equipment.widget.helical module

equipment.widget.helical.translate(context: str, sourceText: str, disambiguation: str = None, n: int = -1) → str

equipment.widget.helical.Rec_Schmidt(di, Dc)

Calculates critical Reynolds to define transition between laminar and

turbulent flow using using the correlation of Schmidt (1967)

\[Re_c = 2300 \left(1+8.6\left(\frac{di}{Dc}\right)^{0.45}\right)\]

Parameters:

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

Recfloat

Critical reynolds number, [-]

References

[3] Schmidt, E.F.; Wärmeübergand und Druckverlust in Rohrschlangen. Chemie Ingenieur Technik 39(13) (1967) 781-789

equipment.widget.helical.Rec_Ito(di, Dc)

Calculates critical Reynolds to define transition between laminar and

turbulent flow using using the correlation of Ito (1959)

\[Re_c = 2x10^4 \left(\frac{di}{Dc}\right)^{0.32}\]

Parameters:

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

Recfloat

Critical reynolds number, [-]

References

[4] Ito, H.; Friction Factors for Turbulent Flow in Curved Pipes. J. Basic Eng. 81 (1959) 123-134

equipment.widget.helical.Rec_Kubair(di, Dc)

Calculates critical Reynolds to define transition between laminar and

turbulent flow using using the correlation of Kubair-Kuloor (1966)

\[Re_c = 1.273x10^4 \left(\frac{di}{Dc}\right)^{0.2}\]

Parameters:

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

Recfloat

Critical reynolds number, [-]

References

[5] Kubair, V., Kuloor, N.R.; Heat Transfer to Newtonian Fluids in Coiled Pipes in Laminar Flow. Int. J. Heat Mass Transfer 9 (1966) 63-75

equipment.widget.helical.Rec_Srinivasan(di, Dc)

Calculates critical Reynolds to define transition between laminar and

turbulent flow using using the correlation of Srinivasan (1968) as shown in [1]. Recomended method by [2].

\[Re_c = 2100 \left(1 + 12\sqrt{\frac{d_i}{D_c}}\right)\]

Parameters:

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

Recfloat

Critical reynolds number, [-]

References

[6] Srinivasan, P.S., Nandapurkar, S.S., Holland, F.A.; Pressure Drop and Heat Transfer in Coils. Chem. Eng. 218 (1968) 113-119

[1] El-Genk, M.S., Timothy, M.S.; A Review and Correlations for Convection Heat Transfer and Pressure Losses in Toroidal and Helically Coiled Tubes. Heat Transfer Eng. 38(5) (2017) 447-474

[2] ; Perry’s Chemical Engineers’ Handbook 9th Edition. McGraw-Hill (2019)

equipment.widget.helical.Rec_Kutateladze(di, Dc)

Calculates critical Reynolds to define transition between laminar and

turbulent flow using using the correlation of Kutateladze (1966).

\[Re_c = 2300 + 10500 \left(\frac{d_i}{D_c}\right)^{0.3}\]

Parameters:

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

Recfloat

Critical reynolds number, [-]

References

[7] Kutateladze, S.S., Borishanskii, V.M. ; A Concise Encyclopedia of Heat Transfer. Pergamon Press (1966)

equipment.widget.helical.Rec_SethStahel(di, Dc)

Calculates critical Reynolds to define transition between laminar and

turbulent flow using using the correlation of Seth-Stahel (1969).

\[Re_c = 1900 \left(1 + 8 \sqrt{\frac{d_i}{D_c}}\right)\]

Parameters:

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

Recfloat

Critical reynolds number, [-]

References

[20] Seth, K.K., Stahel, E.P.; Heat Transfer from Helical Coils Immersed in Agitated Vessels. Ind. Eng. Chem. 61(6) (1969) 39-49

equipment.widget.helical.Rec_Cioncolini(di, Dc)

Calculates critical Reynolds to define transition between laminar and

turbulent flow using using the correlation of Cioncolini-Santini (2006).

\[Re_c = 30,000 \left(\frac{d_i}{D_c}\right)^{0.47}\]

Parameters:

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

Recfloat

Critical reynolds number, [-]

References

[26] Ciencolini, A., Santini, L.; An experimental investigation regarding the laminar to turbulent flow transition in helically coiled pipes. Exp. Thermal Fluid Sci. 30 (2006) 367-380

equipment.widget.helical.f_Schmidt(Re, di, Dc)

Calculate friction factor for internal flow of a helical coil using

the correlation of Schmidt (1967)

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

ffloat

Friction factor, [-]

References

[3] Schmidt, E.F.; Wärmeübergand und Druckverlust in Rohrschlangen. Chemie Ingenieur Technik 39(13) (1967) 781-789

equipment.widget.helical.f_MoriNakayama(Re, di, Dc)

Calculates friction factor for internal flow of a helical coil in

laminar flow using the method of Mori-Nakayama (1965).

\[\frac{f_c}{f_s}=\left(\frac{0.108De^{0.5}}{1-3.253 De^{-0.5}}\right)\]

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

ffloat

Friction factor, [-]

References

[9] Mori, Y., Nakayama, W.; Study on Forced Convective Heat Transfer in Curved Pipes (1st Report, Laminar Region). Int. J. Heat Mass Transfer 8(1) (1965) 67-82

[10] Mori, Y., Nakayama, W.; Study on Forced Convective Heat Transfer in Curved Pipes (2nd Report, Turbulent Region). Int. J. Heat Mass Transfer 10(1) (1967) 37-59

equipment.widget.helical.f_Ju(Re, di, Dc)

Calculates friction factor for internal flow of a helical coil using

the method of Ju et al. (2001).

