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7/25/2019 Tank Example
1/27
TANK
Sample Printout2014
Lauterbach Verfahrenstechnik GmbH 1 2014
Layout
Input values: 1.234 or 1.234
Calculated values: 1.234 or 1.234
Critical values: 1.234 or 1.234
Estimated values: 1.234 or 1.234
Table of contents
Table of contents ......................................................................... 1
Calculation of heat loss of storage tanks ................................................. 2
Properties tank medium*................................................................... 6
Gas properties*........................................................................... 7
Outside heat transfer coefficient, roof*.................................................. 8
Inside heat transfer coefficient, bottom*................................................ 10
Outside heat transfer coefficient, shell*................................................ 12
Inside heat transfer coefficient, wet shell*............................................. 14
Inside heat transfer coefficient, dry shell*............................................. 16
Inside heat transfer coefficient, roof*.................................................. 18
Heat transfer radiation inside, roof*.................................................... 20
Physical properties of heating medium*................................................... 21
Tube-side heat transfer*................................................................. 22
Heat transfer coil around tubes*......................................................... 25
Pressure drop in coil*................................................................... 27
7/25/2019 Tank Example
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TANK
Sample Printout2014
Lauterbach Verfahrenstechnik GmbH 2 2014
Global conditions
Product temperature tP 50 CInside pressure pi 1 bar
Air temperature tL -20 C
Wind speed Wv 10 m/s
Ground temperature tB -20 C
Geometry of storage tank
Ground plan Round sketch
Diameter DT 12 m
Circumference 37.7 m
Area 113.1 m
Tank height HT 15 m
Filling level HF 14 m
Properties:
Storage medium HFO 180
Density 897.9 kg/m
Specific heat capacity cp 1930 J/(kgK)
Thermal conductivity 0.124 W/(mK)Dynamic viscosity 171 mPasKinematic viscosity 0.000190 m/sCoefficient of thermal expansion 0.000707 1/K
Gas above storage medium
Medium name air
Density 1.078 kg/m
Specific heat capacity cp 1008 J/(kgK)
Thermal conductivity 0.02808 W/(mK)
Dynamic viscosity 0.01964 mPasKinematic viscosity 0.000018 m/sCoefficient of thermal expansion 0.003101 1/K
Wall thickness and thermal conductivity of the tank and the insulation
Bottom Shell Roof
Tank wall thickness 8 mm 8 mm 8 mm
Thermal conductivity 52 W/(mK) 52 W/(mK) 52 W/(mK)
Insulation thickness 250 mm 100 mm 100 mm
Thermal conductivity 2.5 W/(mK) 0.04 W/(mK) 0.04 W/(mK)
Heat losses
Bottom Shell wet part Shell dry part Roof
23.63kW
14.32kW
0.9186kW
2.881kW
Total heat loss Qtot 41.75 kW
Calculation of heat loss of storage tanks
7/25/2019 Tank Example
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TANK
Sample Printout2014
Lauterbach Verfahrenstechnik GmbH 3 2014
Bottom
Thickness of the wall siB 8 mm
Thermal conductivity of the wall iB 52 W/(mK)
Thermal resistance of the wall iB 0.000154 mK/WThickness of the insulation saB 250 mm
