# Heat transfer and pressure drop across tube bundles (ht.conv_tube_bank)¶

ht.conv_tube_bank.ESDU_tube_angle_correction(angle)[source]

Calculates the tube bank inclination correction factor according to [1] for heat transfer across a tube bundle.

$F_3 = \frac{Nu_{\theta}}{Nu_{\theta=90^{\circ}}} = (\sin(\theta))^{0.6}$
Parameters
anglefloat

The angle of inclination of the tuba bank with respect to the longitudinal axis (90° for a straight tube bank)

Returns
F3float

ESDU tube inclination correction factor, [-]

Notes

A curve is given in [1] but it is so close the function, it is likely the function is all that is used. [1] claims this correction is valid for $$100 < Re < 10^{6}$$.

For angles less than 10°, the problem should be considered internal flow, not flow across a tube bank.

References

1(1,2,3)

“Convective Heat Transfer During Crossflow of Fluids Over Plain Tube Banks.” ESDU 73031 (November 1, 1973).

Examples

>>> ESDU_tube_angle_correction(75)
0.9794139080247666

ht.conv_tube_bank.ESDU_tube_row_correction(tube_rows, staggered=True, Re=3000.0, method='Hewitt')[source]

Calculates the tube row correction factor according to [1] as shown in [2] for heat transfer across a tube bundle. This is also used for finned bundles. The correction factors are slightly different for staggered vs. inline configurations.

This method is a tabular lookup, with values of 1 when the tube row count is 10 or more.

Parameters
tube_rowsint

Number of tube rows per bundle, [-]

staggeredbool, optional

Whether in the in-line or staggered configuration, [-]

Refloat, optional

The Reynolds number of flow through the tube bank using the bare tube outer diameter and the minimum flow area through the bundle, [-]

methodstr, optional

‘Hewitt’; this may have another option in the future, [-]

Returns
F2float

ESDU tube row count correction factor, [-]

Notes

In [1], for line data, there are two curves given for different Reynolds number ranges. This is not included in [2] and only an average curve is given. This is not implemented here; Re is an argument but does not impact the result of this function.

For tube counts 1-7, [3] claims the factors from [1] are on average: [0.65, 0.77, 0.84, 0.9, 0.94, 0.97, 0.99].

References

1(1,2,3)

“Convective Heat Transfer During Crossflow of Fluids Over Plain Tube Banks.” ESDU 73031 (November 1, 1973).

2(1,2)

Hewitt, G. L. Shires, T. Reg Bott G. F., George L. Shires, and T. R. Bott. Process Heat Transfer. 1st edition. Boca Raton: CRC Press, 1994.

3

Rabas, T. J., and J. Taborek. “Survey of Turbulent Forced-Convection Heat Transfer and Pressure Drop Characteristics of Low-Finned Tube Banks in Cross Flow.” Heat Transfer Engineering 8, no. 2 (January 1987): 49-62.

Examples

>>> ESDU_tube_row_correction(4, staggered=True)
0.8984
>>> ESDU_tube_row_correction(6, staggered=False)
0.9551

ht.conv_tube_bank.Nu_ESDU_73031(Re, Pr, tube_rows, pitch_parallel, pitch_normal, Pr_wall=None, angle=90.0)[source]

Calculates the Nusselt number for crossflow across a tube bank with a specified number of tube rows, at a specified Re according to [1], also shown in [2].

$\text{Nu} = a \text{Re}^m\text{Pr}^{0.34}F_1 F_2$

The constants a and m come from the following tables:

In-line tube banks:

Re

a

m

10-300

0.742

0.431

300-2E5

0.211

0.651

2E5-2E6

0.116

0.700

Staggered tube banks:

Re

a

m

10-300

1.309

0.360

300-2E5

0.273

0.635

2E5-2E6

0.124

0.700

Parameters
Refloat

Reynolds number with respect to average (bulk) fluid properties and tube outside diameter, [-]

Prfloat

Prandtl number with respect to average (bulk) fluid properties, [-]

tube_rowsint

Number of tube rows per bundle, [-]

pitch_parallelfloat

Distance between tube center along a line parallel to the flow; has been called longitudinal pitch, pp, s2, SL, and p2, [m]

pitch_normalfloat

Distance between tube centers in a line 90° to the line of flow; has been called the transverse pitch, pn, s1, ST, and p1, [m]

Pr_wallfloat, optional

Prandtl number at the wall temperature; provide if a correction with the defaults parameters is desired; otherwise apply the correction elsewhere, [-]

anglefloat, optional

The angle of inclination of the tuba bank with respect to the longitudinal axis (90° for a straight tube bank)

Returns
Nufloat

Nusselt number with respect to tube outside diameter, [-]

Notes

The tube-row count correction factor F2 can be disabled by setting tube_rows to 10. The property correction factor F1 can be disabled by not specifying Pr_wall. A Prandtl number exponent of 0.26 is recommended in [1] for heating and cooling for both liquids and gases.