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

ffloat

Friction factor, [-]

References

[12] Ju, H., Huang, Z., Xu, Y., Duan, B, Yu, Y.; Hydraulic Performance of Small Bending Radius Helical Coil-Pipe. J. Nuclear Sci. Eng. 38(10) (2001) 826-831

equipment.widget.helical.f_MishraGupta(Re, di, Dc)

Calculates friction factor for internal flow of a helical coil using

the method of Mishra-Gupta (1979).

\[\frac{f_c}{f_s} = 1 - \left(1-\left(\frac{11.6}{De}\right)^{0.45} \right)^{\frac{1}{0.45}}\]

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

ffloat

Friction factor, [-]

References

[13] Mishra, P., Gupta, S.N.; Momentum Transfer in Curved Pipes. 1. Newtonian Fluids. Ind. Eng. Chem. Process Des. Dev. 18(1) (1979) 130-137

equipment.widget.helical.f_Prasad(Re, di, Dc)

Calculates friction factor for internal flow of a helical coil using

the method of Prasad et al. (1989).

For laminar flow use a modified Write correlation:

\[\frac{f}{f_s} = \frac{1}{1-\left(1-\left(\frac{B}{De}\right)^{0.45} \right)^{\frac{1}{0.45}}}\]

For turbulent flow use a modified Ito correlation:

\[\frac{f}{f_s} = 1 + 0.18\left(Re \left(\frac{d_i}{D_c}\right)^2\right)^{0.25}\]

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

ffloat

Friction factor, [-]

References

[18] Prasad, B.V.S.S.S., Das, D.H., Prabhaker, A.K.; Pressure Drop, Heat Transfer and Performance of a Helically Coiled Tubular Exchanger. Heat Recovery Systems & CHP 9(3) (1989) 249-256

equipment.widget.helical.f_Ali(Re, di, Dc, p)

Calculates friction factor for internal flow of a helical coil using

the method of Ali (2001).

Define four flow regime fitted with the correlation:

\[f = Eu\frac{d}{L}=\alpha\left(\frac{d_i}{D_{eq}}\right)^{0.15}Re^{\beta}\]

with the equivalent diameter of coil:

\[D_{eq} = \sqrt{\frac{p^2+\left(\pi D\right)^2}{pi}}\]

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

pfloat

Pitch for twist of 2π radians (360º), [m]

Returns:

ffloat

Friction factor, [-]

References

[21] Ali, S.; Pressure drop correlations for flow through regular helical coil tubes. Fluid Dyn. Research 28 (2001) 295-310

equipment.widget.helical.f_ElGenkSchriener(Re, di, Dc, p)

Calculates friction factor for internal flow of a helical coil using

the method of ElGenk-Schriener (2017).

\[\frac{f_c}{f_s} = 1 + 0.00325 De_m\]

where modified Dean number is defined as:

\[De_m = De^{0.86} \delta^{0.09} \left(\frac{d_i}{D_c}\right)^{-0.38}\]

δ is the curvature defined as:

\[\delta = \frac{d_i/D_c}{1+4\pi^2 \tan^2 \alpha}\]

α is the helix angle:

\[\alpha = \tan^{-1}{\frac{p}{\pi D}}\]

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

pfloat

Pitch for twist of 2π radians (360º), [m]

Returns:

ffloat

Friction factor, [-]

References

[1] El-Genk, M.S., Timothy, M.S.; A Review and Correlations for Convection Heat Transfer and Pressure Losses in Toroidal and Helically Coiled Tubes. Heat Transfer Eng. 38(5) (2017) 447-474

equipment.widget.helical.f_Srinivasan(Re, di, Dc)

Calculates friction factor for internal flow of a helical coil using

the method of Srinivasan (1968) as explain in [49].

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

ffloat

Friction factor, [-]

References

[6] Srinivasan, P.S., Nandapurkar, S.S., Holland, F.A.; Pressure Drop and Heat Transfer in Coils. Chem. Eng. 218 (1968) 113-119

[49] Ghobadi, M., Muzychka, Y.S.; A Review of Heat Transfer and Pressure Drop Correlations for Laminar Flow in Curved Circular Ducts. Heat Transfer Eng. 37(10) (2016) 815-839

equipment.widget.helical.f_Ito(Re, di, Dc)

Calculates friction factor for internal flow of a helical coil using

the method of Ito (1969).

For laminar flow:

\[\frac{f_c}{f_s} = 0.1033 De^{0.5} \left(\left(1+\frac{1.729}{De}\right) ^{0.5} - \frac{1.315}{De^{0.5}}\right)^{-3}\]

For turbulent flow:

\[f_c = 4 \left(0.029 sqrt{\frac{d_i}{D_c}} + 0.304 Re^{-0.25}\right)\]

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

ffloat

Friction factor, [-]

References

[23] Ito, H.; Laminar Flow in Curved Pipes. Z. Angew. Math. Mech. 11 (1969) 653-663

[4] Ito, H.; Friction Factors for Turbulent Flow in Curved Pipes. J. Basic Eng. 81 (1959) 123-134

equipment.widget.helical.f_laminar_White(Re, di, Dc)

Calculates friction factor for internal flow of a helical coil in

laminar flow using the method of White (1929).

\[\frac{f_c}{f_s} = 1 - \left(1-\left(\frac{11.6}{De}\right)^{0.45} \right)^{\frac{1}{0.45}}\]

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

ffloat

Friction factor, [-]

References

[8] White, C.M.; Streamline Flow through Curved Pipes. Proc. R .Soc. London A 123 (1929) 645-663

equipment.widget.helical.f_laminar_Hart(Re, di, Dc)

Calculates friction factor for internal flow of a helical coil in

laminar flow using the method of Hart (1988).

\[\frac{f_c}{f_s} = 1 + 0.09 \frac{De^{1.5}}{70+De}\]

Recomended method in [2] for friction factor in laminar flow.