Thermal conductivity of the insulation aB 2.5 W/(mK)Thermal resistance of the insulation aB 0.1 mK/W
Heat transfer coefficient outside aB 5 W/(mK)Heat transfer coefficient inside iB 28.67 W/(mK)
Contact surface AB = 113.1 m
Temperature inside tiB = 42.71 C
Temperature (wall-insulation) tgB = 42.68 C
Temperature outside taB = 21.79 C
Heating performance QhB 0 kW
Heat flow from inside QiB = 23.63 kW
Heat flow to outside QaB = 23.63 kW
Shell
Thickness of the wall siM 8 mm
Thermal conductivity of the wall iM 52 W/(mK)Thermal resistance of the wall iM 0.000154 mK/W
Thickness of the insulation saM 100 mm
Thermal conductivity of the insulation aM 0.04 W/(mK)Thermal resistance of the insulation aM 2.5 mK/W
Heat transfer coefficient outside aM 41.67 W/(mK)
Wet part
Heat transfer coefficient inside iMb 17.68 W/(mK)
Contact surface AMb = 527.8 m
Temperature inside tiMb = 48.47 CTemperature (wall-insulation) tgMb = 48.46 C
Temperature outside taMb = -19.35 C
Heating performance QhMb 0 kW
Heat flow from inside QiMb = 14.32 kW
Heat flow to outside QaMb = 14.32 kW
Dry part
Heat transfer coefficient inside iMt 2.868 W/(mK)
Contact surface AMt = 37.7 m
Temperature inside tiMt = 41.5 C
Temperature (wall-insulation) tgMt = 41.5 C
Temperature outside taMt = -19.42 C
Heating performance QhMt 0 kW
Heat flow from inside QiMt = 0.9186 kW
Heat flow to outside QaMt = 0.9186 kW
7/25/2019 Tank Example
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TANK
Sample Printout2014
Lauterbach Verfahrenstechnik GmbH 4 2014
Roof
Thickness of the wall siD 8 mm
Thermal conductivity of the wall iD 52 W/(mK)
Thermal resistance of the wall iD 0.000154 mK/WThickness of the insulation saD 100 mm
Thermal conductivity of the insulation aD 0.04 W/(mK)Thermal resistance of the insulation aD 2.5 mK/W
Emissivity of the roof D 0.8 -Emissivity of the product P 0.9 -Heat transfer coefficient outside aD 19.77 W/(mK)Heat transfer coefficient inside (total) iD 5.067 W/(mK)
Contact surface AD = 113.1 m
Temperature inside tiD = 44.97 C
Temperature (wall-insulation) tgD = 44.97 C
Temperature outside taD = -18.71 C
Heating performance QhD 0 kW
Heat flow from inside QiD = 2.881 kW
Heat flow to outside QaD = 2.881 kW
Balance
Heating performance Qh_ges = 0 kW
Heat flow from inside Qi_ges = 41.75 kW
Heat flow to outside Qa_ges = 41.75 kW
7/25/2019 Tank Example
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TANK
Sample Printout2014
Lauterbach Verfahrenstechnik GmbH 5 2014
Calculation of the heating coil
Heating medium Transcal LT
Mass flow m 7963 kg/hVolume flow V 10 m/h
Pressure (abs.) P 3 bar
Inlet temperature e 140 COutlet temperature a 131.9 CMean temperature m 136 C
Tube outside diameter da 60.3 mm
Tube wall thickness s 2.9 mm
Tube inside diameter di 54.5 mm
Thermal conductivity of tube material R 52 W/(mK)Fouling inside fi 0 mK/W
Fouling outside fa 0 mK/W
Properties of the heating medium
Density 796.9 kg/mSpecific heat capacity cp 2342 J/(kgK)
Thermal conductivity 0.125 W/(mK)Dynamic viscosity 1.183 mPas
Kinematic viscosity 1.484 mm/s
Properties of the storage medium at 87.85 CDensity 874.3 kg/mSpecific heat capacity cp 2062 J/(kgK)
Thermal conductivity 0.1214 W/(mK)Dynamic viscosity 33.19 mPas
Kinematic viscosity 0.000038 m/sCoefficient of thermal expansion 0.00072 1/K
ResultTube-side velocity u 1.191 m/s
Heat transfer coefficient inside i 1076 W/(mK)Heat transfer coefficient outside a 124.9 W/(mK)Overall heat transfer coefficient k 110 W/(mK)
