The heat transfer per meter length of the duct, in watts,

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Direction: An un-insulated air conditioning duct of rectangular cross section 1 m × 0.5 m, carrying air at 20°C with a velocity of 10 m/s, is exposed to an ambient of 30°C. Neglect the effect of duct construction material. For air in the range of 20 – 30°C, data is as follows: thermal conductivity = 0.025 W/mK; viscosity = 18 μPa.s; Prandtl number = 0.73; density =1.2 kg/m³. For laminar flow Nusselt number is 3.4 for constant wall temperature conditions and, for turbulent flow, Nu = 0.023 Re^0.8Pr^0.33

The heat transfer per meter length of the duct, in watts, is

1. 3.8
2. 5.3
3. 89
4. 769

Correct Option: D

As Re > 4000, the flow is turbulent
Nu = 0.023 Re^0.8Pr^0.33
hL/k = 0.023 × (4.44 × 10⁵)^0.8 × (0.73)^0.33
h × 0.0667/0.25 = 683.173
h = 25.60 W/m²K
Surface area of duct
A = 2 × al + 2 × bl
where, l = length of duct
∴ A = 3l
Heat transfer rate, Q = h A(T₀ – T)
Q = 25.60 × 3l × (30 – 20)
Q/l = 769W