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

ffloat

Friction factor, [-]

References

[11] Hart, J., Ellenberger, J., Hamersma, P.J.; Single- and Two-Phase Flow Through Helically Coiled Tubes. Chem. Eng. Sci. 43(4) (1988) 775-783

[2] ; Perry’s Chemical Engineers’ Handbook 9th Edition. McGraw-Hill (2019)

equipment.widget.helical.f_laminar_ManlapazChurchill(Re, di, Dc, p)

Calculates friction factor in laminar regimen for internal flow of a

helical coil using the method of Manlapaz-Churchill (1980).

\[\frac{f_c}{f_{s,L}} = \left[\left(1 - \frac{0.18}{\left(1+\left(\frac{35}{De}\right)^2\right)^{1/2}}\right)^m + \left(1+\frac{d_i}{3 D_c}\right)^2 \frac{De}{88.33}\right]^{1/2}\]

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

pfloat

Pitch for twist of 2π radians (360º), [m]

Returns:

ffloat

Friction factor, [-]

References

[17] Manlapaz, R.L., Churchill, S.W.; Fully Developed Laminar Flow in a Helically Coiled Tube of Finite Pitch. Chem. Eng. Communications 7 (1980) 57-78

equipment.widget.helical.f_laminar_LiuMasliyah(Re, di, Dc, p)

Calculates friction factor for internal flow of a helical coil in

laminar flow using the method of Liu-Masliyah (1993).

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

pfloat

Pitch for twist of 2π radians (360º), [m]

Returns:

ffloat

Friction factor, [-]

References

[19] Liu, S., Masliyah, J.H.; Axially invariant laminar flow in helical pipes with a finite pitch. J. Fluid Mech. 251 (1993) 315-353

equipment.widget.helical.f_laminar_TarbellSamuels(Re, di, Dc)

Calculates friction factor for internal flow of a helical coil in

laminar flow using the method of Tarbell-Samuels (1973).

\[\frac{f_c}{f_s} = 1 + \left( 8.279e^{-4} + \frac{7.964e{-3}}{d_i/D_c}\right) Re - 2.096e-7 Re^2\]

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

ffloat

Friction factor, [-]

References

[24] Tarbell, J.M., Samuels, M.R.; Momentum and Heat Transfer in Helical Coils. Chem. Eng. J. 5(2) (1973) 117-127

equipment.widget.helical.f_laminar_Adler(Re, di, Dc)

Calculates friction factor for internal flow of a helical coil in

laminar flow using the method of Adler (1934).

\[\frac{f_c}{f_s} = 0.1064 \sqrt{De}\]

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

ffloat

Friction factor, [-]

References

[27] Adler, M.; Strömung in gekrümmten Rohren. Z. Angew. Math. Mech. 14(5) 257-275

equipment.widget.helical.f_laminar_Barua(Re, di, Dc)

Calculates friction factor for internal flow of a helical coil in

laminar flow using the method of Barua (1963).

\[\frac{f_c}{f_s} = 0.509 + 0.0918 \sqrt{De}\]

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

ffloat

Friction factor, [-]

References

[28] Barua, S.N.; On Secondary Flow in Stationary Curved Pipes. Quart. J. Mech. Appl. Math. 16(1) (1963) 61-77

equipment.widget.helical.f_laminar_PimentaCampos(Re, di, Dc)

Calculates friction factor for internal flow of a helical coil in

laminar flow using the method of Pimenta-Campos (2012)

\[\frac{f_c}{f_s} = 1 + \frac{0.028 De^{1.68}}{70+De}\]

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

ffloat

Friction factor, [-]

References

[29] Pimenta, T.A., Campos, J.B.L.M.; Friction losses of Newtonian and non-Newtonian fluids flowing in laminar regime in a helical coil. Exp. Thermal Fluid Sci. 36 (2012) 194-204

equipment.widget.helical.f_laminar_Yanase(Re, di, Dc)

Calculates friction factor for internal flow of a helical coil in

laminar flow using the method of Yanase et al. (1989)

\[\frac{f_c}{f_s} = 0.557 + 0.0938 \sqrt{De}\]

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

ffloat

Friction factor, [-]

References

[30] Yanase, S., Goto, N., Yamamoto, K.; Dual solutions of the flow through a curved tube. Fluid Dyn. Research 5 (1989) 191-201

equipment.widget.helical.f_laminar_Dennis(Re, di, Dc)

Calculates friction factor for internal flow of a helical coil in

laminar flow using the method of Dennis (1980)

\[\frac{f_c}{f_s} = 0.388 + 0.1015 \sqrt{De}\]

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

ffloat

Friction factor, [-]

References

[31] Dennis, S.C.R.; Calculation of the steady flow through a curved tube using a new finite-difference method. J. Fluid Mech. 99(3) (1980) 449-467

equipment.widget.helical.f_laminar_vanDyke(Re, di, Dc)

Calculates friction factor for internal flow of a helical coil in

laminar flow using the method of Van Dyke (1978)

\[\frac{f_c}{f_s} = 0.47136 De^{0.25}\]

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

ffloat

Friction factor, [-]

References

[32] Van Dyke, M.; Extended Stokes series: laminar flow through a loosely coiled pipe. J. Fluid Mech. 86(1) 129-145

equipment.widget.helical.f_laminar_CollinsDennis(Re, di, Dc)

Calculates friction factor for internal flow of a helical coil in

laminar flow using the method of Collins-Dennis (1975)

\[\frac{f_c}{f_s} = 0.38036 + 0.1028 \sqrt{De}\]

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

ffloat

Friction factor, [-]

References

[33] Collins, W.M., Dennis, S.C.R.; The Steady Motion of a Viscous Fluid in a Curved Tube. Q. J. Mech. Appl. Math. 28(2) (1975) 133-156

equipment.widget.helical.f_laminar_Dean(Re, di, Dc)

Calculates friction factor for internal flow of a helical coil in

laminar flow using the method of Dean (1928)

\[\frac{f_c}{f_s} = 0.38036 + 0.1028 \sqrt{De}\]

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

ffloat

Friction factor, [-]

Notes

Correlation only valid for De < 20

References

[34] Dean, W.R.; The stream-line motion of fluid in a curved pipe (Second paper). London Edinburgh Dublin Phil. Mag. J. Sci. Serie 7 5(30) (1928) 673-695

equipment.widget.helical.f_laminar_Abushammala(Re, di, Dc, p)

