tankexamplenov2016 - lv softlv-soft.com/software/fachbereiche/waermeuebertrager/paketwaerme/... ·...

TankExampleNov2016

Lauterbach Verfahrenstechnik GmbH 1 07.11.2016

Task ......................................................................................................................................................................................... 2

Calculation of heat loss of storage tanks ............................................................................................................................ 3

Properties ambient air Properties of air .............................................................................................................................. 7

Heat transfer outside, roof Heat transfer in flow past a plane wall ................................................................................. 8

Properties tank medium Properties of heavy fuel oils ...................................................................................................... 9

Inside heat transfer coefficient, bottom Heat transfer by natural convection around immersed bodies ................. 10

Gas properties Properties of air ......................................................................................................................................... 12

Heat transfer outside, shell Heat loss of walls and pipeworks ...................................................................................... 13

Inside heat transfer coefficient, wet shell Heat transfer by natural convection around immersed bodies .............. 14

Inside heat transfer coefficient, dry shell Heat transfer by natural convection around immersed bodies ............... 15

Inside heat transfer coefficient, roof Heat transfer by free convection in enclosed fluid layers ............................... 16

Physical properties of heating medium Properties of thermal oils ................................................................................ 18

Tube-side heat transfer Heat transfer in pipe flow .......................................................................................................... 19

Heat transfer coil around tubes Heat transfer by natural convection around immersed bodies .............................. 21

Pressure drop in coil Pressure drop in flow through pipes ............................................................................................ 23

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

TankExampleNov2016


Task Heavy fuel oil HFO 180 shall be stored in a storage tank with circular cross section at a minimum temperature of 50°C. Dimensions of the tank:

inside diameter: 12 m Height: 15 m Filling level: 14 m

The shell of the tank consists of 8 mm steel (St steel λ = 52 W/(m·K)) and is insulated shell side and roof side with 100 mm mineral wool (λ = 0,04 W/(m·K)). It is placed on a 250 mm thick concrete plate with λ = 2,5 W/(m·K). What is the heat loss of the tank in the winter at an air temperature and ground temperature of - 20°C and a wind velocity of 10 m/s? For compensating the heat losses the tank is heated with a flat coil. The heat transfer takes place by ‘free convection’.

Heating medium : Thermal oil Transcal LT Volume Flow: 10 m³/h Inlet temperature: 140 °C

Flat coil: DN 50 (60.3 x 2.9 mm) Material: Steel Thermal conductivity 52 W/(m·K)

A possible fouling of the coil is not considered.

What is the heat transfer area?

TankExampleNov2016


Calculation of heat loss of storage tanks

Global conditions ϑP Product temperature 50 °C pi Inside pressure 100000 Pa ϑL Air temperature -20 °C

10 uW Wind speed m/s ϑB Ground temperature -20 °C

Geometry of storage tank Ground plan Round sketch

DT Tank inside diameter 12000 mm 37699 Circumference mm 113.1 Area m²

HT Tank height 15000 mm 14000 HF Filling level mm

Properties Storage medium HFO 180

897.9 Density ρ kg/m³ 1930 Specific heat capacity cp J/(kg·K)

0.124 Thermal conductivity λ W/(m·K) 171 Dynamic viscosity η mPa·s

1.904e-4 Kinematic viscosity ν m²/s 7.072e-4 Coefficient of thermal expansion β 1/K

Gas above storage medium Medium name Air


0.02795 Thermal conductivity λ W/(m·K) 0.01955 Dynamic viscosity η mPa·s

1.803e-5 Kinematic viscosity ν m²/s 0.003119 Coefficient of thermal expansion β 1/K

Wall thickness and thermal conductivity of baseplat e, tank and the insulation Bottom Shell Roof

8 Thickness of the wall

8 8 mm mm mm

52 Thermal conductivity

52 52 W/(m·K) W/(m·K) W/(m·K)

Insulation thickness 100 100 mm mm mm

Thermal conductivity

0.04 0.04 W/(m·K) W/(m·K) W/(m·K)