The pitches are used to determine whhether or not to use data for staggered or inline tube banks.

The inline coefficients are valid for a normal pitch to tube diameter ratio from 1.2 to 4; and the staggered ones from 1 to 4. The overall accuracy of this method is claimed to be 15%.

References

1(1,2)

“High-Fin Staggered Tube Banks: Heat Transfer and Pressure Drop for Turbulent Single Phase Gas Flow.” ESDU 86022 (October 1, 1986).

2

Hewitt, G. L. Shires, T. Reg Bott G. F., George L. Shires, and T. R. Bott. Process Heat Transfer. 1st edition. Boca Raton: CRC Press, 1994.

Examples

>>> Nu_ESDU_73031(Re=1.32E4, Pr=0.71, tube_rows=8, pitch_parallel=.09,
... pitch_normal=.05)
98.2563319140594

ht.conv_tube_bank.Nu_Grimison_tube_bank(Re, Pr, Do, tube_rows, pitch_parallel, pitch_normal)[source]

Calculates Nusselt number for crossflow across a tube bank of tube rows at a specified Re, Pr, and D using the Grimison methodology as described in [1].

$\bar{Nu_D} = 1.13C_1Re_{D,max}^m Pr^{1/3}C_2$
Parameters
Refloat

Reynolds number with respect to average (bulk) fluid properties and tube outside diameter, [-]

Prfloat

Prandtl number with respect to average (bulk) fluid properties, [-]

Dofloat

Tube outer diameter, [m]

tube_rowsint

Number of tube rows per bundle, [-]

pitch_parallelfloat

Distance between tube center along a line parallel to the flow; has been called longitudinal pitch, pp, s2, SL, and p2, [m]

pitch_normalfloat

Distance between tube centers in a line 90° to the line of flow; has been called the transverse pitch, pn, s1, ST, and p1, [m]

Returns
Nufloat

Nusselt number with respect to tube outside diameter, [-]

Notes

Tube row correction factors are applied for tube row counts less than 10, also published in [1].

References

1(1,2)

Grimson, E. D. (1937) Correlation and Utilisation of New Data on Flow Resistance and Heat Transfer for Cross Flow of Gases over Tube Banks. Trans. ASME. 59 583-594

Examples

>>> Nu_Grimison_tube_bank(Re=10263.37, Pr=.708, tube_rows=11,
... pitch_normal=.05, pitch_parallel=.05, Do=.025)
79.07883866010

>>> Nu_Grimison_tube_bank(Re=10263.37, Pr=.708, tube_rows=11,
... pitch_normal=.07, pitch_parallel=.05, Do=.025)
79.92721078571

ht.conv_tube_bank.Nu_HEDH_tube_bank(Re, Pr, Do, tube_rows, pitch_parallel, pitch_normal)[source]

Calculates Nusselt number for crossflow across a tube bank of tube rows at a specified Re, Pr, and D using the Heat Exchanger Design Handbook (HEDH) methodology, presented in [1].

$Nu = Nu_m f_N$
$Nu_m = 0.3 + \sqrt{Nu_{m,lam}^2 + Nu_{m,turb}^2}$
$Nu_{m,turb} = \frac{0.037Re^{0.8} Pr}{1 + 2.443Re^{-0.1}(Pr^{2/3} -1)}$
$Nu_{m,lam} = 0.664Re^{0.5} Pr^{1/3}$
$\psi = 1 - \frac{\pi}{4a} \text{ if b >= 1}$
$\psi = 1 - \frac{\pi}{4ab} \text{if b < 1}$
$f_A = 1 + \frac{0.7}{\psi^{1.5}}\frac{b/a-0.3}{(b/a) + 0.7)^2} \text{if inline}$
$f_A = 1 + \frac{2}{3b} \text{elif partly staggered}$
$f_N = \frac{1 + (n-1)f_A}{n}$
Parameters
Refloat

