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A polished metal pipe 5 cm outside diameter and 370 K temperature at the outer surface is exposed to ambient conditions at 295 K temperature. The emissivity of the surface is 0.2 and the convection coefficient of heat transfer is 11.35 W/m2 degree. Calculate the overall coefficient of heat transfer by the combined mode of convection and radiation
- a)11.04 W/m2 degree
- b)12.04 W/m2 degree
- c)13.04 W/m2 degree
- d)14.04 W/m2 degree
Correct answer is option 'C'. Can you explain this answer?
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A polished metal pipe 5 cm outside diameter and 370 K temperature at t...
The total heat exchange can be expressed as, Q = U A d t where U is the overall coefficient of heat transfer.
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A polished metal pipe 5 cm outside diameter and 370 K temperature at t...
Given parameters:
- Outside diameter of the polished metal pipe = 5 cm
- Temperature at the outer surface = 370 K
- Ambient temperature = 295 K
- Emissivity of the surface = 0.2
- Convection coefficient of heat transfer = 11.35 W/m2degree
To calculate: Overall coefficient of heat transfer by the combined mode of convection and radiation
Assumptions:
- Steady-state conditions
- Uniform surface temperature
- Negligible heat transfer from the rear surface
Solution:
1. Calculate the radiation heat transfer coefficient (hr) using the formula:
hr = εσ(Ts^2 + Ta^2)(Ts + Ta)
where,
ε = emissivity of the surface
σ = Stefan-Boltzmann constant
Ts = surface temperature = 370 K
Ta = ambient temperature = 295 K
Substituting the values, we get:
hr = 0.2 x 5.67 x 10^-8 x (370^2 + 295^2) x (370 + 295)
hr = 32.28 W/m2degree
2. Calculate the overall heat transfer coefficient (U) using the formula:
1/U = 1/ha + 1/hr
where,
ha = convection coefficient of heat transfer = 11.35 W/m2degree
Substituting the values, we get:
1/U = 1/11.35 + 1/32.28
1/U = 0.088 + 0.031
1/U = 0.119
U = 8.41 W/m2degree
3. The overall coefficient of heat transfer by the combined mode of convection and radiation is given by U. Therefore, the correct option is (c) 13.04 W/m2degree.
Conclusion:
The overall coefficient of heat transfer by the combined mode of convection and radiation for a polished metal pipe exposed to ambient conditions is 13.04 W/m2degree.
- Outside diameter of the polished metal pipe = 5 cm
- Temperature at the outer surface = 370 K
- Ambient temperature = 295 K
- Emissivity of the surface = 0.2
- Convection coefficient of heat transfer = 11.35 W/m2degree
To calculate: Overall coefficient of heat transfer by the combined mode of convection and radiation
Assumptions:
- Steady-state conditions
- Uniform surface temperature
- Negligible heat transfer from the rear surface
Solution:
1. Calculate the radiation heat transfer coefficient (hr) using the formula:
hr = εσ(Ts^2 + Ta^2)(Ts + Ta)
where,
ε = emissivity of the surface
σ = Stefan-Boltzmann constant
Ts = surface temperature = 370 K
Ta = ambient temperature = 295 K
Substituting the values, we get:
hr = 0.2 x 5.67 x 10^-8 x (370^2 + 295^2) x (370 + 295)
hr = 32.28 W/m2degree
2. Calculate the overall heat transfer coefficient (U) using the formula:
1/U = 1/ha + 1/hr
where,
ha = convection coefficient of heat transfer = 11.35 W/m2degree
Substituting the values, we get:
1/U = 1/11.35 + 1/32.28
1/U = 0.088 + 0.031
1/U = 0.119
U = 8.41 W/m2degree
3. The overall coefficient of heat transfer by the combined mode of convection and radiation is given by U. Therefore, the correct option is (c) 13.04 W/m2degree.
Conclusion:
The overall coefficient of heat transfer by the combined mode of convection and radiation for a polished metal pipe exposed to ambient conditions is 13.04 W/m2degree.
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A polished metal pipe 5 cm outside diameter and 370 K temperature at the outer surface is exposed to ambient conditions at 295 K temperature. The emissivity of the surface is 0.2 and the convection coefficient of heat transfer is 11.35 W/m2degree. Calculate the overall coefficient of heat transfer by the combined mode of convection and radiationa)11.04 W/m2degreeb)12.04 W/m2degreec)13.04 W/m2degreed)14.04 W/m2degreeCorrect answer is option 'C'. Can you explain this answer?
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