please solve the questions right here are the answers just show me the steps and put the assumptions please

a.13.81 minutes

b.p furnace= 8.68 MW

C. q released=11.71 W

D

Question 3 (40 points) Annealing process is a very common practice in metal industry to produce hard materials for construction and load-bearing applications. In annealing, a piece of metal is slowly cooled from high temperature or maintained at a certain fixed temperature for a long time, allowing the individual atoms or molecules occupy state of lowest energy (equilibrium state) which becomes difficult to break or bend; resulting in hard, tough metallic parts. Consider an annealing process where a total of 3000 steel balls used in ball bearing, each of diameter 10 mm are annealed by heating them from 50C to 900C in a convection furnace (using hot air free convection in furnace with h=8.5W/m2k at 1500C ), followed by cooling to 100C in ambient air at 25C. The average convective heat transfer coefficient for ambient air is 75W/m2k. a. Calculate the time required by complete annealing cycle (heating and cooling) by Lumped Capacitance Resistance method and Heisler Charts. If the values are different by both methods, please comment on the accuracy of each method in YOUR WORDS. b. If efficiency of furnace is 70%, and efficiency of heating is 80%, How big the furnace should be and of what power requirements? If the maximum volume of furmace available in the market is 1 m3, how many furnaces you would require to heat 3000 balls? c. Calculate the total heat released by the steal balls in the room during cooling process. d. Assume that you are standing in the room while balls are cooling down and your body's average temperature is 37C (considering that you have a normal body type with surface area 1.9m2 ). what will be your body surface temperature? You can assume emissivity and absorptivity of human body to be 0.97 , and approximately 10% of heat released by steel balls is directed towards you. Properties of carbon steel: =7833kg/m3;k=54W/m.C;cp=0.465kJ/kg.C;=1.474106m2/s Question 3 (40 points) Annealing process is a very common practice in metal industry to produce hard materials for construction and load-bearing applications. In annealing, a piece of metal is slowly cooled from high temperature or maintained at a certain fixed temperature for a long time, allowing the individual atoms or molecules occupy state of lowest energy (equilibrium state) which becomes difficult to break or bend; resulting in hard, tough metallic parts. Consider an annealing process where a total of 3000 steel balls used in ball bearing, each of diameter 10 mm are annealed by heating them from 50C to 900C in a convection furnace (using hot air free convection in furnace with h=8.5W/m2k at 1500C ), followed by cooling to 100C in ambient air at 25C. The average convective heat transfer coefficient for ambient air is 75W/m2k. a. Calculate the time required by complete annealing cycle (heating and cooling) by Lumped Capacitance Resistance method and Heisler Charts. If the values are different by both methods, please comment on the accuracy of each method in YOUR WORDS. b. If efficiency of furnace is 70%, and efficiency of heating is 80%, How big the furnace should be and of what power requirements? If the maximum volume of furmace available in the market is 1 m3, how many furnaces you would require to heat 3000 balls? c. Calculate the total heat released by the steal balls in the room during cooling process. d. Assume that you are standing in the room while balls are cooling down and your body's average temperature is 37C (considering that you have a normal body type with surface area 1.9m2 ). what will be your body surface temperature? You can assume emissivity and absorptivity of human body to be 0.97 , and approximately 10% of heat released by steel balls is directed towards you. Properties of carbon steel: =7833kg/m3;k=54W/m.C;cp=0.465kJ/kg.C;=1.474106m2/s