A 4-m-long section of an air heating system of a house passes through an unheated space in the attic. The inner diameter of the circular duct of the heating system is 21 cm. Hot air enters the duct at...

A 4-m-long section of an air heating system of a house passes through an unheated space in the attic. The inner diameter of the circular duct of the heating system is 21 cm. Hot air enters the duct at 100 kPa and 65.8°C at an average velocity of 3.5 m/s. The temperature of the air in the duct drops to 59.5°C as a result of heat loss to the cool space in the attic. Determine the rate of heat loss from the air in the duct to the attic under steady conditions. Also, determine the cost of this heat loss per hour if the house is heated by a natural gas furnace having an efficiency of 83 percent, and the cost of the natural gas in that area is $0.58/therm (1 therm = 105,500 kJ). Answer in $/hr and four(4) decimal places.