A pipe, 4.5 cm in diameter and 1×104 cm in length, transports superheated vapor at a rate of 1.08× 106 grams/h. The pipe, which is located in a power plant at 300 K, has a uniform surface temperature of 370 K. If the temperature drop between the inlet and exit of the pipe is 35 K, determine the heat transfer coefficient as a result of convection between the pipe surface and the surroundings. Assume, the specific heat of the vapor is 2190 J/kg.K. (20 points)

Respuesta :

Answer:

h = 23.237 W/m2 K

Explanation:

given data:

flow rate = 1.08*10^6 gm/h = 0.3 kg/s

D = 4.5 cm = 0.045 m

L = 10^4 cm = 100 m

surface temperature = 370 K

[tex]\Delta T = 35K[/tex]

Surface heat of vapor = 2190 J/kg.k

From energy conservation principle we have

heat transfer btwn surface and air  = heat loss due to flow and temp. drop

where

heat transfer btwn surface and air is due to convection

[tex]Q _{convection} = hA_s (T_S - T_∞)[/tex]

WHERE

[tex]T_S = 370 K[/tex]

[tex]T_∞ = 300 K[/tex]

[tex]Heat\ loss  = Q_{loss} = \dot m Cp \Delta T[/tex]

[tex]\dot m = 0.3 kg/s[/tex]

from both above equation we have

[tex]Q_{convection} = Q_{loss} [/tex]

[tex]hA_s (T_S - T_∞) = \dot m Cp \Delta T[/tex]

putting all value to get heat transefer coefficient

[tex]h = \frac{\dot m Cp \Delta T}{A_S((T_S - T_∞)}[/tex]

[tex]h = \frac{0.3*2190*35}{14.137*(370-300)}[/tex]

h = 23.237 W/m2 K