Pressure drop (straight tube without bends) P 5736 PaTube length L 23.33 m
Area A 4.419 m
7/25/2019 Tank Example
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TANK
Sample Printout2014
Lauterbach Verfahrenstechnik GmbH 6 2014
Properties of Heavy Fuel Oils (HFO)
Selected oil: HFO 180
Oil selection: 7
State 1: State 2:
Temperature 50 C 87.86 C
Density 897.9 kg/m 874.1 kg/m
Specific heat capacity cp 1930 J/(kgK) cp 2062 J/(kgK)
Dynamic viscosity 171 mPas 33.19 mPasKinematic viscosity 0.000190 m/s 0.000038 m/sThermal conductivity 0.124 W/(mK) 0.1213 W/(mK)Coef. of thermal expansion 0.000707 1/K 0.000720 1/K
Prandtl number Pr 2661 - Pr 564 -
Thermal diffusivity a 7.155E-8 m/s a 6.731E-8 m/s
Pr = /a = cp/a = /(cp)
Properties tank medium*
*Properties of heavy fuel oils
7/25/2019 Tank Example
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TANK
Sample Printout2014
Lauterbach Verfahrenstechnik GmbH 7 2014
Properties of air
State 1 State 2
Temperature 1 50 C 2 CPressure p1 1 bar p2 Pa
Density 1.078 kg/m kg/m
Specific heat capacity cp 1008 J/(kgK) cp J/(kgK)
Thermal conductivity 0.02808 W/(mK) W/(mK)Dynamic viscosity 0.01964 mPas mPasKinematic viscosity 0.000018 m/s m/sPrandtl number Pr 0.7046 - Pr -
Thermal diffusivity a 0.000026 m/s a m/s
Compressibility factor Z 0.9999 - Z -
Specific enthalpy h 25180 J/kg h J/kgSpecific entropy s 84.9 J/(kgK) s J/(kgK)
Thermal expansion 0.003101 1/K 1/KVelocity of sound w 360.5 m/s w m/s
Molar mass M 28.96 g/mol
Gas constant R 287.1 J/(kgK)
Standard density S 1.293 kg/m
Critical data
Critical temperature Tc -140.6 C
Critical pressure pc 3786000 Pa
Critical density c 342.6 kg/m
Validity range:
-150 C 1000 C1 bar p 1000 bar
Composition of the air:
Mol-% Wt-%
N2 : 78.12 75.570
O2 : 20.96 23.161
Ar: 0.92 1.269
Normalization of Enthalpy and Entropy:
h = 0 kJ/kg, s = 0 kJ/(kgK) at T = 298.15 K = 25C, p = 1.01325 bar
for the pure components
Gas properties*
*Properties of air
7/25/2019 Tank Example
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TANK
Sample Printout2014
Lauterbach Verfahrenstechnik GmbH 8 2014
Geometry:
Heated plate length l 12000 mm
Flow velocity w 10 m/s
Properties:
Mean pressure p 100000 Pa
Mean temperature -20 C
Density 1.078 kg/m
Specific heat capacity Cp 1008 J/(kgK)
Specific thermal conductivity 0.02808 W/(mK)
Dynamic viscosity 0.01964 mPas
Kinematic viscosity = 0.000018 m/s
Prandtl number Pr = 0.7046 -
Mean wall temperature W 44.97 C
Prandtl number at wall temperature PrW 0.7046 -
Phase (liquid = 1 / gas = 2) 2
Exponent for liquids nF 0.25 -
Exponent for gases nG 0 -
Heat transfer:
Reynolds number Re = 6587625 -
Nusselt-number laminar Nulam = 1517 - (1)
Nusselt-number turbulent Nuturb = 8312 - (2)
Nusselt number average Nul,0 = 8449 - (5)Nusselt number with wall correction Nu = 8449 - (6)
Heat transfer coefficient = 19.77 W/(mK)
Outside heat transfer coefficient, roof*
*Heat transfer in single-phase flow
7/25/2019 Tank Example
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TANK
Sample Printout2014
Lauterbach Verfahrenstechnik GmbH 9 2014
Equations:
l 19.77 12
Nu = 8449 = 0.02808
w l 10 12
Re = 6587625 =
0.000018
Nu = Nu0 K 8449 = 8449 1 (6)
2 2
Nul,0 = Nulam + Nuturb (5)
8449 = 1517 + 8312
3
Nulam = 0.664 Re Pr (1)
3
1517 = 0.664 6587625 0.7046
0.037 Re.
Pr
Nuturb = (2)1 + 2.443 Re
- . (Pr
/- 1)
0.037 6587625.