Calculates friction factor for internal flow of a helical coil in

laminar flow using the method of Abushammala et al. (2019)

\[f_c = f_s + A B e^{-C}\]

with:

\[A = p_1 D \left(\frac{D}{Re}\right)^{p_2}\]

\[B = \left(\frac{D_c}{2 d_i} + \frac{2 d_i}{D_c}\right)^{p_3}\]

\[C = p_4 D \frac{p}{d_i} \left(\frac{D_c}{2 d_i}\right)^{-p_5}\]

\[D = \left(\left(\frac{D_c}{2 d_i}\right)^{-p6} \left(1 + \left( \frac{p/d_i}{2 \pi D_c/2/d_i}\right)^2\right)\right)^{-p_7}\]

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

pfloat

Pitch for twist of 2π radians (360º), [m]

Returns:

ffloat

Friction factor, [-]

Notes

Correlation only valid for De < 20

References

[35] Abushammala, O., Hreiz, R., Lamaître, C., Favre, E.; Laminar flow friction factor in highly curved helical pipes: Numerical investigation, predictive correlation and experimental validation using a 3D-printed model. Chem. Eng. Sci. 207(7) (2019) 1030-1039

equipment.widget.helical.f_turbulent_Czop(Re, di, Dc)

Calculates friction factor for internal flow of a helical coil in

turbulent flow using the method of Czop (1994).

\[f_c = \frac{0.096}{De^{-0.1517}}\]

The paper give this correlation for single phase flow. Give too correlations for two phase flow.

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

ffloat

Friction factor, [-]

References

[14] Czop, V., Barbier, D., Dong, S.; Pressure drop, void fraction and shear stress measurements in an adiabatic two-phase flow in a coiled tube. Nuclear Eng. Design 149 (1994) 323-333

equipment.widget.helical.f_turbulent_Guo(Re, di, Dc)

Calculates friction factor for internal flow of a helical coil in

turbulent flow using the method of Guo et al. (2001).

\[f_c = 2.552 Re^{-0.15} \left(\frac{d_i}{D_c}\right)^{0.51}\]

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

ffloat

Friction factor, [-]

References

[22] Guo, L., Feng, Z, Chen, X.; An experimental investigation of the frictional pressure drop of steam–water two-phase flow in helical coils. Int. J. Heat Mass Transfer 44(14) (2001): 2601-2610

equipment.widget.helical.f_turbulent_MandalNigam(Re, di, Dc)

Calculates friction factor for internal flow of a helical coil in

turbulent flow using the method of Mandal-Nigam (2009).

\[\frac{f_c}{f_s} = 1 + 0.03{De}^{0.27}\]

Parameters:

Refloat

Reynolds number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

ffloat

Friction factor, [-]

References

[25] Mandal, M. M., Nigam, K.D.P.; Experimental Study on Pressure Drop and Heat Transfer of Turbulent Flow in Tube in Tube Helical Heat Exchanger. Ind. Eng. Chem. Res. 48(20) (2009) 9318-9324

equipment.widget.helical.Nu_Schmidt(Re, Pr, di, Dc)

Calculates Nusselt number for internal flow of a helical coil using the

correlation of Schmidt (1967)

Parameters:

Refloat

Reynolds number, [-]

Prfloat

Prandtl number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

Nufloat

Nusselt number, [-]

References

[3] Schmidt, E.F.; Wärmeübergand und Druckverlust in Rohrschlangen. Chemie Ingenieur Technik 39(13) (1967) 781-789

equipment.widget.helical.Nu_MoriNakayama(Re, Pr, di, Dc, simple=False)

Calculates Nusselt number for internal flow of a helical coil in

laminar flow using the method of Mori-Nakayama (1965).

Parameters:

Refloat

Reynolds number, [-]

Prfloat

Prandtl number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

Nufloat

Nusselt number, [-]

References

[9] Mori, Y., Nakayama, W.; Study on Forced Convective Heat Transfer in Curved Pipes (1st Report, Laminar Region). Int. J. Heat Mass Transfer 8(1) (1965) 67-82

[10] Mori, Y., Nakayama, W.; Study on Forced Convective Heat Transfer in Curved Pipes (2nd Report, Turbulent Region). Int. J. Heat Mass Transfer 10(1) (1967) 37-59

[46] Mori, Y., Nakayama, W.; Study on Forced Convective Heat Transfer in Curved Pipes (3rd Report, Theoretical Analysis under the Condition of Uniform Wall Temperature and Practical Formulae). Int. J. Heat Mass Transfer 10(5) (1967) 681-695

equipment.widget.helical.Nu_XinEbadian(Re, Pr, di, Dc)

Calculates Nusselt number for internal flow of a helical coil using the

correlation of Xin-Ebadian (1997)

For laminar flow:

\[Nu = \left(2.153 + 0.318 \left(Re \frac{d_i}{D_c}\right)^{0.643}\right) Pr^{0.177}\]

For turbulent flow:

\[Nu = 0.00619 Re^{0.92} Pr^{0.4} \left(1 + 3.455 \frac{d_i}{D_c}\right)\]

Parameters:

Refloat

Reynolds number, [-]

Prfloat

Prandtl number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

Nufloat

Nusselt number, [-]

References

[15] Xin, R.C., Ebadian, M.A. ; The Effects of Prandtl Numbers on Local and Average Convective Heat Transfer Characteristics in Helical Pipes. J. Heat Transfer 119(3) (1997) 467-73

equipment.widget.helical.Nu_SebanMcLaughlin(Re, Pr, di, Dc)

Calculates Nusselt number for internal flow of a helical coil using the

correlation of Seban-McLaughlin (1963)

For laminar flow:

\[Nu = 1.04 \left(\frac{Re}{1-\left(1-\left(1-\frac{11.6}{De}\right) ^{0.45}\right)^{1/0.45}}\right)^{1/3} Pr^{1/3}\]

For turbulent flow:

\[Nu = 0.023 Re^{0.85} Pr^{0.4} \left(\frac{d_i}{D_c}\right)^{0.1}\]

Parameters:

Refloat

Reynolds number, [-]

Prfloat

Prandtl number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

Nufloat

Nusselt number, [-]

References

[16] Seban R.A., McLaughlin, E.F.; Heat Transfer in Tube Coils with Laminar and Turbulent Flow. Int. J. Heat Mass Transfer 6() (1963) 387-395

equipment.widget.helical.Nu_Prasad(Re, Pr, di, Dc)

Calculates nusselt number for internal flow of a helical coil using

the method of Prasad et al. (1989).