Soil Thermal conductivity

2 W/(m·K)

Heat losses Bottom Shell Roof

3.28 14.32 2.948 wet part kW kW kW

0.9189 dry part kW

21.46 Qtotal Total heat loss kW

TankExampleNov2016


Bottom sW,B Thickness of the wall 8 mm λW,B Thermal conductivity of the wall 52 W/(m·K)

1.538e-4 βW,B Thermal resistance of the wall m²·K/W sInsu,B Thickness of the insulation mm λInsu,B Thermal conductivity of the insulation W/(m·K) βInsu,B Thermal resistance of the insulation m²·K/W

17.5 αi,B Heat transfer coefficient inside W/(m²·K) λSoil Thermal conductivity of soil 2 W/(m·K)

113.1 AB Contact surface m² cA,B Correction factor for contact surface 1

48.34 ϑi,B Wall temperature inside, bottom °C ϑg,B Temperature (wall-insulation) °C

48.34 ϑa,B Temperature outside, bottom °C 3.28 Qa,B Heat flow to outside kW

Shell 8 sW,M Thickness of the wall mm

52 λW,M Thermal conductivity of the wall W/(m·K) 1.538e-4 βW,M Thermal resistance of the wall m²·K/W

sInsu,M Thickness of the insulation 100 mm λInsu,M Thermal conductivity of the insulation 0.04 W/(m·K)

2.5 βInsu,M Thermal resistance of the insulation m²·K/W 41.67 αa,M Heat transfer coefficient outside W/(m²·K)

Shell wet part 17.67 αi,M,b Heat transfer coefficient inside W/(m²·K)

527.8 AM,b Contact surface m² cA,M,b Correction factor for contact surface 1

48.47 ϑi,M,b Wall temperature inside, shell °C 48.46 ϑg,M,b Temperature (wall-insulation) °C

-19.35 ϑa,M,b Temperature insulation outside, shell °C

Qh,M,b Heating performance 0 kW 14.32 Qi,M,b Heat flow from inside kW 14.32 Qa,M,b Heat flow to outside kW

Shell dry part 2.876 αi,M,t Heat transfer coefficient inside W/(m²·K)

37.7 AM,t Contact surface m² cA,M,t Correction factor for contact surface 1

41.52 ϑi,M,t Wall temperature inside, shell °C 41.52 ϑg,M,t Temperature (wall-insulation) °C

-19.42 ϑa,M,t Temperature insulation outside, shell °C

Qh,M,t Heating performance 0 kW 0.9189 Qi,M,t Heat flow from inside kW 0.9189 Qa,M,t Heat flow to outside kW

TankExampleNov2016


Roof sW,D Thickness of the wall 8 mm λW,D Thermal conductivity of the wall 52 W/(m·K)

1.538e-4 βW,D Thermal resistance of the wall m²·K/W sInsu,D Thickness of the insulation 100 mm λInsu,D Thermal conductivity of the insulation 0.04 W/(m·K)

2.5 βInsu,D Thermal resistance of the insulation m²·K/W 0.8 εD Emissivity of the roof 0.9 εP Emissivity of the product

23.01 αa,D Heat transfer coefficient outside W/(m²·K) 7.037 αi,D Heat transfer coefficient inside (total) W/(m²·K)

113.1 AD Contact surface m² cA,D Correction factor for contact surface 1

46.3 ϑi,D Wall temperature inside, roof °C 46.29 ϑg,D Temperature (wall-insulation) °C

-18.87 ϑa,D Temperature insulation outside, roof °C

Qh,D Heating performance 0 kW 2.948 Qi,D Heat flow from inside kW 2.948 Qa,D Heat flow to outside kW

Balance 0 Qh,total Heating performance kW

Qi,total Heat flow from inside kW 21.46 Qa,total Heat flow to outside kW

TankExampleNov2016


Calculation of the heating coil

Number of parallel heating circuits 1 Heating medium Transcal LT

7957 Mass flow m kg/h Volume flow V 10 m³/h Pressure (abs.) P 300000 Pa

140 Inlet temperature ϑe °C 135.9 Outlet temperature ϑa °C 137.9 Mean temperature ϑm °C

60.3 Tube outside diameter da mm 2.9 Tube wall thickness s mm

54.5 Tube inside diameter di mm 52 λR Thermal conductivity of tube material W/(m·K) 0 fi Fouling inside m²·K/W 0 fa Fouling outside m²·K/W