0.7046
8312 =1 + 2.443 6587625
- . ( 0.7046
/- 1 )
Influence of the dependence of the properties on the temperature:
Liquids:
nF 0.25
KF = (Pr / PrW ) 1 = ( 0.7046 / 0.7046 )
Gases:
nG 0
KG = (T / TW ) 1 = ( 253.2 / 318.1 )
7/25/2019 Tank Example
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TANK
Sample Printout2014
Lauterbach Verfahrenstechnik GmbH 10 2014
4. Horizontal plane surfaces
Heat emission at upper side (lower surface cooled)
Boundary conditions:
Area of the body flown-around A 113.1 m
Perimeter of the projection surface U 37699 mm
Characteristic length l 3000 mm (11)
Acceleration due to gravity g 9.81 m/s
Temperature on the surface 0 42.71 CTemp. of fluid outside the boundary layer 50 CTemperature difference (0 - ) 7.287 K
Properties:
Mean temperature (0 + ) / 2 m 46.36 CDensity 897.9 kg/mSpecific heat capacity cp 1930 J/(kgK)
Dynamic viscosity 171 mPasKinematic viscosity 0.000190 m/sThermal conductivity 0.124 W/(mK)Coefficient of thermal expansion 0.000707 1/K
Chararcteristic values:
Prandtl number Pr 2661 -
Grashof number Gr 3.765E+7 - (3)Rayleigh number Ra 1.00E+11 - (4)
Prandtl function f2(Pr) 0.9874 - (20)
Nusselt number laminar Nu_l 121.1 - (18)
Nusselt number turbulent Nu_t 693.7 - (19)
Nusselt number Nu 693.7 -
Heat transfer:
Heat transfer coefficient a 28.67 W/(mK) (2)Exchange surface A 113.1 m
Convective heat flux Q -23.63 kW
Inside heat transfer coefficient, bottom*
*Heat transfer by natural convection around immersed bodies
7/25/2019 Tank Example
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TANK
Sample Printout2014
Lauterbach Verfahrenstechnik GmbH 11 2014
Equations:
a = Nu / l (2)
= 693.7 0.124 / 3 = 28.67 W/(mK)
g l
Gr = (3)
9.81 3
= 0.000707 7.287 = 3.765E+7 -
0.000190
Ra = Gr Pr = 3.765E+7 2661 = 1.00E+11 - (4)
l = A / U = 113.1 / 37.7 = 3000 mm (11)
1/5
Nul = 0.766 Ra f2 (Pr) (18)
1/5
= 0.766 1.00E+11 0.9874 = 121.1 -
1/3
Nut = 0.15 Ra f2 (Pr) (19)
1/3
= 0.15 1.00E+11 0.9874 = 693.7 -
11/20 -20/11
f2 (Pr) = 1 + 0.322 / Pr (20)
11/20 -20/11
= 1 + 0.322 / 2661 = 0.9874 -
7/25/2019 Tank Example
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TANK
Sample Printout2014
Lauterbach Verfahrenstechnik GmbH 12 2014
Heat loss in insulated pipelines (exposed)
Parameters:
Temperature medium inside i 50 CAir temperature a -20 CInside diameter of the pipe d1 12000 mm
Inside heat transfer coefficient i 17.68 W/(mK)Wind velocity w 10 m/s
Heat transfer:
Wall thickness Thermal conductivity
Tube s0 8 mm 0 52 W/(mK)Insulation 1 s1 100 mm 1 0.04 W/(mK)Insulation 2 s2 0 mm 2 1 W/(mK)
Calculation:
Outside diameter of the pipe d2 12016 mm
Outside diameter of the insulation 1 d3 12216 mm
Outside diameter of the insulation 2 d4 12216 mm
Temperature difference i -a 70 CAuxiliary variable D 2.578 mK/W
Outside heat transfer coefficient a 41.67 W/(mK)
Heat loss per unit of length Q/l -1032 W/m
Pipe length l mm
Heat loss absolute Q kW
Temperatures:
Temperature medium inside i 50 CWall temperature inside Wi 48.45 CWall temperature outside Wa 48.45 CInsulation Iso -19.35 CSurface temperature O -19.35 CAir temperature a -20 C
Outside heat transfer coefficient, shell*
*Heat loss of walls and pipeworks
7/25/2019 Tank Example
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TANK
Sample Printout2014