For laminar flow:

\[Nu = 0.25 \left(\frac{f}{8} Re^2\right)^{1/3} Pr^{1/3}\]

For turbulent flow:

\[Nu = \frac{f}{8} Re\]

Parameters:

Refloat

Reynolds number, [-]

Prfloat

Prandtl number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

Nufloat

Nusselt number, [-]

References

[18] Prasad, B.V.S.S.S., Das, D.H., Prabhaker, A.K.; Pressure Drop, Heat Transfer and Performance of a Helically Coiled Tubular Exchanger. Heat Recovery Systems & CHP 9(3) (1989) 249-256

equipment.widget.helical.Nu_PawarSunnapwar(Re, Pr, di, Dc)

Calculates nusselt number for internal flow at constant heat flux

boundary condition of a helical coil using the method of Pawar-Sunnapwar (2013).

For laminar flow:

\[Nu = 0.02198 Re^{0.9314} Pr^{0.4} \left(\frac{d_i}{D_c}\right)^{0.391}\]

For turbulent flow:

\[Nu = 0.0472 De^{0.8346} Pr^{0.4}\]

Parameters:

Refloat

Reynolds number, [-]

Prfloat

Prandtl number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

Nufloat

Nusselt number, [-]

References

[42] Pawar, S.S., Sunnapwar, V.K.; Studies on convective heat transfer through helical coils. Heat Mass Transfer 49(12) (2013) 1741-1754

[45] Pawar, S.S., Sunnapwar, V.K.; Experimental studies on heat transfer to Newtonian and non-Newtonian fluids in helical coils with laminar and turbulent flow. Exp. Thermal Fluid Sci. 44 (2013) 792-804

equipment.widget.helical.Nu_ElGenkSchriener(Re, Pr, di, Dc, p)

Calculates nusselt number for internal flow of a helical coil using

the method of ElGenk-Schriener (2017).

For fluids with Pr < 15:

\[Nu_c = 3.66 + 0.014 Re_m^{0.86} Pr^{0.4}\]

For fluids with Pr > 15:

\[Nu_c = 3.66 + 0.02 Re_m^{0.7} Pr^{0.4}\]

using a modified Reynolds number:

\[Re_m = Re \left(1+3.4 \delta\right)\]

Parameters:

Refloat

Reynolds number, [-]

Prfloat

Prandtl number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

pfloat

Pitch for twist of 2π radians (360º), [m]

Returns:

Nufloat

Nusselt number, [-]

References

[1] El-Genk, M.S., Timothy, M.S.; A Review and Correlations for Convection Heat Transfer and Pressure Losses in Toroidal and Helically Coiled Tubes. Heat Transfer Eng. 38(5) (2017) 447-474

equipment.widget.helical.Nu_laminar_KalbSeader(Re, Pr, di, Dc)

Calculates nusselt number for internal flow at constant heat flux

boundary condition of a helical coil in laminar flow using the method of Kalb-Seader (1972).

For Pr < 0.05:

\[Nu = 3.31 De^{0.115} Pr^{0.0108}\]

For Pr > 0.7

\[Nu = 0.913 De^{0.476} Pr^{0.2}\]

Parameters:

Refloat

Reynolds number, [-]

Prfloat

Prandtl number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

Nufloat

Nusselt number, [-]

References

[36] Kalb, C.E., Seader, J.D.; Heat and Mass Transfer Phenomena for Viscous Flow in Curved Circular Tubes. Int. J. Heat Mass TRansfer 15() (1972) 801-817

equipment.widget.helical.Nu_laminar_Dravid(Re, Pr, di, Dc)

Calculates nusselt number for internal flow at constant heat flux

boundary condition of a helical coil in laminar flow using the method of Dravid et al. (1971).

\[Nu = \left(0.76 + 0.65 De^{0.5}\right) Pr^{0.175}\]

Parameters:

Refloat

Reynolds number, [-]

Prfloat

Prandtl number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

Nufloat

Nusselt number, [-]

References

[37] Dravid, A.N., Smith, K.A., Merrill, E.W., Brian, P.L.T.; Effect of Secondary Fluid Motion on Laminar Flow Heat Transfer in Helically Coiled Tubes. AIChE J. 17(5) (1971) 1114-1122

equipment.widget.helical.Nu_laminar_JanssenHoogendoorn(Re, Pr, di, Dc, f)

Calculates nusselt number for internal flow at constant heat flux

boundary condition of a helical coil in laminar flow using the method of Janssen-Hoogendoorn (1978).

\[Nu = 0.6166 \left(f Re^2\right)^{0.26} Pr^{1/6}\]

Parameters:

Refloat

Reynolds number, [-]

Prfloat

Prandtl number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

ffloat

Friction factor, [-]

Returns:

Nufloat

Nusselt number, [-]

References

[38] Janssen, L.A.M., Hoogendoorn, C.J.; Laminar Convective Heat Transfer in Helical Coiled Tubes. Int. J. Heat Mass Transfer 21(9) (1978) 1197-1206

equipment.widget.helical.Nu_laminar_ManlapazChurchill(Re, Pr, di, Dc, p)

Calculates nusselt number for internal flow at constant heat flux

boundary condition of a helical coil in laminar flow using the method of Manlapaz-Churchill (1981).

\[Nu = \left(\left(3.657 + \frac{4.343}{\left(1+\frac{957}{Pr He^2} \right)^2}\right)^3 + 1.158 \left(\frac{He}{1+\frac{0.477}{Pr}}\right) ^{1.5}\right)^{1/3}\]

Parameters:

Refloat

Reynolds number, [-]

Prfloat

Prandtl number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

pfloat, optional

Pitch for twist of 2π radians (360º), [m]

