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Pérdidas de calor en tuberías
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Client: XXXProject No: XXXProject Title: XXXDocument: Colour KeySheet Ref: Manual InputRevision: ResultsLast Updated: 03/01/2011 Do not use
Revision detail: Assumptions and important notesSources and titles
Reference Method Used:
Main Data InputPhysical Properties Units Air density at related temperature and pressure
Liquid Air Room Pressure P 101.325 kPaMol. Wt of air M 29 kg/kmol
Liquid in the tank Etylenediamine (EDA) Gas const R 8.31 kJ/kmol K
Density,ρ 897 1.34 Vapour/air Temp t -10Specific Heat,Cp 2.8 1.005 kJ/kg K T 263.15 K
2847 1005 J/kg K Air Density, PM/RT 1.34Viscosity,µ 1.8 - cP or m.Pa.s
0.0018 0.0000198 kg/m.s Thermal ConductiviEtylenediamine (EDA)
Thermal conductivity,k 0.257 0.0257 W/m.K
Co-efficient of volumetric expansion, ß 0.000108 0.00343 1/K Thermal Conductivit k = 0.224 W/m.K
Molecular Mass of liquid,M 60.1 - kg/kmol
11.14 -
Units
Wet wall 5000 Source: Chemical Engineering Design by Coulson and Richardson, Volume 6, Page 640
Thermal Conductivities/thickness Units
45 W/m K Source: Metal wall thickness 3.68 mm
0.00368 m
0.038 W/m K Source: Insulation thickness 25 mm
0.025 m
Surface Emissivity Units
Wall, ε 0.9 Assumed - less than 1
Gravitational constant, g 9.81
Pipe dimensions Units
Inside pipe diameter Di,p 0.041 mOutsidepipe diameter Do,p 0.048 mMean pipe diameter Dm,p 0.045 mOutisde diameter insulation Do,i 0.098 mLog mean diameter insulatioDlm,i 0.070 m
e, absolute roughness 0.00005 m
Temperature Units
21 Temperature just after loading Summary Units
Problem Description:
Important values and calculations
kg/m3 oC
ρair = kg/m3
k = 3.56 x 10 -5 x Cp ( ρ4/M)1/3 ------------> from Coulson & Richardson. Vol 6, Page 321
Melting Point, oC oC
Assumed fouling coefficient, hF
W/m2 K
Metal walls (Carbon Steel, max 0.5% Carbon),kM Engg Toolbox : Thermal Conductivity of some common Materials
Insulation (Armaflex), kI Engg Toolbox : Thermal Conductivity of some common Materials
m/s2
Engg Toolbox: Surface roughness several materials
Liquid in pipe, TLoC
-10 velocity 1.00 m/swind factor 6.2 -ambient -10 ˚C
Summary of temperatures used in calcs Units Heat loss/unit length 9.8 W/m
294.2 K
263.2 K
First Guess 278.7 K
After iteration 293.7 K 293.5
First Guess 278.7 K
After iteration 265.0 K 265.6
Summary of flow conditions in pipe Units
Velocity 1.0 m/s
Reynolds Number 20401.7666666667 Colebrook equation for friction factorA 6.07406 A=-2.0*LOG[(e/(D*3.7))+(12/Re)]B 5.93527 B=-2.0*LOG[(e/(D*3.7))+(2.51*A/Re)]C 5.94915 C=-2.0*LOG[(e/(D*3.7))+(2.51*B/Re)]f 0.02827 f=[A-(B-A)^2/(C-2B+A)]^-2
Calculation
2.63E+08
2.63E+08
1.55E+08
1.55E+08
= Cp x µ /k
19.95
0.77
Outside air, TAoC
Liquid in pipe, TL
Outside air, TA
Tw=(TL + TA )/ 2
Tw Tw=TL-(Utot/hi)(TL-TA)
Tws=(TL + TA )/ 2
Tws Tws=(Utot/(hRo + h*wo))(TL-TA)+TA
NRe = (ρ x v x Di) / µ
Calculation of Grashof Number (N GR)
Grashof Number, NGr = L3 x ρ2 x g x ß x ΔT /µ2
NGr for the liquid phase ( ρ2 x g x ß x /µ2 ) ( ρ2 x g x ß x /µ2 ) L3 x ΔT x L3 x ΔT
NGr for outside air ( ρ2 x g x ß x /µ2 ) ( ρ2 x g x ß x /µ2 ) L3 x ΔT x L3 x ΔT
Calculation of Prandtl Number (N Pr)
Prandtl Number,NPr
NPr for the liquid phase
NPr for outside air
Calculation of Rayleigh Number (N Ra)
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
Iteration:
Put the right values manually into respective yellow cells untill difference between the two values approache zero
