Question

A rectangular forced air heating duct is suspended from the ceiling of a basement whose air and walls are at a temperature of ∞T∞=Tsur= 5°C. The duct is 15 m long, and its cross section is 350 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 ρ= 1.10 kg/m³ and cρ= 1008 J/kg·K, respectively.

first step

Find the rate of heat loss from the duct by convection, in W.

q _{conv = w}

step 2

Find the rate of heat loss from the duct by radiation, in W.

q _{rad =}   w

step 3

What is the total rate of heat loss from the duct, in W?

q= w

step 4

What is the mass flow rate of the air through the duct, in kg/s?
M = kg/s

step 5

Find the outlet air temperature, in °C.

To=  °C

Answer 1