Tank Example

7/25/2019 Tank Example

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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


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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


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


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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


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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


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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


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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


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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


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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


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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 )


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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


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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 -


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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


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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


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2. Vertical areas (cylinders)


Height of the cylinder h 14000 mm

Diameter of the cylinder D 12000 mm

Characteristic length l 14000 mm



Properties:

Mean temperature (0 + ) / 2 m 49.23 CDensity 897.9 kg/m


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


Inside heat transfer coefficient, wet shell*



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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 -


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2. Vertical areas (cylinders)


Height of the cylinder h 1000 mm

Diameter of the cylinder D 12000 mm

Characteristic length l 1000 mm



Properties:

Mean temperature (0 + ) / 2 m 45.75 CDensity 1.078 kg/m


Dynamic viscosity 0.01964 mPas

Kinematic viscosity 0.000018 m/sThermal conductivity 0.02808 W/(mK)Coefficient of thermal expansion 0.003101 1/K


Prandtl number Pr 0.7046 -

Grashof number Gr 7.789E+8 - (3)



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


Inside heat transfer coefficient, dry shell*



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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 -


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4. Horizontal plane surfaces

Heat emission at lower surface (upper surface cooled)


Area of the body flown-around A 113.1 m

Perimeter of the projection surface U 37699 mm

Characteristic length l 3000 mm (11)



Properties:


Dynamic viscosity 0.01964 mPasKinematic viscosity 0.000018 m/sThermal conductivity 0.02808 W/(mK)Coefficient of thermal expansion 0.003101 1/K



Grashof number Gr 1.24E+10 - (3)Rayleigh number Ra 8.768E+9 - (4)


Nusselt number Nu 47.26 - (21)

Heat transfer:

Heat transfer coefficient a 0.4424 W/(mK) (2)Exchange surface A 113.1 m


Inside heat transfer coefficient, roof*



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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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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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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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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


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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


Temperatures and properties:



Dynamic viscosity 33.19 mPasKinematic viscosity 0.000038 m/sThermal conductivity 0.1214 W/(mK)Coefficient of thermal expansion 0.00072 1/K



Grashof number Gr 315094 - (3)


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


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*



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TANK

Sample Printout2014


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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TANK

Sample Printout2014

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*

Tank Example

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