Reference no: EM131282255

A plastic tube of 7.6-cm-ID and 1.27-cm wall thickness has a thermal conductivity of 1.7 W/m K, a density of 2400 kg/m3 , and a specific heat of 1675 J/kg K. It is cooled from an initial temperature of 77°C by passing air at 20°C inside and outside the tube parallel to its axis. The velocities of the two airstreams are such that the coefficients of heat transfer are the same on the interior and exterior surfaces. Measurements show that at the end of 50 min, the temperature difference between the tube surfaces and the air is 10% of the initial temperature difference. A second experiment has been proposed in which a tube of a similar material with an inside diameter of 15 cm and a wall thickness of 2.5 cm will be cooled from the same initial temperature, again using air at 20°C and feeding it to the inside of the tube the same number of kilograms of air per hour that was used in the first experiment. The air-flow rate over the exterior surfaces will be adjusted to give the same heat transfer coefficient on the outside as on the inside of the tube. It can be assumed that the air-flow rate is so high that the temperature rise along the axis of the tube can be neglected. Using the experience gained initially with the 4.5-cm tube, estimate how long it will take to cool the surface of the larger tube to 27°C under the conditions described. Indicate all assumptions and approximations in your solution.