Reynolds number with respect to average (bulk) fluid properties and tube outside diameter, [-]

Prfloat

Prandtl number with respect to average (bulk) fluid properties, [-]

Dofloat

Tube outer diameter, [m]

tube_rowsint

Number of tube rows per bundle, [-]

pitch_parallelfloat

Distance between tube center along a line parallel to the flow; has been called longitudinal pitch, pp, s2, SL, and p2, [m]

pitch_normalfloat

Distance between tube centers in a line 90° to the line of flow; has been called the transverse pitch, pn, s1, ST, and p1, [m]

Returns
Nufloat

Nusselt number with respect to tube outside diameter, [-]

Notes

Prandtl number correction left to an outside function, although a set of coefficients were specified in [1] because they depent on whether heating or cooling is happening, and for gases, use a temperature ratio instaed of Prandtl number.

The claimed range of validity of these expressions is $$10 < Re < 1E5$$ and $$0.6 < Pr < 1000$$.

References

1(1,2)

Schlunder, Ernst U, and International Center for Heat and Mass Transfer. Heat Exchanger Design Handbook. Washington: Hemisphere Pub. Corp., 1987.

2

Baehr, Hans Dieter, and Karl Stephan. Heat and Mass Transfer. Springer, 2013.

Examples

>>> Nu_HEDH_tube_bank(Re=1E4, Pr=7., tube_rows=10, pitch_normal=.05,
... pitch_parallel=.05, Do=.03)
382.4636554404698


Example 3.11 in [2]:

>>> Nu_HEDH_tube_bank(Re=10263.37, Pr=.708, tube_rows=11, pitch_normal=.05,
... pitch_parallel=.05, Do=.025)
149.18735251017594

ht.conv_tube_bank.Nu_Zukauskas_Bejan(Re, Pr, tube_rows, pitch_parallel, pitch_normal, Pr_wall=None)[source]

Calculates Nusselt number for crossflow across a tube bank of tube number n at a specified Re according to the method of Zukauskas [1]. A fit to graphs from [1] published in [2] is used for the correlation. The tube row correction factor is obtained from digitized graphs from [1], and a lookup table was created and is used for speed.

The formulas are as follows:

Aligned tube banks:

$\bar Nu_D = 0.9 C_nRe_D^{0.4}Pr^{0.36}\left(\frac{Pr}{Pr_w}\right)^{0.25} \text{ for } 1 < Re < 100$
$\bar Nu_D = 0.52 C_nRe_D^{0.5}Pr^{0.36}\left(\frac{Pr}{Pr_w}\right)^{0.25} \text{ for } 100 < Re < 1000$
$\bar Nu_D = 0.27 C_nRe_D^{0.63}Pr^{0.36}\left(\frac{Pr}{Pr_w}\right)^{0.25} \text{ for } 1000 < Re < 20000$
$\bar Nu_D = 0.033 C_nRe_D^{0.8}Pr^{0.36}\left(\frac{Pr}{Pr_w}\right)^{0.25} \text{ for } 20000 < Re < 200000$

Staggered tube banks:

$\bar Nu_D = 1.04C_nRe_D^{0.4}Pr^{0.36}\left(\frac{Pr}{Pr_w}\right)^{0.25} \text{ for } 1 < Re < 500$
$\bar Nu_D = 0.71C_nRe_D^{0.5}Pr^{0.36}\left(\frac{Pr}{Pr_w}\right)^{0.25} \text{ for } 500 < Re < 1000$
$\bar Nu_D = 0.35 C_nRe_D^{0.6}Pr^{0.36}\left(\frac{Pr}{Pr_w}\right)^{0.25} \left(\frac{X_t}{X_l}\right)^{0.2} \text{ for } 1000 < Re < 20000$
$\bar Nu_D = 0.031 C_nRe_D^{0.8}Pr^{0.36}\left(\frac{Pr}{Pr_w}\right)^{0.25} \left(\frac{X_t}{X_l}\right)^{0.2} \text{ for } 20000 < Re < 200000$
Parameters
Refloat

Reynolds number with respect to average (bulk) fluid properties and tube outside diameter, [-]

Prfloat

Prandtl number with respect to average (bulk) fluid properties, [-]

tube_rowsint

Number of tube rows per bundle, [-]

pitch_parallelfloat

Distance between tube center along a line parallel to the flow; has been called longitudinal pitch, pp, s2, SL, and p2, [m]

pitch_normalfloat

Distance between tube centers in a line 90° to the line of flow; has been called the transverse pitch, pn, s1, ST, and p1, [m]

Pr_wallfloat, optional

Prandtl number at the wall temperature; provide if a correction with the defaults parameters is desired; otherwise apply the correction elsewhere, [-]

Returns
Nufloat

Nusselt number with respect to tube outside diameter, [-]

Notes

If Pr_wall is not provided, the Prandtl number correction is not used and left to an outside function. A Prandtl number exponent of 0.25 is recommended in [1] for heating and cooling for both liquids and gases.

