Question

5. An HVAC (heating,ventilation, and air-conditioning) system in a house delivers warm air to various rooms in a house. A section of the ductwork (7” = 18 cm diameter duct) must pass through an unheated crawl space. This section of the duct is 8 m long. The air entering the duct has a mean temperature of 100F (38C) and a volumetric flow rate of 150cfm (0.07 m3/s). The house owner has insulated the duct with a 2 cm layer of foam insulation having k = 0.03 W/(mK). The temperature of the air in the crawl space is 41F (5C). You can assume that there is a uniform velocity passing over the duct (crossflow) with a velocity of 0.2 m/s. You can also ignore the conductive resistance of the pipe.
(a) Assuming the temperature and flow profiles are fully-developed, what is the temperature at the exit of the pipe. (answer: 36 C)

(b) If the flow enters the duct as a uniform flow, what distance is required for the flow to become fully-developed. (answer: 1.8 m)

(c) What is the total rate at which heat is lost from the pipe (answer: 150 W)

Answer 1