Along steel shaft of 10 cm diameter is austenised at 870°c and then quenched in a liquid at 30oc. the average surface heat transfer coefficient is 2000 w/m2. °c. the relevant thermophysical properties of the shaft are: p=7800 kg/m", k=20 w/mk, cp=0.46 kj/kg. k calculate: a)-the time required for the center temperature to drop to 200°c. b)-the temperature at half-radius at that moment. c)-the amount of heat that had been transferred to the liquid by that time per meter length of the shaft

To save energy, the air supply to a 2000 ft office has been shut off overnight and the room temperature has dropped to 40°f. in the morning, the thermostat is reset to 70°f and warm air at 120 f begins to flov in at 200ft'/min. the air is well mixed within the room, and an equal mass flow of air at room temperature (changing with time) is withdrawn through a return duct. the air pressure is nearly 1 atm everywhere. ignoring heat transfer with the surroundings and kinetic and potential energy effects, estimate how long it takes for the room temperature to reach 70°f. plot the room temperature as a function of time.