Properties of the heating medium 795.7 Density ρ kg/m³ 2349 Specific heat capacity cp J/(kg·K)


1.446e-6 Kinematic viscosity ν m²/s

88.73 Properties of the storage medium at ϑ °C 873.7 Density ρ kg/m³ 2064 Specific heat capacity cp J/(kg·K)


3.68e-5 Kinematic viscosity ν m²/s 7.209e-4 Coefficient of thermal expansion β 1/K

Result 1.191 Tube-side velocity u m/s 1101 αi Heat transfer coefficient inside W/(m²·K)

127 αa Heat transfer coefficient outside W/(m²·K) Overall heat transfer coefficient k 111.9 W/(m²·K)

2819 Pressure drop (straight tube without bends) ∆P Pa 11514 Tube length per heating circuit L mm

Area per heating circuits A 2.181 m² 11514 Ltotal Total tube length of all heating circuits mm 2.181 Atotal Total area of all heating circuits m²

TankExampleNov2016


Properties ambient air Properties of air

State 1 State 2 ϑ1 ϑ2 Temperature -19.43 °C °C p1 p2 Pressure 1.013 bar bar

1.393 Density ρ ρ kg/m³ kg/m³ 1006 cp cp Specific heat capacity J/(kg·K) J/(kg·K)

0.02286 Thermal conductivity λ λ W/(m·K) W/(m·K) 0.01623 Dynamic viscosity η η mPa·s mPa·s

1.166e-5 Kinematic viscosity ν ν m²/s m²/s 0.7143 Prandtl number Pr Pr

1.632e-5 Thermal diffusivity a a m²/s m²/s 0.9991 Compressibility factor Z Z -44700 Specific enthalpy h h J/kg J/kg -162.4 Specific entropy s s J/(kg·K) J/(kg·K)

0.00396 Coefficient of thermal expansion β β 1/K 1/K

319.4 Speed of sound w w m/s m/s

Constants Molecular weight M 28.96 g/mol Gas constant R 287.1 J/(kg·K)

ρN Standard density 1.293 kg/m³

Critical data Tc Critical temperature -140.6 °C pc Critical pressure 3786000 Pa ρc Critical density 342.6 kg/m³

Validity range -150 °C ≤ ϑ ≤ 1000 °C 1 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/(kg·K) T = 298.15 K = 25°C, p = 1.01325 bar for the pure components

TankExampleNov2016


Heat transfer outside, roof Heat transfer in flow past a plane wall

Geometry 12000 Heated plate length l mm

10 Flow velocity w m/s

Properties Mean pressure p 101325 Pa Mean temperature ϑ -20 °C

Fluid liquid /gaseous? gaseous ρ Density 1.393 kg/m³ cp Specific heat capacity 1006 J/(kg·K) λ Thermal conductivity 0.02286 W/(m·K) η Dynamic viscosity 0.01623 mPa·s

1.166e-5 ν Kinematic viscosity m²/s 0.7143 Pr Prandtl number

ϑW Mean wall temperature -18.87 °C nG Exponent for gases 0.12

Heat transfer 1.03e+7 Reynolds number Re

1904 Nulam Nusselt number laminar (1) 11935 Nuturb Nusselt number turbulent (2) 12086 Nul,0 Nusselt number average (5) 12079 Nusselt number with wall correction Nu (6)

23.01 Heat transfer coefficient α W/(m²·K)

Equations

(1)

(2)

(5)

(6)

Correction factor K (Effect of temperature dependent property variations) Gases

TankExampleNov2016


Properties tank medium Properties of heavy fuel oils Properties of Heavy Fuel Oils (HFO) Selected oil: HFO 180