Returns:

Nufloat

Nusselt number, [-]

References

[39] Manlapaz, R.L., Churchill, S.W.; Fully Developed Laminar Convection From a Helical Coil. Chem. Eng. Commun. 9 (1981) 185-200

equipment.widget.helical.Nu_laminar_Salimpour(Re, Pr, di, Dc, p)

Calculates nusselt number for internal flow at constant heat flux

boundary condition of a helical coil in laminar flow using the method of Salimpour (2009).

\[Nu = 0.152De^{0.431}Pr^{1.06}\left(\frac{b}{2 \pi D_c}\right)^{-0.277}\]

Parameters:

Refloat

Reynolds number, [-]

Prfloat

Prandtl number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

pfloat, optional

Pitch for twist of 2π radians (360º), [m]

Returns:

Nufloat

Nusselt number, [-]

References

[40] Salimpour, M.R.; Heat transfer coefficients of shell and coiled tube heat exchangers. Exp. Thermal Fluid Sci. 33(2) (2009) 203-207

equipment.widget.helical.Nu_laminar_PimentaCampos(Re, Pr, di, Dc)

Calculates nusselt number for internal flow at constant heat flux

boundary condition of a helical coil in laminar flow using the method of Pimenta-Campos (2013).

\[Nu = \left(0.5 De^{0.481} - 0.465\right) Pr^{0.367}\]

Parameters:

Refloat

Reynolds number, [-]

Prfloat

Prandtl number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

Nufloat

Nusselt number, [-]

References

[41] Pimenta, T.A., Campos, J.B.L.M.; Heat transfer coefficients from Newtonian and non-Newtonian fluids flowing in laminar regime in a helical coil. Int. J. Heat Mass Transfer 58 (2013) 676-690

equipment.widget.helical.Nu_laminar_Hardik(Re, Pr, di, Dc)

Calculates nusselt number for internal flow at constant heat flux

boundary condition of a helical coil in laminar flow using the method of Hardik et al. (2015).

\[Nu = 0.0456 Re^{0.8} Pr^{0.4} \left(\frac{d_i}{D_c}\right)^{0.16}\]

Parameters:

Refloat

Reynolds number, [-]

Prfloat

Prandtl number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

Nufloat

Nusselt number, [-]

References

[43] Hardik, B.K., Baburajan, P.K., Prabhu, S.V.; Local heat transfer coefficient in helical coils with single phase flow. Int. J. Heat Mass Transf. 89 (2015) 522-538

equipment.widget.helical.Nu_turbulent_MandalNigam(Re, Pr, di, Dc)

Calculates nusselt number for internal flow of a helical coil in

turbulent flow using the method of Mandal-Nigam (2009).

\[Nu = 0.55 De^{0.637} Pr^{0.4}\]

Parameters:

Refloat

Reynolds number, [-]

Prfloat

Prandtl number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

Nufloat

Nusselt number, [-]

References

[25] Mandal, M. M., Nigam, K.D.P.; Experimental Study on Pressure Drop and Heat Transfer of Turbulent Flow in Tube in Tube Helical Heat Exchanger. Ind. Eng. Chem. Res. 48(20) (2009) 9318-9324

equipment.widget.helical.Nu_turbulent_RogersMayhew(Re, Pr, di, Dc)

Calculates nusselt number for internal flow of a helical coil in

turbulent flow using the method of Rogers-Mayhew (1964).

\[Nu = 0.023 Re^{0.85} Pr^{0.4} \left(\frac{d_i}{D_c}\right)^{0.1}\]

Parameters:

Refloat

Reynolds number, [-]

Prfloat

Prandtl number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

Nufloat

Nusselt number, [-]

References

[44] Rogers, G.F.C., Mayhew, Y.R.; Heat Transfer and Pressure Loss in Helically Coiled Tubes with Turbulent Flow. Int. J. Heat Mass Transfer 7(11) (1964) 1207-1216

equipment.widget.helical.Nu_turbulent_Shchukin(Re, Pr, di, Dc)

Calculates nusselt number for internal flow of a helical coil in

turbulent flow using the method of Shchukin (1969) as show in [1]

For math:Re (d_i/D_c)^2 < 20

\[Nu = 0.0316 Re^{0.8} Pr^{0.4} \left(\frac{d_i}{D_c}\right)^{0.05}\]

For math:Re (d_i/D_c)^2 > 20

\[Nu = 0.0266 Re^{0.85} Pr^{0.4} \left(\frac{d_i}{D_c}\right)^{0.15}\]

Parameters:

Refloat

Reynolds number, [-]

Prfloat

Prandtl number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

Nufloat

Nusselt number, [-]

References

[44] Rogers, G.F.C., Mayhew, Y.R.; Heat Transfer and Pressure Loss in Helically Coiled Tubes with Turbulent Flow. Int. J. Heat Mass Transfer 7(11) (1964) 1207-1216

[1] El-Genk, M.S., Timothy, M.S.; A Review and Correlations for Convection Heat Transfer and Pressure Losses in Toroidal and Helically Coiled Tubes. Heat Transfer Eng. 38(5) (2017) 447-474

equipment.widget.helical.Nu_turbulent_Guo(Re, Pr)

Calculates nusselt number for internal flow of a helical coil in

turbulent flow using the method of Guo (1998).

\[Nu = 0.023 Re^{0.58} Pr^{0.4}\]

This correlation don’t include any helical coil geometrical parameters dependence.

