Double Pipe Heat Exchanger Project #3 Calculations

5/26/2018 Double Pipe Heat Exchanger Project #3 Calculations

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Design Requirements: Properties of Kerosene (In

1) Heats 2.5 kg/s of kerosene from 25 C to 35 C m.k= 2.50

2) Schedule 40 Steel Pipe .k = 730

3) Water at 90 C available to heat the kerosene kf.k = 0.132

4) Maximum pressure drop in each pipe is 70 kPa v.k = 5.47945E-07

.k = 0.0004

Schedule 40 Steel Pipe: Cp.k = 2470

Acceptable Pipe Sizes Pr.k = 7.48

ND.t = 2 ND.a = 3 .k = 7.32073E-08

ID.t = 0.05252 m ID.a = 0.07792 m t1 = 25

OD.t = 0.06034 m OD.a = 0.0889 m t2 = 35

A.t = 0.002166 m A.a = 0.004769 m Rd= 0.0002

Hydraulic Diameter, Dh= 0.01758 m .k = 7.32073E-08

Effective Diameter, De = 0.040282 m Pr.k = 7.48

Assumptions:

1) The double pipe heat exchanger is operating in counterflow.

2) The properties of Kerosense are taken from problem 43 on page 443 in the textbook

3)

q=(m.k)(Cp.k)(t2-t1)

q = 61750 J/s

Economic Velocity Range for Kerosene: 1.4 m/s 2.8 m/s

Mass Flow Rates for Velocity Range: 2.214 kg/s 4.428 kg/s

Economic Velocity Range for Water: 1.4 m/s 2.8 m/s

Flow Areas

At= 0.002166403 m

Aa= 0.001908997 m

Fluid Velocities

Vt= 1.58 m/s

Va= 2.20 m/s

Reynolds Numbers

Ret= 151518.4

Rea= 269362.4

Assuming we are operating under the assumption that there are no heat losses inside the heat exchanger, is

warmer fluid must be equal to the heat gained by the cooler fluid?


2/12

Nusselt Numbers

Nut= 717.42

Nua= 630.55

Convection Coefficients

hi= 1803.112 W/m*K

ha= 10550.395 W/m*K

ht= 1569.430 W/m*K

Exchanger Coefficient

U0= 1366.20 W/m*K

Outlet Temperature Calculations

R = 0.350

A0= 1.148 m L = 6.06 m

Ecounter= 0.848T2= 86.50 C T2=

86.50 C

t2= 35 C

Log Mean Temperature Difference

LMTD = 58.19 C t1= 55 C LMTD =

t2= 61.50426 C

Heat Balance

qw= 61750

qc= 61750

q =

U = 924.3

Friction Factors

= 0.000046 m

/IDt= 0.000875857

/Dh= 0.00261661

Re.a = 117556.231

ft= 0.021

fa= 0.027

Pressure Drop:

pt= 2219.89 Pa 2.2 kPa

pa= 24630.23 Pa 24.6 kPa

Effectiveness


3/12

N = 0.254

C = 0.350

E = 0.216


4/12

Dh

er Tube): Properties of Water (Annular Tube):

kg/s m.w= 4.20 kg/s p.max = 70000 Pa

kg/m .w = 1000 kg/m L = 6.056641 m

W/m*K kf.w = 0.674 W/m*K L = 0.001

m/s v.w = 3.29E-07 m/s

N*s/m .w = 0.000329 N*s/m

J/kg*K Cp.w = 4206 J/kg*K C = 0.349574

Pr.w = 2.05

m/s .w = 1.66E-07 m/s

C T1 = 90 C

C T2 = 86.50 C

m*K/W Rd= 0.00015 m*K/W

m/s .w = 1.6E-07 m/s

Pr.w = 2.05

it possible to assume that the that the heat lost by the


5/12

58.19 C


6/12

Design Requirements: Properties of Kerosene (In

1) Heats 2.5 kg/s of kerosene from 25 C to 35 C m.k= 2.50

2) Schedule 40 Steel Pipe .k = 730

3) Water at 90 C available to heat the kerosene kf.k = 0.132

4) Maximum pressure drop in each pipe is 70 kPa v.k = 5.47945E-07

.k = 0.0004

Schedule 40 Steel Pipe: Cp.k = 2470

Acceptable Pipe Sizes Pr.k = 7.48

ND.t = 1.25 ND.a = 2 .k = 7.32073E-08

ID.t = 0.03504 m ID.a = 0.05252 m t1 = 25

OD.t = 0.04216 m OD.a = 0.06034 m t2 = 35

A.t = 0.0009643 m A.a = 0.002166 m Rd= 0.0002

Hydraulic Diameter, Dh= 0.01036 m .k = 7.32073E-08

Effective Diameter, De = 0.023266 m Pr.k = 7.48

Assumptions:

1) The double pipe heat exchanger is operating in counterflow.