Oil selection: 7

State 1 State 2 Temperature ϑ ϑ 50 88.75 °C °C

897.9 873.6 Density ρ ρ kg/m³ kg/m³ 1930 2065 Specific heat capacity cp cp J/(kg·K) J/(kg·K)

0.124 0.1213 Thermal conductivity λ λ W/(m·K) W/(m·K) 171 32.15 Dynamic viscosity η η mPa·s mPa·s

1.904e-4 3.681e-5 Kinematic viscosity ν ν m²/s m²/s 2661 547.5 Prandtl number Pr Pr

7.072e-4 7.211e-4 Coefficient of thermal expansion β β 1/K 1/K 7.155e-8 6.722e-8 Thermal diffusivity a a m²/s m²/s

Pr = ν/a = η·cp/λ a = λ/(ρ·cp)

TankExampleNov2016


Inside heat transfer coefficient, bottom Heat transfer by natural convection around immersed bodies 4. Horizontal plane surfaces Heat emission at upper side (lower surface cooled)

Boundary conditions 113.1 Area of the body flown-around A m²

Perimeter of the projection surface U 37699 mm

3000 Characteristic length l (11) mm Acceleration due to gravity g 9.81 m/s²

ϑ0 Temperature on the surface 48.34 °C ϑ∞ Temperature of fluid outside the boundary layer 50 °C

1.658 (ϑ0 - ϑ∞) Temperature difference ∆ϑ K

Properties 49.17 ϑm (ϑ0 + ϑ∞) / 2 Mean temperature °C 897.9 Density ρ kg/m³ 1930 cp Specific heat capacity J/(kg·K)

171 Dynamic viscosity η mPa·s 1.904e-4 Kinematic viscosity ν m²/s

0.124 Thermal conductivity λ W/(m·K) 7.072e-4 Coefficient of thermal expansion β 1/K

Characteristic values 2661 Pr = ν · ρ · cp / λ Prandtl number Pr

8565472 Gr = g · l3 · β · ∆ϑ / ν2 Grashof number Gr (3) 2.28e+10 Rayleigh number Ra (4) Ra = Gr · Pr

0.9874 f2(Pr) Prandtl function (20) 90.09 Nul Nusselt number laminar (18) 423.5 Nut Nusselt number turbulent (19) 423.5 Nusselt number Nu

Heat transfer 17.5 αa Heat transfer coefficient (2) α = Nu · λ / l W/(m²·K)

113.1 Exchange surface A m² -3.282 Convective heat flux Q kW

Equations

(2)

(3)

(4)

(11)

(18)

(19)

(20)

TankExampleNov2016


TankExampleNov2016


Gas properties Properties of air

State 1 State 2 ϑ1 ϑ2 Temperature 48.15 °C °C p1 p2 Pressure 1 bar bar

1.084 Density ρ ρ kg/m³ kg/m³ 1008 cp cp Specific heat capacity J/(kg·K) J/(kg·K)

0.02795 Thermal conductivity λ λ W/(m·K) W/(m·K) 0.01955 Dynamic viscosity η η mPa·s mPa·s

1.803e-5 Kinematic viscosity ν ν m²/s m²/s 0.7048 Prandtl number Pr Pr

2.559e-5 Thermal diffusivity a a m²/s m²/s 0.9999 Compressibility factor Z Z 23319 Specific enthalpy h h J/kg J/kg 79.14 Specific entropy s s J/(kg·K) J/(kg·K)

0.003119 Coefficient of thermal expansion β β 1/K 1/K

359.5 Speed of sound w w m/s m/s

Constants Molecular weight M 28.96 g/mol Gas constant R 287.1 J/(kg·K)

ρN Standard density 1.293 kg/m³

Critical data Tc Critical temperature -140.6 °C pc Critical pressure 3786000 Pa ρc Critical density 342.6 kg/m³

Validity range -150 °C ≤ ϑ ≤ 1000 °C 1 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/(kg·K) T = 298.15 K = 25°C, p = 1.01325 bar for the pure components