References

1(1,2,3,4)

Zukauskas, A. Heat transfer from tubes in crossflow. In T.F. Irvine, Jr. and J. P. Hartnett, editors, Advances in Heat Transfer, volume 8, pages 93-160. Academic Press, Inc., New York, 1972.

2

Bejan, Adrian. “Convection Heat Transfer”, 4E. Hoboken, New Jersey: Wiley, 2013.

Examples

>>> Nu_Zukauskas_Bejan(Re=1E4, Pr=7., tube_rows=10, pitch_parallel=.05, pitch_normal=.05)
175.9202277145248

ht.conv_tube_bank.Zukauskas_tube_row_correction(tube_rows, staggered=True, Re=10000.0)[source]

Calculates the tube row correction factor according to a graph digitized from [1] for heat transfer across a tube bundle. The correction factors are slightly different for staggered vs. inline configurations; for the staggered configuration, factors are available separately for Re larger or smaller than 1000.

This method is a tabular lookup, with values of 1 when the tube row count is 20 or more.

Parameters
tube_rowsint

Number of tube rows per bundle, [-]

staggeredbool, optional

Whether in the in-line or staggered configuration, [-]

Refloat, optional

The Reynolds number of flow through the tube bank using the bare tube outer diameter and the minimum flow area through the bundle, [-]

Returns
Ffloat

Tube row count correction factor, [-]

Notes

The basis for this method is that an infinitely long tube bank has a factor of 1; in practice the factor is reached at 20 rows.

References

1

Zukauskas, A. Heat transfer from tubes in crossflow. In T.F. Irvine, Jr. and J. P. Hartnett, editors, Advances in Heat Transfer, volume 8, pages 93-160. Academic Press, Inc., New York, 1972.

Examples

>>> Zukauskas_tube_row_correction(4, staggered=True)
0.8942
>>> Zukauskas_tube_row_correction(6, staggered=False)
0.9465

ht.conv_tube_bank.baffle_correction_Bell(crossflow_tube_fraction, method='spline')[source]

Calculate the baffle correction factor Jc which accounts for the fact that all tubes are not in crossflow to the fluid - some have fluid flowing parallel to them because they are situated in the “window”, where the baffle is cut, instead of between the tips of adjacent baffles.

Equal to 1 for no tubes in the window, increases to 1.15 when the windows are small and velocity there is high; decreases to about 0.52 for very large baffle cuts. Well designed exchangers should typically have a value near 1.0.

Cubic spline interpolation is the default method of retrieving a value from the graph, which was digitized with Engauge-Digitizer.

The interpolation can be slightly slow, so a Chebyshev polynomial was fit to a maximum error of 0.142%, average error 0.04% - well within the margin of error of the digitization of the graph; this is approximately 10 times faster, accessible via the ‘chebyshev’ method.

The Heat Exchanger Design Handbook [4], [5] provides the linear curve fit, which covers the “practical” range of baffle cuts 15-45% but not the last dip in the graph. This method is not recommended, but can be used via the method “HEDH”.

$J_c = 0.55 + 0.72Fc$
Parameters
crossflow_tube_fractionfloat

Fraction of tubes which are between baffle tips and not in the window, [-]

methodstr, optional

One of ‘chebyshev’, ‘spline’, or ‘HEDH’

Returns
Jcfloat

Baffle correction factor in the Bell-Delaware method, [-]

Notes

max: ~1.1536 at ~0.9066 min: ~0.5328 at 0 value at 1: ~1.0314

For the ‘spline’ method, this function takes ~13 us per call. The other two methods are approximately 10x faster.

References

1

Bell, Kenneth J. Final Report of the Cooperative Research Program on Shell and Tube Heat Exchangers. University of Delaware, Engineering Experimental Station, 1963.

