteristic length of the pipe? E. How would removing the insulation on the pipe change the emissivity and rate of heat loss due to radiation?