Lauterbach Verfahrenstechnik GmbH 13 2014
Equations:
1 1 d2 1 d3 1 d4D = d4 + ln + ln + ln
i d1 2 1 d1 2 2 d2 2 3 d3
1 1 12.02
= 12.22 + ln +
17.68 12 2 52 12
1 12.22 1 12.22
+ ln + ln = 2.578 mK/W
2 0.04 12.02 2 1 12.22
For static air (w=0) is valid:
a = 8 + 0.04 O - a
= 8 + 0.04 -19.35 - -20 = 8.026 W/(mK)
For wind follows: 1/a = 0.024 = f( 10 ; 12.22 )
d4 ( i - a )Q/l =
D + 1 / a
12.22 ( 50 - -20 )= = -1032 W/m
2.578 + 1 / 41.67
7/25/2019 Tank Example
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TANK
Sample Printout2014
Lauterbach Verfahrenstechnik GmbH 14 2014
2. Vertical areas (cylinders)
Boundary conditions:
Height of the cylinder h 14000 mm
Diameter of the cylinder D 12000 mm
Characteristic length l 14000 mm
Acceleration due to gravity g 9.81 m/s
Temperature on the surface 0 48.47 CTemp. of fluid outside the boundary layer 50 CTemperature difference (0 - ) 1.534 K
Properties:
Mean temperature (0 + ) / 2 m 49.23 CDensity 897.9 kg/m
Specific heat capacity cp 1930 J/(kgK)
Dynamic viscosity 171 mPas
Kinematic viscosity 0.000190 m/sThermal conductivity 0.124 W/(mK)Coefficient of thermal expansion 0.000707 1/K
Characteristic values:
Prandtl number Pr 2661 -
Grashof number Gr 8.056E+8 - (3)
Rayleigh number Ra 2.14E+12 - (4)
Prandtl function f1 (Pr) 0.986 - (13)
Nusselt number for plate Nu_P 1995 - (12)
Nusselt number Nu 1996 - (14)
Heat transfer:
Heat transfer coefficient 17.68 W/(mK) (2)Exchange surface A 527.8 m
Convective heat flux Q -14.32 kW
Inside heat transfer coefficient, wet shell*
*Heat transfer by natural convection around immersed bodies
7/25/2019 Tank Example
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TANK
Sample Printout2014
Lauterbach Verfahrenstechnik GmbH 15 2014
Equations:
= Nu / l (2)
= 1996 0.124 / 14 = 17.68 W/(mK)
g l
Gr = (3)
9.81 14
= 0.000707 1.534 = 8.056E+8 -
0.000190
Ra = Gr Pr = = 8.056E+8 2661 = 2.14E+12 - (4)
1/6 2
Nu_P = 0.825 + 0.387 Ra f1 (Pr) (12)
1/6 2
= 0.825 + 0.387 2.14E+12 0.986 = 1995 -
9/16 -16/9
f1 (Pr) = 1 + 0.492 / Pr (13)
9/16 -16/9
= 1 + 0.492 / 2661 = 0.986 -
Nu = Nu_P + 0.87 h / D (14)
= 1995 + 0.87 14 / 12 = 1996 -
7/25/2019 Tank Example
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TANK
Sample Printout2014
Lauterbach Verfahrenstechnik GmbH 16 2014
2. Vertical areas (cylinders)
Boundary conditions:
Height of the cylinder h 1000 mm
Diameter of the cylinder D 12000 mm
Characteristic length l 1000 mm
Acceleration due to gravity g 9.81 m/s
Temperature on the surface 0 41.5 CTemp. of fluid outside the boundary layer 50 CTemperature difference (0 - ) 8.496 K
Properties:
Mean temperature (0 + ) / 2 m 45.75 CDensity 1.078 kg/m
Specific heat capacity cp 1008 J/(kgK)
Dynamic viscosity 0.01964 mPas
Kinematic viscosity 0.000018 m/sThermal conductivity 0.02808 W/(mK)Coefficient of thermal expansion 0.003101 1/K
Characteristic values:
Prandtl number Pr 0.7046 -
Grashof number Gr 7.789E+8 - (3)
Rayleigh number Ra 5.488E+8 - (4)
Prandtl function f1 (Pr) 0.3459 - (13)
Nusselt number for plate Nu_P 102.1 - (12)
Nusselt number Nu 102.1 - (14)
Heat transfer:
Heat transfer coefficient 2.868 W/(mK) (2)Exchange surface A 37.7 m
Convective heat flux Q -0.9186 kW
Inside heat transfer coefficient, dry shell*
*Heat transfer by natural convection around immersed bodies
