Client: Project No: Project Title: Document: Sheet Ref: Revision: Last Updated:
Problem Description:
XXX XXX XXX
Colour Key Manual Input Results Do not use
03/01/2011
Assumptions and important notes Sources and titles
Revision detail:
Important values and calculations
Reference Method Used:
Main Data Input Physical Properties
Units Liquid
Liquid in the tank Density,ρ Specific Heat,Cp
Etylenediamine (EDA) 897 2.8 2847
Viscosity,µ
Molecular Mass of liquid,M o Melting Point, C
Room Pressure Mol. Wt of air Gas const Vapour/air Temp
3
1.34 kg/m 1.005 kJ/kg K 1005 J/kg K
1.8 0.0018 0.257 0.000108
Thermal conductivity,k Co-efficient of volumetric expansion, ß
-
2
5000 W/m K
kg/kmol C
o
Source:
Chemical Engineering Design by Coulson and Richardson, Volume 6, Page 640
45 W/m K 3.68 mm 0.00 0.0036 368 8 m
Source:
Engg Toolbox : Thermal Conductivity of some common Materials
0.038 W/ W /m K 25 mm 0.025 m
Source:
Engg Toolbox : Thermal Conductivity of some common Materials
Thermal Conductivities/thickness
Units
Metal walls (Carbon Steel, max 0.5% Carbon),k M Metal wall thickness
Insulation (Armaflex), k I Insulation thickness
Surface Emissivity
Units
Wall, ε
0.9
Assumed - less than 1 2
Gravitational constant, g
9.81 m/s
Pipe dimensions
Units
Di,p Do,p Dm,p Do,i Dlm,i e, absolute roughness
0.041 0.048 0.045 0.098 0.070 0.00 0.0000 005 5
Temperature
m m m m m m
Engg Toolbox: Surface roughness several several materials
Units 21 C
Liquid in pipe, TL
Temperature just after loading
o
-10 C
Outside air, T A
Summary of temperatures used in calcs
Summary
velocity
wind factor ambient Heat loss/unit length
Units Iteration:
Liquid in pipe, TL
294.2 K
Outside air, T A
263.2 K
First Guess
Tw=(TL + TA )/ 2
278.7 K
After iteration
Tw
293.7 K
First Guess
Tws=(TL + TA )/ 2
278.7 K
After iteration
Tws
265.0 K
Summary of flow conditions in pipe
Put the right values manually into respective yellow cells untill difference between the two values approache zero
20401.76667 6.07406 5.93527 5.94915 0.02827
Calculation Calculation of Grashof Number (NGR) Grashof Number, NGr = L x ρ x g x ß x ΔT /µ NGr for the liquid phase 2
( ρ x g x ß x /µ ) 2 2 3 ( ρ x g x ß x /µ ) L x ΔT
2.63E+08 3 2.63E+08 x L x ΔT
NGr for outside air 2
Tw=TL-(Utot/hi)(TL-T A)
265.6
Tws=(Utot/(hRo + h*wo))(TL-T A)+T A
1.0 m/s
NRe = (ρ x v x D i) / µ A B C f
2
293.5
Units
Velocity
2
( ρ x g x ß x /µ ) 2 2 3 ( ρ x g x ß x /µ ) L x ΔT
1.55E+08 3 1.55E+08 x L x ΔT
Calculation of Prandtl Number (NPr ) Prandtl Number,NPr = Cp x µ /k NPr for the liquid phase
19.95
NPr for outside air
0.77
101.325 29 8.31 -10 263.15 1.34
k Pa kg/kmol kJ/kmol K o C K kg/m
Thermal Conducti Etylenediamine (EDA) -5 4 1/3 k = 3.56 x 10 x Cp ( ρ /M) ------------> from Coulson & Richardson. Vol 6, Page 321 Thermal Conductivi k= 0.224 W/m.K
Units
Assumed fouling coefficient, h F
Reynolds Number
P M R t T ρair =
Air Density, PM/RT
cP or m.Pa.s 0.0000198 kg/m.s 0.0257 W/ W /m.K 0.00343 1/K
60.1 11.14
Wet wall
Inside pipe diameter Outsidepipe diameter Mean pipe diameter Outisde diameter insulation Log mean diameter insulati
Air density at related temperature and pressure
Ai r
Colebrook equation for friction factor A=-2.0*LOG[(e/(D*3.7))+(12/Re)] B=-2.0*LOG[(e/(D*3.7))+(2.51*A/Re)] C=-2.0*LOG[(e/(D*3.7))+(2.51*B/Re)] f=[A-(B-A)^2/(C-2B+A)]^-2
Units 1.00 m/s
6.2 -10 ˚C 9.8 W/m
Summary of temperatures used in calcs
wind factor ambient Heat loss/unit length
Units
6.2 -10 ˚C 9.8 W/m