2

Bell, Kenneth J. Delaware Method for Shell-Side Design. In Heat Transfer Equipment Design, by Shah, R. K., Eleswarapu Chinna Subbarao, and R. A. Mashelkar. CRC Press, 1988.

3

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

4

Schlünder, Ernst U, and International Center for Heat and Mass Transfer. Heat Exchanger Design Handbook. Washington: Hemisphere Pub. Corp., 1987.

5

Serth, R. W., Process Heat Transfer: Principles, Applications and Rules of Thumb. 2E. Amsterdam: Academic Press, 2014.

Examples

For a HX with four groups of tube bundles; the top and bottom being 9 tubes each, in the window, and the two middle bundles having 41 tubes each, for a total of 100 tubes, the fraction between baffle tubes and not in the window is 0.82. The correction factor is then:

>>> baffle_correction_Bell(0.82)
1.1258554691854046

ht.conv_tube_bank.baffle_leakage_Bell(Ssb, Stb, Sm, method='spline')[source]

Calculate the baffle leakage factor Jl which accounts for leakage between each baffle. Cubic spline interpolation is the default method of retrieving a value from the graph, which was digitized with Engauge-Digitizer.

The Heat Exchanger Design Handbook [4], [5] provides a curve fit as well. This method is not recommended, but can be used via the method “HEDH”.

$J_L = 0.44(1-r_s) + [1 - 0.44(1-r_s)]\exp(-2.2r_{lm})$
$r_s = \frac{S_{sb}}{S_{sb} + S_{tb}}$
$r_{lm} = \frac{S_{sb} + S_{tb}}{S_m}$
Parameters
Ssbfloat

Shell to baffle leakage area, [m^2]

Stbfloat

Total baffle leakage area, [m^2]

Smfloat

Crossflow area, [m^2]

methodstr, optional

One of ‘spline’, or ‘HEDH’

Returns
Jlfloat

Baffle leakage factor in the Bell-Delaware method, [-]

Notes

Takes ~5 us per call. If the x parameter is larger than 0.743614, it is clipped to it.

The HEDH curve fits are rather poor and only 6x faster to evaluate. The HEDH example in [6]’s spreadsheet has an error and uses 0.044 instead of 0.44 in the equation.

References

1

Bell, Kenneth J. Final Report of the Cooperative Research Program on Shell and Tube Heat Exchangers. University of Delaware, Engineering Experimental Station, 1963.

2

Bell, Kenneth J. Delaware Method for Shell-Side Design. In Heat Transfer Equipment Design, by Shah, R. K., Eleswarapu Chinna Subbarao, and R. A. Mashelkar. CRC Press, 1988.

3

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

4

Schlünder, Ernst U, and International Center for Heat and Mass Transfer. Heat Exchanger Design Handbook. Washington: Hemisphere Pub. Corp., 1987.

5

Serth, R. W., Process Heat Transfer: Principles, Applications and Rules of Thumb. 2E. Amsterdam: Academic Press, 2014.

6

Hall, Stephen. Rules of Thumb for Chemical Engineers, Fifth Edition. 5th edition. Oxford ; Waltham , MA: Butterworth-Heinemann, 2012.

Examples

>>> baffle_leakage_Bell(1, 3, 8)
0.5906621282470
>>> baffle_leakage_Bell(1, 3, 8, 'HEDH')
0.5530236260777

ht.conv_tube_bank.bundle_bypassing_Bell(bypass_area_fraction, seal_strips, crossflow_rows, laminar=False, method='spline')[source]

Calculate the bundle bypassing effect Jb according to the Bell-Delaware method for heat exchanger design. Cubic spline interpolation is the default method of retrieving a value from the graph, which was digitized with Engauge-Digitizer.

The Heat Exchanger Design Handbook [4] provides a curve fit as well. This method is not recommended, but can be used via the method “HEDH”:

$J_b = \exp\left[-1.25 F_{sbp} (1 - {2r_{ss}}^{1/3} )\right]$

For laminar flows, replace 1.25 with 1.35.

Parameters
bypass_area_fractionfloat

Fraction of the crossflow area which is not blocked by a baffle or anything else and available for bypassing, [-]

seal_stripsint

Number of seal strips per side of a baffle added to prevent bypassing, [-]

crossflow_rowsint

The number of tube rows in the crosslfow of the baffle, [-]

laminarbool

Whether to use the turbulent correction values or the laminar ones; the Bell-Delaware method uses a Re criteria of 100 for this, [-]

methodstr, optional

One of ‘spline’, or ‘HEDH’

Returns
Jbfloat

Bundle bypassing effect correction factor in the Bell-Delaware method, [-]

Notes

Takes ~5 us per call. If the bypass_area_fraction parameter is larger than 0.695, it is clipped to it.

