Boiler tubes exposed to the products of coal combustion in a power plant are subject to fouling by the ash (mineral) content of the combustion gas. The ash forms a solid deposit on the tube outer surface, which reduces heat transfer to a pressurized water/steam mixture flowing through the tubes. Consider a thin-walled boiler tube ( D t = 0.05 m ) whose surface is maintained at T t = 600 K by the boiling process. Combustion gases flowing over the tube at T ∞ = 1800 K provide a convection coefficient of h ¯ = 100 W/m 2 ⋅ K , while radiation from the gas and boiler walls to the tube may be approximated as that originating from large surroundings at T sur = 1500 K . (a) It the lube surface is diffuse and gray, with ε t = 0.8 , and there is no ash deposit layer, what is the rate of heat transfer per unit length, q’, to the boiler tube? (b) If a deposit layer of diameter D d = 0.06 m and thermal conductivity k = 1 W/m ⋅ K forms on the tube, what is the deposit surface temperature, T d ? The deposit is diffuse and gray, with ε d = 0.9 , and T t , T ∞ , h ¯ , and T sur remain unchanged. What is the net rate of heat transfer per unit length, q’ , to the boiler tube? (c) Explore the effect of Variations in D d and h ¯ on q’ , as well as on relative contributions of convection and radiation to the net heat transfer rate. Represent your results graphically.
Boiler tubes exposed to the products of coal combustion in a power plant are subject to fouling by the ash (mineral) content of the combustion gas. The ash forms a solid deposit on the tube outer surface, which reduces heat transfer to a pressurized water/steam mixture flowing through the tubes. Consider a thin-walled boiler tube ( D t = 0.05 m ) whose surface is maintained at T t = 600 K by the boiling process. Combustion gases flowing over the tube at T ∞ = 1800 K provide a convection coefficient of h ¯ = 100 W/m 2 ⋅ K , while radiation from the gas and boiler walls to the tube may be approximated as that originating from large surroundings at T sur = 1500 K . (a) It the lube surface is diffuse and gray, with ε t = 0.8 , and there is no ash deposit layer, what is the rate of heat transfer per unit length, q’, to the boiler tube? (b) If a deposit layer of diameter D d = 0.06 m and thermal conductivity k = 1 W/m ⋅ K forms on the tube, what is the deposit surface temperature, T d ? The deposit is diffuse and gray, with ε d = 0.9 , and T t , T ∞ , h ¯ , and T sur remain unchanged. What is the net rate of heat transfer per unit length, q’ , to the boiler tube? (c) Explore the effect of Variations in D d and h ¯ on q’ , as well as on relative contributions of convection and radiation to the net heat transfer rate. Represent your results graphically.
Solution Summary: The author calculates the net radiation heat transferper unit length, which is q=54000, the diameter of the gauge, and the surrounding temperature.
Boiler tubes exposed to the products of coal combustion in a power plant are subject to fouling by the ash (mineral) content of the combustion gas. The ash forms a solid deposit on the tube outer surface, which reduces heat transfer to a pressurized water/steam mixture flowing through the tubes. Consider a thin-walled boiler tube
(
D
t
=
0.05
m
)
whose surface is maintained at
T
t
=
600
K
by the boiling process. Combustion gases flowing over the tube at
T
∞
=
1800
K
provide a convection coefficient of
h
¯
=
100
W/m
2
⋅
K
, while radiation from the gas and boiler walls to the tube may be approximated as that originating from large surroundings at
T
sur
=
1500
K
.
(a) It the lube surface is diffuse and gray, with
ε
t
=
0.8
, and there is no ash deposit layer, what is the rate of heat transfer per unit length, q’, to the boiler tube? (b) If a deposit layer of diameter
D
d
=
0.06
m
and thermal conductivity
k
=
1
W/m
⋅
K
forms on the tube, what is the deposit surface temperature,
T
d
? The deposit is diffuse and gray, with
ε
d
=
0.9
, and Tt,
T
∞
,
h
¯
, and
T
sur
remain unchanged. What is the net rate of heat transfer per unit length, q’, to the boiler tube? (c) Explore the effect of Variations in Ddand
h
¯
on q’, as well as on relative contributions of convection and radiation to the net heat transfer rate. Represent your results graphically.
The cylinders that come out of the heat treatment furnace are cooled in a stagnant air environment in a horizontal position. The cylinders have a diameter of 100 mm and a length of 0.1 m. The temperature of the cylinders is 440 ° C and the ambient temperature is 20 ° C.
Calculate the heat transfer from 10 cylinders to the environment.
a) 3125 W
b) 2350 W
C) 1848 W
d) 1354 W
e) 2750 W
Inside a condenser, there is a bank of seven copper tubes with cooling water flowing in them. Steam condenses at a rate of 0.6 kg/s on the outer surfaces of the tubes that are at a constant temperature of 68°C. Each copper tube is 5-m long and has an inner diameter of 25 mm. Cooling water enters each tube at 5°C and exits at 60°C. Determine the average heat transfer coefficient of the cooling water flowing inside each tube and the cooling water mean velocity needed to achieve the indicated heat transfer rate in the condenser.
Engine oil enters a straight tube with a flow rate of 1 kg/s. The tube has a diameter of 5 mm and the surface temperature of the tube is maintained at 150˚C. The engine oil has an inlet temperature 52˚C and it is desired to heat the oil to a mean temperature of 80˚C at the exit of the straight tube. The properties of the engine oil are k = 0.139 W/m.K, Pr = 834, cp = 2072 J/kg.K and μ = 5.62 x 10-2 N.s/m2 Assume the flow is at fully developed region, determine:(a) The required length of the tube. (b) The rate of heat transfers from the tube to the engine oil.
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