Iteration:
Liquid in pipe, TL
294.2 K
Outside air, T A
263.2 K
First Guess
Tw=(TL + TA )/ 2
278.7 K
After iteration
Tw
293.7 K
First Guess
Tws=(TL + TA )/ 2
278.7 K
After iteration
Tws
265.0 K
Summary of flow conditions in pipe
293.5
Tw=TL-(Utot/hi)(TL-T A)
265.6
Tws=(Utot/(hRo + h*wo))(TL-T A)+T A
Units
Velocity Reynolds Number
Put the right values manually into respective yellow cells untill difference between the two values approache zero
1.0 m/s
NRe = (ρ x v x D i) / µ A B C f
20401.76667 6.07406 5.93527 5.94915 0.02827
Colebrook equation for friction factor A=-2.0*LOG[(e/(D*3.7))+(12/Re)] B=-2.0*LOG[(e/(D*3.7))+(2.51*A/Re)] C=-2.0*LOG[(e/(D*3.7))+(2.51*B/Re)] f=[A-(B-A)^2/(C-2B+A)]^-2
Calculation Calculation of Grashof Number (NGR) Grashof Number, NGr = L x ρ x g x ß x ΔT /µ NGr for the liquid phase 2
2
( ρ x g x ß x /µ ) 2 2 3 ( ρ x g x ß x /µ ) L x ΔT
2.63E+08 3 2.63E+08 x L x ΔT
NGr for outside air 2
2
( ρ x g x ß x /µ ) 2 2 3 ( ρ x g x ß x /µ ) L x ΔT
1.55E+08 3 1.55E+08 x L x ΔT
Calculation of Prandtl Number (NPr ) Prandtl Number,NPr = Cp x µ /k NPr for the liquid phase
19.95
NPr for outside air
0.77
Calculation of Rayleigh Number (NRa) Rayleigh Number,NRa = NGr x NPr
Coefficient of liquid at pipe wall at no flow conditions, hwi
Coefficient of liquid at pipe wall at flowing conditions, hwi
L=Di
0.04 m
ΔT = TL – Twl
0.45 K
NGr
2.63E+08 x L x ΔT
NGr
8.12E+03
NRa,l
1.62E+05
L=Di NPr
0.04 m 19.95
NRe f
For horizontal cylinders, Nusselt Number, N Nu
20402 0.02827
For horizontal cylinders, Nusselt Number, N Nu
NNu ={0.60 + (0.387 x (NRa) )/[1+(0.559/NPr ) NNu
]
} Ra ≤ 10
Where Ra ≤ 10
o.k
Coefficient of liquid at wall, h i = NNu x k / Di Coefficient of liquid at wall, h i
Nusselt Equation (Perry 5-13)
Outside coefficient of air at pipe wall/insulation, h'wo
L=Do,i
0.10 m
ΔT = Tws- TA
1.85 K
NGr
1.55E+08 x L x ΔT
NGr
2.72E+05
Nra,A
2.11E+05
For horizontal cylinders, Nusselt Number, N Nu 1/6
NNu ={0.60 + (0.387 x (NRa) )/[1+(0.559/NPr ) NNu 12
]
} Ra ≤ 10
o.k
Coefficient of outside air at wall,h AwV,cyl = NNu x k /Do Coefficient of outside air at wall,h AwV,cyl
9/16 8/27 2
9.58
2.50
Nusselt Equation (Perry 5-13) 2
W/m K
235.87 Where NPr ≤ 2000
o.k
Where NRe ≤ 5e6
o.k
Where NRe ≥ 3000
o.k
Coefficient of liquid at wall, hi = NNu x k / Di Coefficient of liquid at wall, hi
2
W/m K
70.55
Where Ra ≤ 10
NNu =(f/8)(NRe-1000)(NPr )/[1+12,7(f/8) (NPr -1)] NNu
11.24
1480.08
Nusselt Equation (Perry 5-13) 2
W/m K
Refere
NGr
2.63E+08 x L x ΔT
NGr
8.12E+03
NRa,l
1.62E+05
L=Di NPr
0.04 m 19.95
NRe f
For horizontal cylinders, Nusselt Number, N Nu
20402 0.02827
For horizontal cylinders, Nusselt Number, N Nu
NNu ={0.60 + (0.387 x (NRa) )/[1+(0.559/NPr ) NNu
]
} Ra ≤ 10
NNu =(f/8)(NRe-1000)(NPr )/[1+12,7(f/8) (NPr -1)] NNu
11.24 Where Ra ≤ 10
o.k
Coefficient of liquid at wall, h i = NNu x k / Di Coefficient of liquid at wall, h i
Coefficient of liquid at wall, hi
2
W/m K
Outside coefficient of air at pipe wall/insulation, h'wo
L=Do,i
0.10 m
ΔT = Tws- TA
1.85 K
NGr
1.55E+08 x L x ΔT
NGr
2.72E+05
Nra,A
2.11E+05
For horizontal cylinders, Nusselt Number, N Nu 1/6
NNu ={0.60 + (0.387 x (NRa) )/[1+(0.559/NPr ) NNu
9/16 8/27 2
]
} Ra ≤ 10
9.58 Where Ra ≤ 10
12
o.k
Coefficient of outside air at wall,h AwV,cyl = NNu x k /Do Coefficient of outside air at wall,h AwV,cyl
2.50
Nusselt Equation (Perry 5-13) 2
W/m K
Conduction coefficient for metal wall and insulation, h M and hI hM = kM /tM