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TANK
Sample Printout2014
Lauterbach Verfahrenstechnik GmbH 17 2014
Equations:
= Nu / l (2)
= 102.1 0.02808 / 1 = 2.868 W/(mK)
g l
Gr = (3)
9.81 1
= 0.003101 8.496 = 7.789E+8 -
0.000018
Ra = Gr Pr = = 7.789E+8 0.7046 = 5.488E+8 - (4)
1/6 2
Nu_P = 0.825 + 0.387 Ra f1 (Pr) (12)
1/6 2
= 0.825 + 0.387 5.488E+8 0.3459 = 102.1 -
9/16 -16/9
f1 (Pr) = 1 + 0.492 / Pr (13)
9/16 -16/9
= 1 + 0.492 / 0.7046 = 0.3459 -
Nu = Nu_P + 0.87 h / D (14)
= 102.1 + 0.87 1 / 12 = 102.1 -
7/25/2019 Tank Example
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TANK
Sample Printout2014
Lauterbach Verfahrenstechnik GmbH 18 2014
4. Horizontal plane surfaces
Heat emission at lower surface (upper surface cooled)
Boundary conditions:
Area of the body flown-around A 113.1 m
Perimeter of the projection surface U 37699 mm
Characteristic length l 3000 mm (11)
Acceleration due to gravity g 9.81 m/s
Temperature on the surface 0 44.97 CTemp. of fluid outside the boundary layer 50 CTemperature difference (0 - ) 5.027 K
Properties:
Mean temperature (0 + ) / 2 m 47.49 CDensity 1.078 kg/mSpecific heat capacity cp 1008 J/(kgK)
Dynamic viscosity 0.01964 mPasKinematic viscosity 0.000018 m/sThermal conductivity 0.02808 W/(mK)Coefficient of thermal expansion 0.003101 1/K
Characteristic values:
Prandtl number Pr 0.7046 -
Grashof number Gr 1.24E+10 - (3)Rayleigh number Ra 8.768E+9 - (4)
Prandtl function f1 (Pr) 0.3459 - (13)
Nusselt number Nu 47.26 - (21)
Heat transfer:
Heat transfer coefficient a 0.4424 W/(mK) (2)Exchange surface A 113.1 m
Convective heat flux Q -0.2515 kW
Inside heat transfer coefficient, roof*
*Heat transfer by natural convection around immersed bodies
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TANK
Sample Printout2014
Lauterbach Verfahrenstechnik GmbH 19 2014
Equations:
a = Nu / l (2)
= 47.26 0.02808 / 3 0.4424 W/(mK)
g l
Gr = (3)
9.81 3
= 0.003101 5.027 = 1.24E+10 -
0.000018
Ra = Gr Pr = 1.24E+10 0.7046 = 8.768E+9 - (4)
l = A / U = 113.1 / 37.7 = 3000 mm (11)
9/16 -16/9
f1 (Pr) = 1 + 0.492 / Pr (13)
9/16 -16/9
= 1 + 0.492 / 0.7046 = 0.3459 -
1/5
Nu = 0.6 Ra f1 (Pr) (21)
1/5
= 0.6 8.768E+9 0.3459 = 47.26 -
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TANK
Sample Printout2014
Lauterbach Verfahrenstechnik GmbH 20 2014
Calculation of the heat flux by radiation
Area Emissivity Temperature
A1 113.1 m 1 0.9 - T1 50 C (= 50 C )A2 113.1 m 2 0.8 - T2 44.97 C (= 44.97 C )
View factors:
12 0.8466
21 0.8466 21 = A1 /A2 12
Calculation of the emitted energy:
Ei = i Ti ; = 5.6704 10-
W/(m K )
E1 = 556.5 W/m E2 = 464.6 W/m
Calculation of heat flux:
. 1 2 A1 12Q12 = (T1 - T2 )
1 - (1 - 1 )(1 - 2 ) 12 21
.
Q12 = 2.629 kW Q21 = 2.629 kW
Equivalent heat transfer coefficient
.Q
=A (T1 - T2 )
12 = 4.624 W/(mK)
Heat transfer radiation inside, roof*
*Surface radiation
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TANK
Sample Printout2014
Lauterbach Verfahrenstechnik GmbH 21 2014
Name of the oil Transcal LTMaterial structure naphthene base
Manufacturer BP
Former product/Comment
Range of application
State 1 State 2
Temperature 136 C 126.3 C
Density 796.9 kg/m 803.1 kg/mSpecific heat capacity cp 2342 J/(kgK) 2309 J/(kgK)
Dynamic viscosity 1.183 mPas 1.358 mPas
