lib.heatTransfer module

lib.heatTransfer.Nu_vertical_Churchill(Pr, Ra)

Calculates Nusselt number for laminar and turbulent flows near a

vertical surface with Churchill-Chu correlation [3]

\[Nu^{1/2} = 0.825 + \frac{0.387 Ra^{1/6}} {\left(1+(0.492/Pr)^{9/16}\right)^{8/27}}\]

For laminar flow (Ra ≤ 10⁹) use this correlation with a slightly better accuracy

\[Nu = 0.68 + \frac{0.67 Ra^{1/4}} {\left(1+(0.492/Pr)^{9/16}\right)^{4/9}}\]

The correlation originally developed for vertical flat surfaces can be too applied to vertical cylinders if this conditions is satisfied:

\[\frac{D}{L} \ge \frac{35}{Gr_L^{1/4}}\]

Parameters:

Prfloat

Prandtl number [-]

Rafloat

Rayleigh number [-]

Returns:

Nufloat

Nusselt number, [-]

Notes

This method does not exactly represent the behavior in the transition zone between laminar and turbulent flows (10⁸ ≤ Ra ≤ 20⁹), but its accuracy is enought for engineering applications in the entire range of Rayleigh numbers.

References

[1] VDI-Gesellschaft; VDI Heat Atlas 2nd Edition. Berlin, New York. Springer 2010.

[2] Bergman, T.L., Lavine, A.S., Incropera, F.P., DeWitt, D.P.; Introduction to Heat Transfer. 6th Ed.. Wiley, 2011.

[3] Churchill, S.W., Chu, H.H.S.; Correlating Equations for Laminar and Turbulent Free Convection from a Vertical Plate. Int. J. Heat Mass Transfer 18(11) (1975) 1323-29

Examples

From [1], Example 1, pag. 667

>>> print("%0.f" % Nu_vertical_Churchill(0.7, 9.26e8))
120

From [2], Example 9.2, pag. 574:

>>> print("%0.f" % Nu_vertical_Churchill(0.69, 1.813E9))
147

lib.heatTransfer.h_tubeside_laminar_Eubank_Proctor(Gz, Gr, Pr, D, L)

Coeficiente de transferencia de calor por calor sensible en el interior de tubos horizontales en regimen laminar Eubank, D. C. and Proctor W. S. - Effect of natural convection on heat transfer with laminar flow in tubes, MS Thesis, Chemical Engineering Department, Massachusetts Institute of Technology, 1951.

lib.heatTransfer.h_tubeside_laminar_VDI(Re, Pr, D, L)

Coeficiente de transferencia de calor por calor sensible en el interior de tubos horizontales en regimen laminar VDI Heat Atlas G1 Pag 695

lib.heatTransfer.h_tubeside_laminar_Hausen(Gz)

Coeficiente de transferencia de calor por calor sensible en el interior de tubos horizontales en regimen laminar Perry Capitulo 5 pag 15 0.1<Gz<1e4

lib.heatTransfer.h_tubeside_laminar_Sieder_Tate(Gz, Gr)

Coeficiente de transferencia de calor por calor sensible en el interior de tubos horizontales en regimen laminar Sieder and Tate - Heat Transfer and Pressure Drop of Liquids in Tubes, Industrial Engineering Chemistry, Vol. 28, p. 1429, 1936. Perry Capitulo 5 pag 15 Gz>100

lib.heatTransfer.h_tubeside_turbulent_Sieder_Tate(Re, Pr)

Coeficiente de transferencia de calor por calor sensible en el interior de tubos horizontales en regimen turbulento Sieder and Tate - Heat Transfer and Pressure Drop of Liquids in Tubes, Industrial Engineering Chemistry, Vol. 28, p. 1429, 1936. Re>10000 0.7<Pr<16700 L/D > 10

lib.heatTransfer.h_tubeside_turbulent_Colburn(Re, Pr)

Coeficiente de transferencia de calor por calor sensible en el interior de tubos horizontales en regimen turbulento DeltaT pequeña Re>10000 0.7<Pr<160 L/D > 10

lib.heatTransfer.h_tubeside_turbulent_Dittus_Boelter(Re, Pr, calentamiento)

