A circular duct carries hot combustion gases from a furnace. The duct has a temp

Question

A circular duct carries hot combustion gases from a furnace. The duct has a temperature of 309 Cland an outside diameter of 0.1 m. Determine the thickness of insulation (k = 0.4 W m-' K-1) that is necessary to reduce the outside temperature of the insulation to a level that would not injure anyone who touches the surface. The gases have a specific heat capacity of 1170Jkg K a flow rate of 1.9 kgs- and experience a temperature drop of 11 'C over a duct length of 32 m. Assume that the thermal resistance of the duct is small compared to that of the insulation and that the highest temperature that one could be subjected to without injury is 65°C 1 Report your answer in meters.

Explanation / Answer

given duct temperature, Ti = 309 C = 582.15 K
outside diameter, do = 0.1 m
outside radius = ro = 0.05 m
inside radius = ro - t
thickness = t
k = 0.4 W / mK
To = 65 C = 338.16 K
specific heat capacity Cp = 1170 J /kg K
mass flow rate, m' = 1.9 kg/s
temperature drop over l = 32 m of duct, dT = 11 C = 11 K

consider a cylindrical shell of outer radius Ro, inner radius Ri and consider an cylindrical shell at r < Ro, r > Ri
then for a length l of the cylinder, and thickness dr
heat transfer rate, Q' = k*2*pi*r*l*dT/dr
Q'dr/r = 2*k*pi*l*dT
integrating from Ri to Ro
Q'*ln(Ro/Ri) = 2*k*pi*l*(To - Ti)

so for the given problem
Q'/l = m'Cp*dT = 1.9*1170*11 = 222300
hence
222300*ln((0.05)/(0.05 - t)) = 2*0.4*pi*(309 - 65)
t = 1.3774*10^-4 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.