References

1

Bell, Kenneth J. Final Report of the Cooperative Research Program on Shell and Tube Heat Exchangers. University of Delaware, Engineering Experimental Station, 1963.

2

Bell, Kenneth J. Delaware Method for Shell-Side Design. In Heat Transfer Equipment Design, by Shah, R. K., Eleswarapu Chinna Subbarao, and R. A. Mashelkar. CRC Press, 1988.

3

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

4

Schlünder, Ernst U, and International Center for Heat and Mass Transfer. Heat Exchanger Design Handbook. Washington: Hemisphere Pub. Corp., 1987.

Examples

>>> bundle_bypassing_Bell(0.5, 5, 25)
0.8469611760884599

>>> bundle_bypassing_Bell(0.5, 5, 25, method='HEDH')
0.8483210970579099

ht.conv_tube_bank.dP_Kern(m, rho, mu, DShell, LSpacing, pitch, Do, NBaffles, mu_w=None)[source]

Calculates pressure drop for crossflow across a tube bank according to the equivalent-diameter method developed by Kern [1], presented in [2].

$\Delta P = \frac{f (m/S_s)^2 D_s(N_B+1)}{2\rho D_e(\mu/\mu_w)^{0.14}}$
$S_S = \frac{D_S (P_T-D_o) L_B}{P_T}$
$D_e = \frac{4(P_T^2 - \pi D_o^2/4)}{\pi D_o}$
Parameters
mfloat

Mass flow rate, [kg/s]

rhofloat

Fluid density, [kg/m^3]

mufloat

Fluid viscosity, [Pa*s]

DShellfloat

Diameter of exchanger shell, [m]

LSpacingfloat

Baffle spacing, [m]

pitchfloat

Tube pitch, [m]

Dofloat

Tube outer diameter, [m]

NBafflesfloat

Baffle count, []

mu_wfloat

Fluid viscosity at wall temperature, [Pa*s]

Returns
dPfloat

Pressure drop across bundle, [Pa]

Notes

Adjustment for viscosity left out of this function. Example is from [2]. Roughly 10% difference due to reading of graph. Graph scanned from [1], and interpolation is used to read it.

References

1(1,2)

Kern, Donald Quentin. Process Heat Transfer. McGraw-Hill, 1950.

2(1,2)

Peters, Max, Klaus Timmerhaus, and Ronald West. Plant Design and Economics for Chemical Engineers. 5E. New York: McGraw-Hill, 2002.

Examples

>>> dP_Kern(m=11., rho=995., mu=0.000803, mu_w=0.000657, DShell=0.584,
... LSpacing=0.1524, pitch=0.0254, Do=.019, NBaffles=22)
18980.58768759033

ht.conv_tube_bank.dP_Zukauskas(Re, n, ST, SL, D, rho, Vmax)[source]

Calculates pressure drop for crossflow across a tube bank of tube number n at a specified Re. Method presented in [1]. Also presented in [2].

$\Delta P = N_L \chi \left(\frac{\rho V_{max}^2}{2}\right)f$
Parameters
Refloat

Reynolds number, [-]

nfloat

Number of tube rows, [-]

STfloat

Transverse pitch, used only by some conditions, [m]

SLfloat

Longitudal pitch, used only by some conditions, [m]

Dfloat

Tube outer diameter, [m]

rhofloat

Fluid density, [kg/m^3]

Vmaxfloat

Maximum velocity, [m/s]

Returns
dPfloat

Pressure drop, [Pa]

Notes

Does not account for effects in a heat exchanger. Example 2 is from [2]. Matches to 0.3%; figures are very approximate. Interpolation used with 4 graphs to obtain friction factor and a correction factor.

References

1

Zukauskas, A. Heat transfer from tubes in crossflow. In T.F. Irvine, Jr. and J. P. Hartnett, editors, Advances in Heat Transfer, volume 8, pages 93-160. Academic Press, Inc., New York, 1972.

2(1,2)

Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, and David P. DeWitt. Introduction to Heat Transfer. 6E. Hoboken, NJ: Wiley, 2011.