Kinematic viscosity 0.000001 m/s 0.000002 m/sThermal conductivity 0.125 W/(mK) 0.1255 W/(mK)Coef. of thermal expansion 0.000775 1/K 0.000781 1/KThermal diffusivity a 6.694E-8 m/s 6.766E-8 m/s
Prandtl number Pr 22.18 - 24.97 -
Specific enthalpy h 0 kJ/kg 0 kJ/kg
Vapour pressure pD 604.7 Pa 427.1 Pa
Pour point -54 C
Initial boiling point 290 C
Minimum operating temperature -20 C
Maximum operating temperature 260 C
Minimum temperature filling -20 C
Minimum temperature startup 71 CMaximum film temperature 280 C
Flash point 155 C
Ignition temperature 240 C
Neutralization number 0.01 mgKOH/g
Coke residue 0.01 %
Explosion limit Vol-%
Molecular weight kg/kmol
Temperature min max
Density 900 kg/m 732 kg/m
Specific heat capacity cp 1800 J/(kgK) 2770 J/(kgK)
Dynamic viscosity 730 mPas 0.35 mPas
Kinematic viscosity 0.0003 m/s 4.9E-07 m/sThermal conductivity 0.136 W/(mK) 0.118 W/(mK)Vapour pressure pD Pa 28000 Pa
Physical properties of heating medium*
*Properties of heat transfer oils
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TANK
Sample Printout2014
Lauterbach Verfahrenstechnik GmbH 22 2014
Constant wall temperature
Circular pipes
Inlet temperature e 140 COutlet temperature a 131.9 CMean temperature m 136 CDensity of the fluid 796.9 kg/mSpecific heat capacity of the fluid cp 2342 J/(kgK)
Thermal conductivity of the fluid 0.125 W/(mK)Dynamic viscosity of the fluid 1.183 mPas
Kinematic viscosity of the fluid 0.000001 m/sPrandtl number Pr 22.18 -
Prandtl number at wall temperature PrW 24.97 -
Fluid: liquid or gas < 0 >
0 = Circular pipes, 1 = Non-circular pipes < 0
Pipe length l 23326 mmInside diameter of the pipe di 54.5 mm
Cross sectional area of the pipe f 0.002333 m
Perimeter of the pipe u 171.2 mm
Hydraulic diameter dh = 54.5 mm
Total mass flow Mg 7963 kg/h
Total volume flow Vg 9.992 m/h
Number of pipes with parallel flow Z 1 -
Mass flow per pipe M = 7963 kg/h
Velocity w = 1.19 m/s
Reynolds number Re = 43683 -
Balance: Q = Mg cp (a - e ) = -41.75 kW
Results: Constant wall temperature
Nu 469.5 0.125
= = = 1076 W/(mK)dh 0.0545
w dh 1.19 0.0545 796.9Re = = = 43683
/ 1000 1.183 / 1000
Nu_m_ = (laminar non-disturbed flow Re < 2300) [6]Nu_m_ = (laminar entrance flow Re < 2300) [12]Nu_m_T = 475.7 (turbulent flow Re > 10000) [26]
Nu_m = (transition zone 2300
Re
10000) [29]
Factor K:
0.11
Liquids: K = (Pr/PrW ) = 0.987
n
Gases: K = (T/TW ) = for n = 0
Nu = Nu_m(_,T) K = 469.5 [40,41]
Heat transfer: Q = A log
-41746 = 1076 3.994 -9.711
Wall temperature W = 125.7 C
Tube-side heat transfer*
*Heat transfer in pipe flow
7/25/2019 Tank Example
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TANK
Sample Printout2014
Lauterbach Verfahrenstechnik GmbH 23 2014
Calculations:
Laminar flow: Re < 2300
Laminar non-disturbed flow:
HW = Re Pr dh/l = 2263
1/3
Nu_m__2 = 1.615 HW = [5]
3 3 3 1/3
Nu_m_ = 3.66 + 0.7 + Nu_m__2 - 0.7 =[6]
3 3 3 1/3
= 3.66 + 0.7 + - 0.7 =
Laminar entrance flow:
1/6
2
Nu_m__3 = HW =1 + 22 Pr
1/6
2
= 2263 = [11]
1 + 22 22.18
3 3 3 3 1/3Nu_m_ = 3.66 + 0.7 + Nu_m__2 - 0.7 + Nu_m__3 =
[12]
3 3 3 3 1/3
= 3.66 + 0.7 + - 0.7 + =
Turbulent flow: Re > 10000
-2 -2
= [1.8 log Re - 1.5] = [ 1.8 log 43683 - 1.5 ] = 0.0213 [27]
2/3
/8 Re Pr dh
Nu_m_T = 1 + =
2/3 l
1 + 12.7 /8 (Pr -1) [26]
2/3
0.0213 /8 43683 22.18 0.0545
= 1 +
2/3 23.331 + 12.7 0.0213 /8 ( 22.18 -1)
Nu_m_T = 475.7