Parameters:

Refloat

Reynolds number, [-]

Prfloat

Prandtl number, [-]

Returns:

Nufloat

Nusselt number, [-]

References

[48] Guo, L., Chen, X., Feng, Z., Bai, B.; Transie:nt convective heat transfer in a helical coiled tube with pulsatile fully developed turbulent flow. Int. J. Heat Mass Transfer 41() (1998) 2867-2875

equipment.widget.helical.Nu_turbulent_Jayakumar(Re, Pr, di, Dc)

Calculates nusselt number for internal flow of a helical coil in

turbulent flow using the method of Jayakumar et al. (2008)

\[Nu = 0.025 De^{0.9112} Pr^{0.4}\]

Parameters:

Refloat

Reynolds number, [-]

Prfloat

Prandtl number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

Nufloat

Nusselt number, [-]

References

[50] Jayakumar, J.S., Mahajani, S.M., Mandal, J.C., Vijayan, P.K., Bhoi, R.; Experimental and CFD estimation of heat transfer in helically coiled heat exchangers. Chem. Eng. Res. Design 86(3) (2008) 221-232

equipment.widget.helical.Nu_turbulent_Yildiz(Re, Pr, di, Dc)

Calculates nusselt number for internal flow of a helical coil in

turbulent flow using the method of Yildiz et al. (1997)

\[Nu = 0.0551 De^{0.864} Pr^{0.4}\]

Parameters:

Refloat

Reynolds number, [-]

Prfloat

Prandtl number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

Nufloat

Nusselt number, [-]

References

[51] Yildiz, C., Biçer, Y., Pehlivan, D.; Heat Transfer and Pressure Drop in a Heat Exchanger with a Helical Pipe Containing Inside Springs. Energy Convers. Management 38(6) (1997) 619-624

equipment.widget.helical.Nu_turbulent_Wu(Re, Pr, di, Dc)

Calculates nusselt number for internal flow of a helical coil in

turbulent flow using the method of Wu et al. (2025)

\[Nu = 0.023 Re^{0.759} Pr^{0.4} \left(\frac{d_i}{D_c}\right)^{-0.079}\]

Parameters:

Refloat

Reynolds number, [-]

Prfloat

Prandtl number, [-]

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

Returns:

Nufloat

Nusselt number, [-]

References

[52] Wu, Z., Li, K., Zhang, K., Tian, W.; Single-phase flow heat transfer characteristics in helical coils with large coil diameters. Appl. Thermal Eng. 266 (2025) 125776

class equipment.widget.helical.Helical(**kwargs)

Bases: CallableEntity

Helical coil tube used as anhancing heat transfer equipment.

Parameters:

difloat

Inner diameter of the pipe, [m]

Dcfloat

Diameter of the helix, [m]

pfloat, optional

Pitch for twist of 2π radians (360º), [m]

MoriSimpleboolean, optional

Use Simple correlation for Mori-Nakayama nusselt number correlation

Attributes:

ReCritical

Calculate critical Reynolds number to define transition of regimen

isCalculable

Check if all input are defined

Methods

Nu(Re, Pr)	Calculate nusselt number
calculo()	Definition of twisted tape inserts for annuli sections
f(Re)	Calculate friction factor

inputChanged
valueChanged

TEXT_REYNOLDS_CRITICAL = ('Ito (1959)', 'Schmidt (1967)', 'Kubair-Kuloor (1966)', 'Srinivasan (1968)', 'Kutateladze (1966)', 'Seth-Stahel (1969)', 'Cioncolini-Santini (2006)')

TEXT_LAMINAR_FRICTION = ('Schmidt (1967)', 'White (1929)', 'Mori-Nakayama (1965)', 'Hart (1988)', 'Ju (2001)', 'Mishra-Gupta (1979)', 'Manlapaz-Churchill (1980)', 'Prasad (1989)', 'Liu-Masliyah (1993)', 'Ali (2001)', 'Ito (1969)', 'Tarbell-Samuels (1973)', 'Pimenta-Campos (2012)', 'Adler (1934)', 'Barua (1963)', 'Yanase (1989)', 'Dennis (1980)', 'van Dyke (1978)', 'Collins-Dennis (1975)', 'Dean (1928)', 'Abushammala (2019)', 'ElGenk-Schriener (2017)', 'Srinivasan (1968)')

TEXT_TURBULENT_FRICTION = ('Schmidt (1967)', 'Mori-Nakayama (1965)', 'Ju (2001)', 'Mishra-Gupta (1979)', 'Czop (1994)', 'Prasad (1989)', 'Ali (2001)', 'Guo (2001)', 'Mandal-Nigam (2009)', 'ElGenk-Schriener (2017)', 'Srinivasan (1968)', 'Ito (1959)')

TEXT_LAMINAR_HEAT = ('Schmidt (1967)', 'Xin-Ebadian (1997)', 'Mori-Nakayama (1965)', 'Seban-McLaughlin (1963)', 'Prasad (1989)', 'Kalb-Seader (1972)', 'Dravid (1971)', 'Janssen-Hoogendoorn (1978)', 'Manlapaz-Churchill (1981)', 'Salimpour (2009)', 'Pimenta-Campos (2013)', 'Pawar-Sunnapwar (2013)', 'Hardik (2015)', 'ElGenk-Schriener (2017)')

TEXT_TURBULENT_HEAT = ('Schmidt (1967)', 'Xin-Ebadian (1997)', 'Mori-Nakayama (1965)', 'Seban-McLaughlin (1963)', 'Prasad (1989)', 'Mandal-Nigam (2009)', 'Rogers-Mayhew (1964)', 'Pawar-Sunnapwar (2013)', 'ElGenk-Schriener (2017)', 'Shchukin (1969)', 'Guo (1998)', 'Jayakumar (2008)', 'Yildiz (1997)', 'Wu (2025)')

status = 0

msg = ''

kw = {'Dc': 0, 'MoriSimple': False, 'di': 0, 'methodFrictionLaminar': 0, 'methodFrictionTurbulent': 0, 'methodHeatLaminar': 0, 'methodHeatTurbulent': 0, 'methodReCritic': 0, 'p': 0}

valueChanged

pyqtSignal(*types, name: str = …, revision: int = …, arguments: Sequence = …) -> PYQT_SIGNAL

types is normally a sequence of individual types. Each type is either a type object or a string that is the name of a C++ type. Alternatively each type could itself be a sequence of types each describing a different overloaded signal. name is the optional C++ name of the signal. If it is not specified then the name of the class attribute that is bound to the signal is used. revision is the optional revision of the signal that is exported to QML. If it is not specified then 0 is used. arguments is the optional sequence of the names of the signal’s arguments.