------------- Equation 21
hI = kI /tI
------------- Equation 22
hM
12228.26
W/m K
------------- USING Equation 21
hI
1.52
W/m K
------------- USING Equation 22
Radiation coefficient for pipewall to air (h RO)
4
4
hR = 0.1713 ε [((Tws + 460)/100) - ((T A + 460)/100) ]/( Tws - T A)
hR,A
2
Coefficient ( W/m K)
2.341
W/m K
------------- Equation 24
------------- USING Equation 24
Summary
Coefficient of liquid at pipe wall at no flow (free convection), h wi
70.55
Coefficient of liquid at pipe wall at flow (forced convection), h wi,f
1480.08
Outside coefficient of air at pipe wall, h' wo
2.50
Do NOT use this value
15.53
Obtained by multiplying above value by wind enhancement factor
Coefficient of outside air at cylindrical wall considering wind enhancement factor for the assumed wind velocity,
h*wo Conduction coefficient for metal wall hM
12228.26087
Conduction coefficient for insulation hI
1.52
Fouling coefficient, h Fi
5000
Radiation coefficient pipewall (hRO)
2.341
Overall coefficient,Utot
1.40
6.2
Overall Heat Transfer Coefficient per unit length, U tot,l
Overall coefficient, Utot,l per unit length at wind velocity of
0
m/hr
1/Utot,l = 1/(hwi x πDi) + tm/(km x πDm,p) + ti/(ki x πDlm,i) + 1/((h*wo + hrd ) x πDo,i) + 1/(hfi x πDi) 1/Utot,l
3.16 m K/W
Total heat loss per unit length Q/L= (TL-T A)/Utot,l Q/L
9.8 W /m
Where NPr ≤ 2000
o.k
Where NRe ≤ 5e6
o.k
Where NRe ≥ 3000
o.k
Coefficient of liquid at wall, hi = NNu x k / Di
Nusselt Equation (Perry 5-13)
70.55
235.87
1480.08
Nusselt Equation (Perry 5-13) 2
W/m K
Refere
4
4
hR = 0.1713 ε [((Tws + 460)/100) - ((T A + 460)/100) ]/( Tws - T A)
hR,A
2
Coefficient ( W/m K)
2.341
W/m K
------------- Equation 24
------------- USING Equation 24
Summary
Coefficient of liquid at pipe wall at no flow (free convection), h wi
70.55
Coefficient of liquid at pipe wall at flow (forced convection), h wi,f
1480.08
Outside coefficient of air at pipe wall, h' wo
2.50
Do NOT use this value
15.53
Obtained by multiplying above value by wind enhancement factor
Coefficient of outside air at cylindrical wall considering wind enhancement factor for the assumed wind velocity,
h*wo Conduction coefficient for metal wall hM
12228.26087
Conduction coefficient for insulation hI
1.52
Fouling coefficient, h Fi
5000
Radiation coefficient pipewall (hRO)
2.341
Overall coefficient,Utot
1.40
6.2
Overall Heat Transfer Coefficient per unit length, U tot,l
Overall coefficient, Utot,l per unit length at wind velocity of
0
m/hr
1/Utot,l = 1/(hwi x πDi) + tm/(km x πDm,p) + ti/(ki x πDlm,i) + 1/((h*wo + hrd ) x πDo,i) + 1/(hfi x πDi) 1/Utot,l
3.16 m K/W
Total heat loss per unit length Q/L= (TL-T A)/Utot,l Q/L
9.8 W /m
nce: Incropera Page 515
nce: Incropera Page 515
No Flow
Ambient temperature [˚C] 5 5 5 5 0 0 0 0 -10 -10 -10 -10
Windforce [-]
Flow
Q [W/m] 0 3 5 6 0 3 5 6 0 3 5 6
4.4 4.7 4.8 4.9 5.7 6.2 6.3 6.4 8.5 9 9.2 9.5
4.5 4.9 5.1 5.1 6 6.5 6.6 6.7 8.9 9.6 9.8 9.9
No Flow
Ambient temperature [˚C] 5 5 5 5 0 0 0 0 -10 -10 -10 -10
Windforce [-]
Flow
Q [W/m] 0 3 5 6 0 3 5 6 0 3 5 6
4.4 4.7 4.8 4.9 5.7 6.2 6.3 6.4 8.5 9 9.2 9.5
4.5 4.9 5.1 5.1 6 6.5 6.6 6.7 8.9 9.6 9.8 9.9
Heat input
Heatbala Flo
[W/m] 12
10 10 10 10 10 10 10 10 10 10 10 10
10
] W k [ t u p n i / s s o l t a e h
8
6
4
2
0 -15
-10
-5
0
Ambient temperat
ce EDA feedline w conditions
Heat loss @ quiescent air Heat loss @ Beaufort 3 Heat loss @ Beaufort 5 Heat loss @ Beaufort 6 Maximum heat input
5
ure [˚C]
10