TankExampleNov2016


Heat transfer outside, shell Heat loss of walls and pipeworks Heat loss in insulated pipelines (exposed)

Parameters ϑi Temperature medium inside 50 °C ϑa Air temperature -20 °C

12000 d1 Inside diameter of the pipe mm 17.67 αi Inside heat transfer coefficient W/(m²·K)

10 Wind velocity w m/s

Heat transfer

Thickness Thermal conductivity 8 52 s0 λ0 Tube wall mm W/(m·K)

s1 λ1 Insulation 1 100 0.04 mm W/(m·K) s2 λ2 Insulation 2 0 1 mm W/(m·K)

Calculation 12016 d2 Outside diameter of the pipe mm 12216 d3 Outside diameter of the insulation 1 mm 12216 d4 Outside diameter of the insulation 2 mm

70 │ϑi-ϑa│ Temperature difference °C 2.578 Auxiliary variable D m²·K/W

41.67 αa Outside heat transfer coefficient W/(m²·K)

-1032 Heat loss per unit of length Q/l W/m Pipe length l mm Heat loss absolute Q kW

Temperatures ϑi Temperature medium inside 50 °C

48.45 ϑWi Wall temperature inside °C 48.45 ϑWa Wall temperature outside °C

-19.35 ϑIso Insulation °C -19.35 ϑo Surface temperature °C

ϑa Air temperature -20 °C

Equations

For wind (w>0) follows

TankExampleNov2016


Inside heat transfer coefficient, wet shell Heat transfer by natural convection around immersed bodies 2. Vertical areas (Cylinder)

Boundary conditions 14000 Height of the cylinder h mm 12000 Diameter of the cylinder D mm

14000 Characteristic length l mm Acceleration due to gravity g 9.81 m/s²




171 Dynamic viscosity η mPa·s 1.904e-4 Kinematic viscosity ν m²/s

0.124 Thermal conductivity λ W/(m·K) 7.072e-4 Coefficient of thermal expansion β 1/K

Characteristic values 2661 Pr = ν · ρ · cp / λ Prandtl number Pr

8.059e+8 Gr = g · l3 · β · ∆ϑ / ν2 Grashof number Gr (3) 2.14e+12 Rayleigh number Ra (4) Ra = Gr · Pr

0.986 f1(Pr) Prandtl function (13) 1995 NuP Nusselt number for plate (12) 1996 Nusselt number Nu (14)

Heat transfer 17.68 Heat transfer coefficient α (2) α = Nu · λ / l W/(m²·K) 527.8 Exchange surface A m²

-14.32 Convective heat flux Q kW

Equations

(2)

(3)

(4)

(12)

(13)

(14)

TankExampleNov2016


Inside heat transfer coefficient, dry shell Heat transfer by natural convection around immersed bodies 2. Vertical areas (Cylinder)

Boundary conditions Height of the cylinder h 1000 mm

12000 Diameter of the cylinder D mm

1000 Characteristic length l mm Acceleration due to gravity g 9.81 m/s²




0.01955 Dynamic viscosity η mPa·s 1.803e-5 Kinematic viscosity ν m²/s 0.02795 Thermal conductivity λ W/(m·K)

0.003119 Coefficient of thermal expansion β 1/K

Characteristic values 0.7048 Pr = ν · ρ · cp / λ Prandtl number Pr

7.974e+8 Gr = g · l3 · β · ∆ϑ / ν2 Grashof number Gr (3) 5.62e+8 Rayleigh number Ra (4) Ra = Gr · Pr

0.3459 f1(Pr) Prandtl function (13) 102.8 NuP Nusselt number for plate (12) 102.9 Nusselt number Nu (14)

Heat transfer 2.876 Heat transfer coefficient α (2) α = Nu · λ / l W/(m²·K)

37.7 Exchange surface A m² -0.9189 Convective heat flux Q kW

Equations

(2)

(3)

(4)

(12)

(13)

(14)

TankExampleNov2016


Inside heat transfer coefficient, roof Heat transfer by free convection in enclosed fluid layers Horizontal flat layers (heated from below)