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Transition zone: 2300 Re 100001/3
Nu_m__2_2300 = 1.615 (2300 Pr dh/l) = 7.948 [32]
1/6
2
Nu_m__3_2300 = 2300 Pr dh/l = 4.366 [33]1 + 22 Pr
3 3 1/3
Nu_m_L_2300 = 49.371 + Nu_m__2_2300 - 0.7 + Nu_m__3_2300
Nu_m_L_2300 = 8.007 [31]
2/3
(0.0308/8) 10000 Pr dh
Nu_m_T_10000 = 1 +
2/3 l
1 + 12.7 0.0308/8 (Pr -1)
[37]
Nu_m_T_10000 = 135
Re - 2300 43683 - 2300
= = = [30]10000 - 2300 10000 - 2300
Nu_m = (1 - ) Nu_m_L_2300 + Nu_m_T_10000 = [29]
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5. Horizontal curved areas (Cylinder)
Cylinder:
Outside diameter do 60.3 mm
Wall thickness s 2.9 mm
Inside diameter di 54.5 mm
Thermal conductivity 52 W/(mK)Characteristic length l 94.72 mm
Acceleration due to gravity g 9.81 m/s
Temperatures and properties:
Temperature on the surface 0 125.7 CTemp. of fluid outside the boundary layer 50 CTemperature difference (0 - ) 75.7 K
Mean temperature (0 + ) / 2 m 87.85 CDensity 874.3 kg/mSpecific heat capacity cp 2062 J/(kgK)
Dynamic viscosity 33.19 mPasKinematic viscosity 0.000038 m/sThermal conductivity 0.1214 W/(mK)Coefficient of thermal expansion 0.00072 1/K
Characteristic values:
Prandtl number Pr 563.8 -
Grashof number Gr 315094 - (3)
Rayleigh number Ra 1.777E+8 - (4)
Prandtl function f3 (Pr) 0.9647 - (24)Nusselt number Nu 97.47 - (22)
Heat transfer:
Heat transfer coefficient (free convection) o 124.9 W/(mK) (2)Convective heat flux Q 41.75 kW
Balance for the calculation of the surface temperature:
Heating medium
Specific heat capacity cp 2342 J/(kgK)
Density 796.9 kg/m
Mass flow m 7963 kg/h
Volume flow V9.992
m/h
Inlet temperature in 140 COutlet temperature out 131.9 CMean temperature m 136 C
Duty QH -41.75 kW
Tube-side velocity u 1.19 m/s
Heat transfer coefficient inside i 1076 W/(mK)Fouling inside fi 0 mK/W
Fouling outside fo 0 mK/W
Overall heat transfer coefficient k 110 W/(mK)
Length of the cylinder L 23326 mm
Area of the cylinder A 4.419 m
Heat transfer coil around tubes*
*Heat transfer by natural convection around immersed bodies
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Equations:
a = Nu / l (2)
= 97.47 0.1214 / 0.09472 = 124.9 W/(mK)
g l
Gr = (3)
9.81 0.09472
= 0.00072 75.7 = 315094 -
0.000038
Ra = Gr Pr = 315094 563.8 = 1.777E+8 - (4)
1/6 2
Nu = 0.752 + 0.387 Ra f3 (Pr) (22)
1/6 2
= 0.752 + 0.387 1.777E+8 0.9647 = 97.47 -
9/16 -16/9
f3 (Pr) = 1 + 0.559 / Pr (24)
9/16 -16/9= 1 + 0.559 / 563.8 = 0.9647 -
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Straight pipes
Parameters of the pipe:
Length of pipe l 23326 mm
Inside diameter of pipe di 54.5 mm
Absolute roughness K 0.04 mm
Number of pipes with parallel flow NR 1 -
Properties:
Density 796.9 kg/mDynamic viscosity 1.183 mPas
Kinematic viscosity 0.000001 m/s
Total mass flow mg 7963 kg/h
Mass flow per pipe mR 7963 kg/hVolume flow per pipe VR 9.992 m/h
Velocity of the fluid wi 1.19 m/s
Result:
Flow pattern turbulent (Re > 2320)
Pressure drop p 5736 PaReynolds-Number Rei 43683 -
Drag coefficient 0.02376 -
Equations:
wi di 1.19 796.9 0.0545Rei = = = 43683 -
0.001 1.183 0.001
Rei = 43683 > 2320 turbulent flow
1 2.51 K / di= -2 lg +
Rei 3.71
1 2.51 0.00004 / 0.0545
= -2 lg +
0.0237643683
0.02376 3.71
l wi 23.33 796.9 1.19
p = = 0.02376 di 2 0.0545 2
p = 5736 Pa
Pressure drop in coil*