2) The properties of Kerosense are taken from problem 43 on page 443 in the textbook

3)

q=(m.k)(Cp.k)(t2-t1)

q = 61750 J/s

Economic Velocity Range for Kerosene: 1.4 m/s 2.8 m/s

Mass Flow Rates for Velocity Range: 0.986 kg/s 1.971 kg/s

Economic Velocity Range for Water: 1.4 m/s 2.8 m/s

Flow Areas

At= 0.000964313 m

Aa= 0.000770385 m

Fluid Velocities

Vt= 3.55 m/s

Va= 2.20 m/s

Reynolds Numbers

Ret= 227104.7

Rea= 155576.6

Assuming we are operating under the assumption that there are no heat losses inside the heat exchanger, is

warmer fluid must be equal to the heat gained by the cooler fluid?


7/12

Nusselt Numbers

Nut= 991.70

Nua= 406.45

Convection Coefficients

hi= 3735.870 W/m*K

ha= 11774.630 W/m*K

ht= 3104.954 W/m*K

Exchanger Coefficient

U0= 2457.04 W/m*K

Outlet Temperature Calculations

R = 0.866

A0= 0.840 m L = 6.34 m

Ecounter= 0.956T2= 81.34 C T2=

81.34 C

t2= 35 C

Log Mean Temperature Difference

LMTD = 55.67 C t1= 55 C LMTD =

t2= 56.33762 C

Heat Balance

qw= 61750 J/s

qc= 61750 J/s

q = 61750 J/s

U = 1321.0

Friction Factors

= 0.000046 m

/IDt= 0.001312785

/Dh= 0.004440154

Re.a = 69276.59574

ft= 0.022

fa= 0.031

Pressure Drop:

pt= 18499.86 Pa 18.5 kPa

pa= 48393.20 Pa 48.4 kPa

Effectiveness


8/12

N = 0.334

C = 0.866

E = 0.255


9/12

Dh

er Tube): Properties of Water (Annular Tube):

kg/s m.w= 1.69 kg/s p.max = 70000 Pa

kg/m .w = 1000 kg/m L = 6.339982 m

W/m*K kf.w = 0.674 W/m*K L = 0.001

m/s v.w = 3.29E-07 m/s

N*s/m .w = 0.000329 N*s/m

J/kg*K Cp.w = 4206 J/kg*K C = 0.866238

Pr.w = 2.05

m/s .w = 1.66E-07 m/s

C T1 = 90 C

C T2 = 81.34 C

m*K/W Rd= 0.00015 m*K/W

m/s .w = 1.6E-07 m/s

Pr.w = 2.05

it possible to assume that the that the heat lost by the


10/12

55.67 C


11/12

Property 3" x 2" units 1 2" x 1.25" units 2

IDp 0.05252 m 0.03504 m

ODp 0.06034 m 0.04216 m

IDa 0.07792 m 0.05252 m

L 6.06 m 6.34 m

t1 25 C 25 C

t2 35 C 35 C

T1 90 C 90 C

T2 86.50 C 81.34 C

U0 1366.20 W/m*K 2457.04 W/m*K

A0 1.148 m2

0.840 m2

pp 2.22 kPa 18.50 kPa

pa 24.63 kPa 48.39 kPa

E 0.216 0.255

N 0.254 0.334


12/12

Nominal Diameter OD (cm) ID (cm) Area (cm) OD (m) ID (m) Area (m)

0.125 1.029 0.683 0.3664 0.01029 0.00683 0.00003664

0.25 1.372 0.924 0.6706 0.01372 0.00924 0.00006706

0.375 1.714 1.252 1.233 0.01714 0.01252 0.0001233

0.5 2.134 1.58 1.961 0.02134 0.0158 0.0001961

0.75 2.667 2.093 3.441 0.02667 0.02093 0.00034411 3.34 2.664 5.574 0.0334 0.02664 0.0005574

1.25 4.216 3.504 9.643 0.04216 0.03504 0.0009643

1.5 4.826 4.09 13.13 0.04826 0.0409 0.001313

2 6.034 5.252 21.66 0.06034 0.05252 0.002166

2.5 7.303 6.271 30.89 0.07303 0.06271 0.003089

3 8.89 7.792 47.69 0.0889 0.07792 0.004769

3.5 10.16 9.012 63.79 0.1016 0.09012 0.006379

4 11.43 10.23 82.19 0.1143 0.1023 0.008219

5 14.13 12.82 129.1 0.1413 0.1282 0.01291

6 16.83 15.41 186.5 0.1683 0.1541 0.01865

8 21.91 20.27 322.7 0.2191 0.2027 0.03227

10 27.31 25.46 509.1 0.2731 0.2546 0.05091

12 32.39 30.33 722.5 0.3239 0.3033 0.07225

Double Pipe Heat Exchanger Project #3 Calculations

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