Boundary conditions Layer thickness s 1000 mm

113.1 Heated area A m² 0.9 ε1 Emission rate of the heated surface (Ka) 0.8 ε2 Emission rate of the cooled surface (Ka)

Acceleration due to gravity g 9.81 m/s²

ϑ1 Temperature on the heated surface 50 °C ϑ2 Temperature on the cooled surface 46.3 °C

3.704 Temperature difference (ϑ1 - ϑ2) ∆ϑ K 4.914e+8 Temperature difference (T14 - T24) ∆T K^4

Properties 48.15 ϑm Mean temperature °C 1.084 ρ Density kg/m³ 1008 cp Specific heat capacity J/(kg·K)

0.01955 η Dynamic viscosity mPa·s 1.803e-5 ν Kinematic viscosity m²/s 0.02795 λ Thermal conductivity W/(m·K)

2.559e-5 a Thermal diffusivity m²/s 0.003119 β Coefficient of expansion 1/K

Characteristic values 3.485e+8 Grs Grashof number (6)

0.7048 Prandtl number Pr (7) 2.456e+8 Ras Rayleigh number (8)

54.02 Nus Nusselt number (11/12)

Heat transfer 1.51 Heat transfer coefficient α (5) W/(m²·K)

0.6325 QLK Heat flux (conduction and convection) (3) kW

4.166e-8 Radiation exchange coefficient C12 Ka (7) 2.315 QS Heat flux (radiation) Ka (6) kW

2.948 QSLK Total heat flux kW 7.037 αSLK Equivalent heat transfer coefficient W/(m²·K)

TankExampleNov2016


Equations

(6)

(7)

(8)

Ras < 1708 Nus = 1 - without convection

1708 ≤ Ras < 2.2·104 Nus = 0.208 · Ras0.25 - (11) laminar

Ras ≥ 2.2·104 Nus = 0.092 · Ras0.33 - (12) turbulent

(5)

(3)

TankExampleNov2016


Physical properties of heating medium Properties of thermal oils

Name of the oil Transcal LT Material structure naphthene base Manufacturer BP Former product / Comment Range of application

State 1 State 2 Temperature 137.9 128.1 °C °C

795.7 802 Density ρ kg/m³ kg/m³ 2349 2316 Specific heat capacity cp J/(kg·K) J/(kg·K)

0.1248 0.1254 Thermal conductivity λ W/(m·K) W/(m·K) 1.151 1.324 Dynamic viscosity η mPa·s mPa·s

1.355e-6 1.573e-6 Kinematic viscosity ν m²/s m²/s 21.66 24.44 Prandtl number Pr

7.733e-4 7.794e-4 Coef. of thermal expansion β 1/K 1/K 6.679e-8 6.752e-8 Thermal diffusivity a m²/s m²/s

0 0 Specific enthalpy h kJ/kg kJ/kg 516.2 336.8 pD Vapour pressure Pa 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 °C Maximum 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

ϑmin ϑmax Temperature Density ρ 900 732 kg/m³ kg/m³ Specific heat capacity cp 1800 2770 J/(kg·K) J/(kg·K) Thermal conductivity λ 0.136 0.118 W/(m·K) W/(m·K) Dynamic viscosity η 730 0.35 mPa·s mPa·s Kinematic viscosity ν 3e-4 4.9e-7 m²/s m²/s

pD Vapour pressure 28000 Pa Pa

TankExampleNov2016


Tube-side heat transfer Heat transfer in pipe flow Constant wall temperature

140 ϑe Inlet temperature °C 135.9 ϑa Outlet temperature °C 137.9 ϑm Mean temperature °C

Physical properties Fluid liquid /gaseous? liquid



1.446e-6 Kinematic viscosity ν m²/s 21.68 Prandtl number Pr

PrW Prandtl number at wall temperature 24.44 128 ϑW Wall temperature °C

Tube circular / non-circular? Circular tubes

11514 Tube length l mm 54.5 di Tube inside diameter mm

0.002333 Cross sectional area of the tube f m² 171.2 Perimeter of the tube u mm

54.5 dh Hydraulic diameter mm

mtot Total mass flow 7957 kg/h 10 Vtot Total volume flow m³/h

Number of tubes with parallel flow Z 1 7957 m Mass flow per tube kg/h

1.191 w Flow velocity m/s

Heat transfer 44866 Re Reynolds number 481.3 Nusselt number Nu 1101 α Heat transfer coefficient W/(m²·K)