Examples

>>> dP_Zukauskas(Re=13943., n=7, ST=0.0313, SL=0.0343, D=0.0164, rho=1.217, Vmax=12.6)
235.22916169
>>> dP_Zukauskas(Re=13943., n=7, ST=0.0313, SL=0.0313, D=0.0164, rho=1.217, Vmax=12.6)
217.0750033

ht.conv_tube_bank.laminar_correction_Bell(Re, total_row_passes)[source]

Calculate the correction factor for adverse temperature gradient built up in laminar flow Jr.

This correction begins at Re = 100, and is interpolated between the value of the formula until Re = 20, when it is the value of the formula. It is 1 for Re >= 100. The value of the formula is not allowed to be less than 0.4.

$Jr^* = \left(\frac{10}{N_{row,passes,tot}}\right)^{0.18}$
Parameters
Refloat

Shell Reynolds number in the Bell-Delaware method, [-]

total_row_passesint

The total number of rows passed by the fluid, including those in windows and counting repeat passes of tube rows, [-]

Returns
Jrfloat

Correction factor for adverse temperature gradient built up in laminar flow, [-]

Notes

[5] incorrectly uses the number of tube rows per crosslfow section, not total.

References

1

Bell, Kenneth J. Final Report of the Cooperative Research Program on Shell and Tube Heat Exchangers. University of Delaware, Engineering Experimental Station, 1963.

2

Bell, Kenneth J. Delaware Method for Shell-Side Design. In Heat Transfer Equipment Design, by Shah, R. K., Eleswarapu Chinna Subbarao, and R. A. Mashelkar. CRC Press, 1988.

3

Schlünder, Ernst U, and International Center for Heat and Mass Transfer. Heat Exchanger Design Handbook. Washington: Hemisphere Pub. Corp., 1987.

4

Serth, R. W., Process Heat Transfer: Principles, Applications and Rules of Thumb. 2E. Amsterdam: Academic Press, 2014.

5

Hall, Stephen. Rules of Thumb for Chemical Engineers, Fifth Edition. 5th edition. Oxford ; Waltham , MA: Butterworth-Heinemann, 2012.

Examples

>>> laminar_correction_Bell(30, 80)
0.7267995454361379

ht.conv_tube_bank.unequal_baffle_spacing_Bell(baffles, baffle_spacing, baffle_spacing_in=None, baffle_spacing_out=None, laminar=False)[source]

Calculate the correction factor for unequal baffle spacing Js, which accounts for higher velocity of fluid flow and greater heat transfer coefficients when the in and/or out baffle spacing is less than the standard spacing.

$J_s = \frac{(n_b - 1) + (B_{in}/B)^{(1-n_b)} + (B_{out}/B)^{(1-n_b)}} {(n_b - 1) + (B_{in}/B) + (B_{out}/B)}$
Parameters
bafflesint

Number of baffles, [-]

baffle_spacingfloat

Average spacing between one end of one baffle to the start of the next baffle for non-exit baffles, [m]

baffle_spacing_infloat, optional

Spacing between entrace to first baffle, [m]

baffle_spacing_outfloat, optional

Spacing between last baffle and exit, [m]

laminarbool, optional

Whether to use the turbulent exponent or the laminar one; the Bell-Delaware method uses a Re criteria of 100 for this, [-]

Returns
Jsfloat

Unequal baffle spacing correction factor, [-]

References

1

Bell, Kenneth J. Final Report of the Cooperative Research Program on Shell and Tube Heat Exchangers. University of Delaware, Engineering Experimental Station, 1963.

2

Bell, Kenneth J. Delaware Method for Shell-Side Design. In Heat Transfer Equipment Design, by Shah, R. K., Eleswarapu Chinna Subbarao, and R. A. Mashelkar. CRC Press, 1988.

3

Schlünder, Ernst U, and International Center for Heat and Mass Transfer. Heat Exchanger Design Handbook. Washington: Hemisphere Pub. Corp., 1987.

4

Serth, R. W., Process Heat Transfer: Principles, Applications and Rules of Thumb. 2E. Amsterdam: Academic Press, 2014.

5

Hall, Stephen. Rules of Thumb for Chemical Engineers, Fifth Edition. 5th edition. Oxford ; Waltham , MA: Butterworth-Heinemann, 2012.

Examples

>>> unequal_baffle_spacing_Bell(16, .1, .15, 0.15)
0.9640087802805195