A thin-walled tube with a diameter of 6 mm and length of 20 m is used to carry e

Question

A thin-walled tube with a diameter of 6 mm and length of 20 m is used to carry exhaust gas from a smoke stack to the laboratory in a nearby building for analysis. The gas enters the tube at 200°C and with a mass flow rate of 0.002 kg/s. Autumn winds at a temperature of 15°C blow directly across the tube at a velocity of 6 m/s. Assume the thermophysical properties of the exhaust gas are those of air. (Note: 90°C is a reasonable guess for the tube temperature.) What is the value for the Nusselt number on the inside of the tube? Use Nui=0.023 ReD^0.8 Pr0.3 .What is the average inside heat transfer coefficient, in W/m2·K? What is the value of the Nusselt number on the outside of the tube? Use the Zukauskus correlation with C=0.26 , m=0.6 and n=0.37 .What is the average outside heat transfer coefficient, in W/m2·K? What is the overall heat transfer coefficient, U , in W/m2·K? What is the temperature of the gas at the outlet of the tube, in °C?

Explanation / Answer

Tmean = Ti + To / 2

= 200 + 15 / 2 = 107.5oC = 380.5 K

Re is the Reynolds number

Re = 4 m / 3.14 X 0..006 X 221.6 X 10-7

Re = 4 X 0.002 / 3.14 X 0.006 X 221.6 X 10-7

Re = 19161.93

hi = 0.023 X 19161.930.8 X 0.6930.3

hi = 54.94 W/m2 K

Prout = 0.71

Re = 6 X 0.006 / 14.82 X 10-6

Re = 2429.14

Nuout = 0.26 X 2429.14 0.6 X 0.710.37 X ( 0.71 / 0.693 )0.25

Nuout = 24.76

ho = 24.76 X 0.0253 / 0.006

ho = 104.4 W/m2 K

1 / u = 1/ 54.94 +1 / 104.4

U = 35.99 W/m2 K

( T-15 )/ ( 200-15 ) = exp ( 35.99 X 3.14 X 0.006 X 20 / 1012 X 0.002 )

( T-15 ) = 185 X 1.23 X 10-3

T = 0.227 + 15

T = 15.227oC

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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