Hot air flows with a mass flow rate of 0.05 kg/s through an insulated square duct...

Hot air flows with a mass flow rate of 0.05 kg/s through an insulated square duct with side of 0.15m, the hot air enters at 103 ^oC and after a distance of 5m, cools to 85 ^oC. The heat transfer coefficient between the duct outer surface and the ambient air (T_air = 0 ^oC) is 6 W/m² K.

Calculate the heat transfer coefficient between hot air and duct inner wall.

Air Cp = 1.011 KJ/kg K; air k = 0.0306 W/m K, air viscosity = 211.7*10 ^-7 Ns/m2; air Pr = 0.698

Solutions

Expert Solution

Cross-section area A = 0.15^2 = 0.0225 m^2

Perimeter P = 4*0.15 = 0.6 m

Hydraulic dia D = 4A/P = 4*0.0225 / 0.6 = 0.15 m

Average temperature = (103 + 85) / 2 = 94 deg C = 367 K

Air density at 94 deg C is kg/m3

Average velocity V =

= 0.05 / (0.96 * 0.0225)

V = 2.31 m/s

Reynolds number

= 0.96 * 2.31 * 0.15 / (211.7*10^-7)

Re = 15746

Since Re > 2300, flow is turbulent.

Nusselt number

h * 0.15 / 0.0306 = 0.023 * 15746^4/5 * 0.698^0.3

h = 9.6 W/m2/K

samet mamat answered 1 year ago

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