Coeficiente de transferencia de calor por calor sensible en el interior de tubos horizontales en regimen turbulento DeltaT pequeña Re>10000 0.7<Pr<160 L/D > 10

lib.heatTransfer.h_tubeside_turbulent_ESDU(Re, Pr)

Coeficiente de transferencia de calor por calor sensible en el interior de tubos horizontales en regimen turbulento 40000<Re<1e6 0.3<Pr<300 L/D>60

lib.heatTransfer.h_tubeside_turbulent_Gnielinski(Re, Pr, D, L)

Coeficiente de transferencia de calor por calor sensible en el interior de tubos horizontales en regimen turbulento y de transición 3000<Re<5e6 0.5<Pr<2000 Serth - Process heat transfer_ principles and applications pag 63

lib.heatTransfer.h_tubeside_turbulent_VDI(Re, Pr, filas_tubos, alineados)

Coeficiente de transferencia de calor por calor sensible en el interior de tubos horizontales en regimen turbulento Re>10 Pr<600 alineados: indica si los tubos estan colocados en linea filas_tubos: numeros de filas de tubos

lib.heatTransfer.Nu_anulli_Turbulent_Gnielinski(Re, Pr, di, do, L=None, boundary=0, Prw=None)

Calculate Nusselt number for a annuli section in turbulent flow using

the Gnielinski correlation (2009).

Parameters:

Refloat

Reynolds number, [-]

Prfloat

Prandtl number, [-]

difloat

Internal diameter of annuli, [m]

dofloat

External diameter of annuli, [m]

Lfloat, optional

Length of heated pipe, [m]

boundaryinteger

integet to set kind of boundary limit:

0 - Inner surface heated 1 - Outer surface heated 2 - Both surfaces heated

Prwfloat, optional

Prandtl number at wall temperature, [-]

The normal use on geat transfer is using the fluid in internal pipe as

heating/cooling medium so using boundary condition 0

Length of pipe is a optional parameters to calculate effect of developing

flow at entrance

Prw is a optional parameter to calculate efect of variable properties by

diameter of pipe.

Returns:

Nufloat

Nusselt number, [-]

References

[7] Gnielinski, V.; Heat Transfer Coeffients for Turbulent Flow in ConcentricAnnular Ducts. Heat Transfer Eng. 30(6) (2009) 431-436

[8] Stephan, K.; Wärmeübergang bei turbulenter und bei laminarer Strömung in Ringspalten. Chem. Ing. Techn. 34(3) (1962) 207-212

[1] VDI-Gesellschaft; VDI Heat Atlas 2nd Edition. Berlin, New York. Springer 2010.

Examples

G2-7 from VDI Heat Atlas Pag 705

>>> print("%0.2f" % Nu_anulli_Turbulent_Gnielinski(
... 23041, 15.88, 0.02, 0.04, 10, 0, 8.66))
227.02

# 239.20

>>> print("%0.2f" % (Nu_anulli_Turbulent_Gnielinski(
... 10000, 15.88, 0.02, 0.04, 13, 0, 8.66)))
111.82

# 108.78

lib.heatTransfer.Nu_anulli_Turbulent_Dirker(Re, Pr, di, do, mu=None, muW=None)

Calculate Nusselt number for a annuli section in turbulent flow using

the Dirker and Meyer correlation (2005).

Parameters:

Refloat

Reynolds number, [-]

Prfloat

Prandtl number, [-]

difloat

Internal diameter of annuli, [m]

dofloat

External diameter of annuli, [m]

mufloat

Bulk flow temperature viscosity, [Pa·s]

muWfloat

Wall flow temperature viscosity, [Pa·s]

Returns:

Nufloat

Nusselt number, [-]

References

[9] Dirker, J., Meyer, J.P.; Convective Heat Transfer Coefficients in Concentric Annuli. Heat Transfer Eng. 26(2) (2005) 38-44

lib.heatTransfer.Nu_anulli_Turbulent_Stein(Re, Pr, di, do)

Calculate Nusselt number for a annuli section in turbulent flow using

the Stein and Begell correlation (1958).