-21.46 Q = mtot · cp · (ϑa - ϑe ) Heat duty Q kW

TankExampleNov2016


Results Constant wall temperature Turbulent flow (Re > 10000)

Correction factor K (Effect of temperature dependent property variations) Liquids

TankExampleNov2016


Heat transfer coil around tubes Heat transfer by natural convection around immersed bodies 5. Horizontal curved areas (Cylinder)

Cylinder 60.3 do Outside diameter mm

2.9 Wall thickness s mm 54.5 di Inside diameter mm

52 Thermal conductivity λ W/(m·K) 94.72 Characteristic length l mm

Acceleration due to gravity g 9.81 m/s²

Temperatures and properties 127.5 ϑ0 Temperature on the surface °C

ϑ∞ Temperature of fluid outside the boundary layer 50 °C 77.47 (ϑ0 - ϑ∞) Temperature difference ∆ϑ K

88.73 ϑm (ϑ0 + ϑ∞) / 2 Mean temperature °C 873.7 Density ρ kg/m³ 2064 cp Specific heat capacity J/(kg·K)

32.15 Dynamic viscosity η mPa·s 3.68e-5 Kinematic viscosity ν m²/s 0.1213 Thermal conductivity λ W/(m·K)

7.209e-4 Coefficient of thermal expansion β 1/K

Characteristic values 547.2 Pr = ν · ρ · cp / λ Prandtl number Pr

343770 Gr = g · l3 · β · ∆ϑ / ν2 Grashof number Gr (3) 1.881e+8 Rayleigh number Ra (4) Ra = Gr · Pr

0.9641 f3(Pr) Prandtl function (24) 99.19 Nusselt number Nu (22)

Heat transfer 127 αa Heat transfer coefficient (free

convection) (2) α = Nu · λ / l W/(m²·K)

Convective heat flux Q 21.46 kW

Balance for the calculation of the surface temperat ure Heating medium

cp Specific heat capacity 2349 J/(kg·K) Density ρ 795.7 kg/m³ Mass flow m 7957 kg/h

10 Volume flow V m³/h 140 ϑe Inlet temperature °C

135.9 ϑa Outlet temperature °C 137.9 ϑm Mean temperature °C

-21.46 QH Duty kW

1.191 Tube-side velocity u m/s

1101 αi Heat transfer coefficient inside W/(m²·K) 0 fi Fouling inside m²·K/W 0 fa Fouling outside m²·K/W

111.9 Overall heat transfer coefficient k W/(m²·K)

11515 Length of the cylinder L mm 2.181 Area of the cylinder A m²

TankExampleNov2016


Equations

(2)

(3)

(4)

(22)

(24)

TankExampleNov2016


Pressure drop in coil Pressure drop in flow through pipes

Straight pipes

Parameters of the pipe 11.51 Pipe length l m

54.5 di Pipe inside diameter mm Absolute roughness k 0.04 mm

NR Number of pipes with parallel flow 1

Physical properties 795.7 Density ρ kg/m³ 1.151 Dynamic viscosity η mPa·s

1.446e-6 Kinematic viscosity ν m²/s

2.21 mg Total mass flow kg/s mR Mass flow per pipe 7957 kg/h

10 VR Volume flow per pipe m³/h 1.191 Velocity w m/s

Results Flow pattern Turbulent flow (Re > 2320)

2819 Pressure drop ∆p Pa 44867 Reynolds number Re

0.02366 Drag coefficient ξ

Equations

44867 Re = > Turbulent flow → 2320

tankexamplenov2016 - lv softlv-soft.com/software/fachbereiche/waermeuebertrager/paketwaerme/... ·...

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