Question

A rectangular forced air heating duct is suspended from the ceiling of a basement whose air and walls are at a temperature of [infinity] 5°C. The duct is 15 m long, and its cross section is 400 mm × 188 mm. (1) For an uninsulated duct whose average surface temperature is 50°C, estimate the rate of heat loss from the duct. The surface emissivity and convection coefficient are approximately 0.5 and 4 W/m2·K, respectively. (2) If heated air enters the duct at 58°C and a velocity of 4 m/s and the heat loss corresponds to the result of part (1), what is the outlet temperature? The density and specific heat of the air may be assumed to be 1.10 kg/m3 and 1008 J/kg·K, respectively.

Answer 1

1) 5631.46 W

2) 41.12⁰c

Step-by-step explanation:

Given Data:

duct length = 15 m

cross section = 400 * 188 mm^2

air and wall temperature = 5⁰c = 278 k

density (p) = 1.1 kg/m^3

specific heat of Air (cp) = 1008 j/kg-k = 1.008 kj/kg-k

1) Estimate the rate of heat loss from the duct

given surface emissivity = 0.5

surface temp = 50 ⁰c

convection coefficient (h)= 4 W/m2-k

first we calculate the surface area = 2 ( 0.4 + 0.188 ) *15 = 17.64 m^2

attached below is the detailed solution

2) determine the outlet temperature

given heated air at : 58⁰c

velocity at 4 m/s

attached below is the detailed solution