Correlation based only in water data, valid for Re > 30000

Parameters:

Refloat

Reynolds number, [-]

Prfloat

Prandtl number, [-]

difloat

Internal diameter of annuli, [m]

dofloat

External diameter of annuli, [m]

Returns:

Nufloat

Nusselt number, [-]

References

[10] Stein, R.P., Begell, W.; Heat Transfer to Water in Turbulent Flow in Internally Heated Annuli. AIChE Journal 4(2) (1958) 127-131

lib.heatTransfer.Nu_anulli_Turbulent_Crookston(Re, Pr, di, do)

Calculate Nusselt number for a annuli section in turbulent flow using

the Crookston-Rothfus-Kermode correlation (1968).

Correlation based only in water data, valid for Re > 17000

Parameters:

Refloat

Reynolds number, [-]

Prfloat

Prandtl number, [-]

difloat

Internal diameter of annuli, [m]

dofloat

External diameter of annuli, [m]

Returns:

Nufloat

Nusselt number, [-]

References

[11] Crookston, R.B., Rothfus, R.R., Kermode, R.I.; Turbulent Heat Transfer in Annuli with Small Cores. Int. J. Heat Mass Transfer 11(3) (1968) 415-426

lib.heatTransfer.Nu_anulli_Laminar(Re, Pr, di, do, L=0, boundary=0, Prw=None)

Calculate Nusselt number for a annuli section in laminar flow

References

[1] VDI-Gesellschaft; VDI Heat Atlas 2nd Edition. Berlin, New York. Springer 2010.

lib.heatTransfer.Nu_anulli_Transition(Re, Pr, di, do, method, **kw)

Calculate Nusselt number for a annuli section in turbulent flow

References

[1] VDI-Gesellschaft; VDI Heat Atlas 2nd Edition. Berlin, New York. Springer 2010.

lib.heatTransfer.Nu_anulli(Re, Pr, di, do, method=0, **kw)

Calculate Nusselt number for a annuli section

lib.heatTransfer.Nu_Convection_Free_External_Horizontal_Plate(Pr, Ra)

Calculo del Nusselt en convección natural externa de una pared horizontal

lib.heatTransfer.h_tube_Condensation_Akers(fluid, Di)

ref Pag 557 Kakac: Boiler…

lib.heatTransfer.h_tube_Condensation_Cavallini(fluid, Di)

ref Pag 557 Kakac: Boiler…

lib.heatTransfer.h_tube_Condensation_Boyko(fluid, Di)

ref Pag 557 Kakac: Boiler…

lib.heatTransfer.h_tube_Condensation_Shah(fluid, Di)

ref Pag 557 Kakac: Boiler…

lib.heatTransfer.h_tube_Condensation_Kosky(fluid, Di)

ref Pag 558 Kakac: Boiler…

lib.heatTransfer.h_tube_Condensation_Traviss(fluid, Di, X)

ref Pag 558 Kakac: Boiler…

lib.heatTransfer.effectiveness(NTU, Cr, flux, mixed='Cmin', exact='True')

Calculate heat exchanger efectiveness

Parameters:

NTUfloat

Number of transfer units, [-]

Crfloat

Heat capacity rates ratio, Cmin/Cmax, in 0-1 range, [-]

fluxstr

The flux type of heat exchanger

mixedstr, optional

Mixed stream definition only necessary for CrFSMix model, Cmin or Cmax

exactboolean, optional

Use the exact recursion solutión

Returns:

effectivenessfloat

Thermal effectiveness of heat exchanger, [-]

Notes

Flujo vendra definido por su acronimo

CF: Counter flow PF: Parallel flow CrFMix: Crossflow, both fluids mixed CrFSMix: Crossflow, one fluid mixed, other unmixed CrFunMix: Crossflow, both fluids unmixed 1-2TEMAE: 1-2 pass shell and tube exchanger

Notes

Flux would be the key code of exchanger:

• CF: Counter flow

• PF: Parallel flow

• CrFMix: Crossflow, both fluids mixed

• CrFSMix: Crossflow, one fluid mixed, other unmixed

• CrFunMix: Crossflow, both fluids unmixed

• 1-2TEMAE: 1-2 pass shell and tube exchanger

In case CrFunMix is possible calculate the exact recursion solution or the approximate correlation from Triboix [5]

References

[2] Bergman, T.L., Lavine, A.S., Incropera, F.P., DeWitt, D.P.; Introduction to Heat Transfer. 6th Ed.. Wiley, 2011.