inputChanged

pyqtSignal(*types, name: str = …, revision: int = …, arguments: Sequence = …) -> PYQT_SIGNAL

types is normally a sequence of individual types. Each type is either a type object or a string that is the name of a C++ type. Alternatively each type could itself be a sequence of types each describing a different overloaded signal. name is the optional C++ name of the signal. If it is not specified then the name of the class attribute that is bound to the signal is used. revision is the optional revision of the signal that is exported to QML. If it is not specified then 0 is used. arguments is the optional sequence of the names of the signal’s arguments.

property isCalculable

Check if all input are defined

calculo()

Definition of twisted tape inserts for annuli sections

property ReCritical

Calculate critical Reynolds number to define transition of regimen flow from laminar to turbulent

Nu(Re, Pr)

Calculate nusselt number

f(Re)

Calculate friction factor

class equipment.widget.helical.UI_Helical(parent=None)

Bases: ToolGui

Helical coil dialog

Methods

loadUI()	Add widget
setVisibleMod()	Enable widget with special parameters for selected method

title = 'Use helical coil'

loadUI()

Add widget

setVisibleMod()

Enable widget with special parameters for selected method

class equipment.widget.helical.Dialog(parent=None)

Bases: QDialog

Component list config dialog

__init__(parent=None)

References

[1] (1,2,3,4,5,6)

El-Genk, M.S., Timothy, M.S.; A Review and Correlations for Convection Heat Transfer and Pressure Losses in Toroidal and Helically Coiled Tubes. Heat Transfer Eng. 38(5) (2017) 447-474

[2] (1,2,3,4)

; Perry’s Chemical Engineers’ Handbook 9th Edition. McGraw-Hill (2019)

[3] (1,2,3)

Schmidt, E.F.; Wärmeübergand und Druckverlust in Rohrschlangen. Chemie Ingenieur Technik 39(13) (1967) 781-789

[4] (1,2)

Ito, H.; Friction Factors for Turbulent Flow in Curved Pipes. J. Basic Eng. 81 (1959) 123-134

[5]

Kubair, V., Kuloor, N.R.; Heat Transfer to Newtonian Fluids in Coiled Pipes in Laminar Flow. Int. J. Heat Mass Transfer 9 (1966) 63-75

[6] (1,2)

Srinivasan, P.S., Nandapurkar, S.S., Holland, F.A.; Pressure Drop and Heat Transfer in Coils. Chem. Eng. 218 (1968) 113-119

[7]

Kutateladze, S.S., Borishanskii, V.M. ; A Concise Encyclopedia of Heat Transfer. Pergamon Press (1966)

[8]

White, C.M.; Streamline Flow through Curved Pipes. Proc. R .Soc. London A 123 (1929) 645-663

[9] (1,2)

Mori, Y., Nakayama, W.; Study on Forced Convective Heat Transfer in Curved Pipes (1st Report, Laminar Region). Int. J. Heat Mass Transfer 8(1) (1965) 67-82

[10] (1,2)

Mori, Y., Nakayama, W.; Study on Forced Convective Heat Transfer in Curved Pipes (2nd Report, Turbulent Region). Int. J. Heat Mass Transfer 10(1) (1967) 37-59

[11]

Hart, J., Ellenberger, J., Hamersma, P.J.; Single- and Two-Phase Flow Through Helically Coiled Tubes. Chem. Eng. Sci. 43(4) (1988) 775-783

[12]

Ju, H., Huang, Z., Xu, Y., Duan, B, Yu, Y.; Hydraulic Performance of Small Bending Radius Helical Coil-Pipe. J. Nuclear Sci. Eng. 38(10) (2001) 826-831

[13]

Mishra, P., Gupta, S.N.; Momentum Transfer in Curved Pipes. 1. Newtonian Fluids. Ind. Eng. Chem. Process Des. Dev. 18(1) (1979) 130-137

[14]

Czop, V., Barbier, D., Dong, S.; Pressure drop, void fraction and shear stress measurements in an adiabatic two-phase flow in a coiled tube. Nuclear Eng. Design 149 (1994) 323-333

[15]

Xin, R.C., Ebadian, M.A. ; The Effects of Prandtl Numbers on Local and Average Convective Heat Transfer Characteristics in Helical Pipes. J. Heat Transfer 119(3) (1997) 467-73

[16]

Seban R.A., McLaughlin, E.F.; Heat Transfer in Tube Coils with Laminar and Turbulent Flow. Int. J. Heat Mass Transfer 6() (1963) 387-395

[17]

Manlapaz, R.L., Churchill, S.W.; Fully Developed Laminar Flow in a Helically Coiled Tube of Finite Pitch. Chem. Eng. Communications 7 (1980) 57-78

[18] (1,2)

Prasad, B.V.S.S.S., Das, D.H., Prabhaker, A.K.; Pressure Drop, Heat Transfer and Performance of a Helically Coiled Tubular Exchanger. Heat Recovery Systems & CHP 9(3) (1989) 249-256

[19]

Liu, S., Masliyah, J.H.; Axially invariant laminar flow in helical pipes with a finite pitch. J. Fluid Mech. 251 (1993) 315-353

[20]

Seth, K.K., Stahel, E.P.; Heat Transfer from Helical Coils Immersed in Agitated Vessels. Ind. Eng. Chem. 61(6) (1969) 39-49

[21]

Ali, S.; Pressure drop correlations for flow through regular helical coil tubes. Fluid Dyn. Research 28 (2001) 295-310

[22]

Guo, L., Feng, Z, Chen, X.; An experimental investigation of the frictional pressure drop of steam–water two-phase flow in helical coils. Int. J. Heat Mass Transfer 44(14) (2001): 2601-2610

[23]

Ito, H.; Laminar Flow in Curved Pipes. Z. Angew. Math. Mech. 11 (1969) 653-663

[24]

Tarbell, J.M., Samuels, M.R.; Momentum and Heat Transfer in Helical Coils. Chem. Eng. J. 5(2) (1973) 117-127

[25] (1,2)

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