Question

Hot air (k = 0.035 W/m-K) at an average temperature of 120oC flows through a 4 m long duct at 10 m/s. The tube has inside dimensions of 40 mm x 200 mm, surface temperature of 20oC, and the Nussalt number is 89. What is the rate of heat transfer from the air to the tube?

Answer 1

Answer:3.879 kJ

Step-by-step explanation:

Given

Cross-section of duct
`A=40* 200=8000 mm^2`

i.e. characteristic diameter
`=(4A)/(P)=(4* 8000)/(2(200+40))=66.66 mm`

`k=0.035 W/m-K`

Temperature of Hot gases
`T_(\infty )=120^(\circ)C`

Length of Duct
`L=4 m`

Surface Temperature of duct
`T_s=20^(\circ)C`

Nusselt Number
`Nu=89`

`Nu=89=(hD)/(k)`

`89=(h* 66.66* 10^(-3))/(0.035)`

`h=46.77 W/m^2-K`

`Q=hA\Delta T`

`Q=46.77* \pi d\cdot L\cdot \Delta T`

`Q=46.77* \pi * 0.066* 4* (120-20)`

`Q=3.879 kJ`