A steel ball is placed in an air stream. The steel ball is at 300 °C initially and is placed in an air stream that is at 25 °C. The diameter of the steel ball is 1 cm and the steel ball's thermophysical properties are k = 20 W/mK, cp = 400 J/kg K, and p = 8500 kg/m³. For the thermophysical properties of air, please refer to the Appendix in the textbook. (a) (10 pts) Assume that the convection coefficient between the steel ball and the air is h = 400 W/m²K. How long will it take for the steel ball to reach 200 °C? Use lumped system analysis. (b) (20 pts) Assume external forced convection for the heat transfer between the air stream and steel ball. The pressure of the air stream is 1 atm and the stream velocity is 3 m/s. Determine the convection heat transfer coefficient and estimate how long it will take for the temperature at the center of the sphere to reach 200°C. Use one-term approximation for the transient solution for the conduction. (c) (15 pts) Assume internal forced convection for the heat transfer between the air stream and the steel ball. The steel ball is suspended inside a long 20cm-diameter tube as shown in the figure below. The air stream is not affected by the steel ball since the steel ball is very small when compared to the tube diameter. The average speed of the air at the position where the steel ball is located is found to be 10 m/s and the steel ball is located 3 m away from the inlet. Determine the convection heat transfer coefficient. Assume that the tube surface is smooth. (d) (10 pts) Assume that the steel ball is placed in the open air and natural convection dominates. Determine the convection heat transfer coefficient.