L=Di 0.04 m
0.45 KL=Di 0.04 m
2.63E+08 19.95
8.12E+03 20402f 0.02827
1.62E+05
Reference: Incropera Page 515
11.24 235.87
o.k o.k
o.k
o.k
Nusselt Equation (Perry 5-13) Nusselt Equation (Perry 5-13)
70.55 1480.08
L=Do,i 0.10 m
1.85 K
1.55E+08
2.72E+05
2.11E+05
9.58
o.k
Nusselt Equation (Perry 5-13)
2.50
------------- Equation 21
------------- Equation 22
12228.26 ------------- USING Equation 21
1.52 ------------- USING Equation 22
ΔT = TL – Twl
NGr x L3 x ΔT NPr
NGr NRe
NRa,l
For horizontal cylinders, Nusselt Number, NNu For horizontal cylinders, Nusselt Number, NNu
NNu ={0.60 + (0.387 x (NRa)1/6)/[1+(0.559/NPr)9/16]8/27}2 Ra ≤ 1012 NNu =(f/8)(NRe-1000)(NPr)/[1+12,7(f/8)1/2(NPr2/3-1)]
NNu NNu
Where Ra ≤ 1012 Where NPr ≤ 2000
Where NRe ≤ 5e6
Where NRe ≥ 3000
Coefficient of liquid at wall, hi = NNu x k / Di
Coefficient of liquid at wall, hi = NNu x k / Di
Coefficient of liquid at wall, hi W/m2 KCoefficient of liquid
at wall, hi W/m2 K
Outside coefficient of air at pipe wall/insulation, h'wo
ΔT = Tws- TA
NGr x L3 x ΔT
NGr
Nra,A
For horizontal cylinders, Nusselt Number, NNu
NNu ={0.60 + (0.387 x (NRa)1/6)/[1+(0.559/NPr)9/16]8/27}2 Ra ≤ 1012
NNu
Where Ra ≤ 1012
Coefficient of outside air at wall,hAwV,cyl = NNu x k /Do
Coefficient of outside air at wall,hAwV,cyl W/m2 K
Conduction coefficient for metal wall and insulation, hM and hI
hM = kM /tM
hI = kI /tI
hM W/m2 K
hI W/m2 K
------------- Equation 24
2.341 ------------- USING Equation 24
Summary
70.55
1480.08
2.50 Do NOT use this value
15.53
12228.2608695652 6.2
1.52
5000
2.341
1.40
0 m/hr
3.16 m K/W
Total heat loss per unit length
Q/L 9.8 W/m
Radiation coefficient for pipewall to air (hRO)
hR = 0.1713 ε [((Tws + 460)/100)4 - ((TA + 460)/100)4]/( Tws - TA)
hR,A W/m2 K
Coefficient ( W/m2 K)
Coefficient of liquid at pipe wall at no flow (free convection), hwi
Coefficient of liquid at pipe wall at flow (forced convection), hwi,f
Outside coefficient of air at pipe wall, h'wo
Coefficient of outside air at cylindrical wall considering wind enhancement factor for the assumed wind velocity, h*wo
Obtained by multiplying above value by wind enhancement factor
Conduction coefficient for metal wall hM
Conduction coefficient for insulation hI
Fouling coefficient, hFi
Radiation coefficient pipewall (hRO)
Overall coefficient,Utot
Overall Heat Transfer Coefficient per unit length, U tot,l
Overall coefficient, Utot,l per unit length at wind velocity of
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
Q/L= (TL-TA)/Utot,l
Reference: Incropera Page 515
No Flow Flow
Windforce Q[˚C] [-] [W/m]
5 0 4.4 4.55 3 4.7 4.95 5 4.8 5.15 6 4.9 5.10 0 5.7 60 3 6.2 6.50 5 6.3 6.60 6 6.4 6.7
-10 0 8.5 8.9-10 3 9 9.6-10 5 9.2 9.8-10 6 9.5 9.9
Ambient temperature
Heat input
[W/m]
101010101010101010101010
-12 -10 -8 -6 -4 -2 0 2 4 60
2
4
6
8
10
12
Heatbalance EDA feedlineFlow conditions
Heat loss @ quiescent airPolynomial (Heat loss @ quiescent air)Heat loss @ Beaufort 3Polynomial (Heat loss @ Beaufort 3)Heat loss @ Beaufort 5Polynomial (Heat loss @ Beaufort 5)Heat loss @ Beaufort 6
Ambient temperature [˚C]
heat
loss
/inpu
t [kW
]
-12 -10 -8 -6 -4 -2 0 2 4 60
2
4
6
8
10
12
Heatbalance EDA feedlineFlow conditions
Heat loss @ quiescent airPolynomial (Heat loss @ quiescent air)Heat loss @ Beaufort 3Polynomial (Heat loss @ Beaufort 3)Heat loss @ Beaufort 5Polynomial (Heat loss @ Beaufort 5)Heat loss @ Beaufort 6
Ambient temperature [˚C]
heat
loss
/inpu
t [kW
]