[4] Shah, R.K., Sekulić, D.P.; Fundamentals of Heat Exchanger Design. John Wiley & Sons

[5] Triboix, A.; Exact and approximate formulas for cross flow heat exchangers with unmixed fluids. Int. Comm. Heat Mass Transfer 36(2) (2009)

lib.heatTransfer.TemperatureEffectiveness(NTU, R, flux, **kwargs)

Calculo de la temperatura efectividad del cambiador Flujo vendra definido por su acronimo

CF: Counter flow PF: Parallel flow CrFMix: Crossflow, both fluids mixed CrFSMix: Crossflow, one fluid mixed, other unmixed CrFunMix: Crossflow, both fluids unmixed 1-2TEMAE: 1-2 TEMA E 1-2TEMAE2: 1-2 TEMA E, shell fluid flow divided 1-3TEMAE: 1-3 TEMA E 1-4TEMAE: 1-4 TEMA E 1-1TEMAG: 1-1 TEMA G 1-2TEMAG: 1-2 TEMA G 1-1TEMAH: 1-1 TEMA H 1-2TEMAH: 1-2 TEMA H 1-1TEMAJ: 1-1 TEMA J 1-2TEMAJ: 1-2 TEMA J 1-4TEMAJ: 1-4 TEMA J

kwargs: Opciones adicionales:

mixed: corriente mezclada para CrFSMix

1, 2

lib.heatTransfer.CorrectionFactor(P, R, flux, **kwargs)

Calculo de la factor de correccion Flujo vendra definido por su acronimo

CF: Counter flow PF: Parallel flow CrFMix: Crossflow, both fluids mixed CrFSMix: Crossflow, one fluid mixed, other unmixed CrFunMix: Crossflow, both fluids unmixed 1-2TEMAE: 1-2 pass shell and tube exchanger

kwargs: Opciones adicionales:

mixed: corriente mezclada para CrFSMix

Cmin, Cmax

lib.heatTransfer.NTU_fPR(P, R, flux, **kwargs)

Calculo de la factor de correccion Flujo vendra definido por su acronimo

CF: Counter flow PF: Parallel flow CrFMix: Crossflow, both fluids mixed CrFSMix: Crossflow, one fluid mixed, other unmixed CrFunMix: Crossflow, both fluids unmixed 1-2TEMAE: 1-2 pass shell and tube exchanger

kwargs: Opciones adicionales:

mixed: corriente mezclada para CrFSMix

Cmin, Cmax

lib.heatTransfer.Fi(P, R, flux, **kwargs)

References

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

VDI-Gesellschaft; VDI Heat Atlas 2nd Edition. Berlin, New York. Springer 2010.

[2] (1,2,3)

Bergman, T.L., Lavine, A.S., Incropera, F.P., DeWitt, D.P.; Introduction to Heat Transfer. 6th Ed.. Wiley, 2011.

[3] (1,2)

Churchill, S.W., Chu, H.H.S.; Correlating Equations for Laminar and Turbulent Free Convection from a Vertical Plate. Int. J. Heat Mass Transfer 18(11) (1975) 1323-29

[4]

Shah, R.K., Sekulić, D.P.; Fundamentals of Heat Exchanger Design. John Wiley & Sons

[5]

Triboix, A.; Exact and approximate formulas for cross flow heat exchangers with unmixed fluids. Int. Comm. Heat Mass Transfer 36(2) (2009)

[6]

Sieder, E.N., Tate, G.E.; Heat Transfer and Pressure Drop of Liquids in Tubes. Ind. & Eng. Chemistry 28(12) (1936) 1929-1935

[7]

Gnielinski, V.; Heat Transfer Coeffients for Turbulent Flow in ConcentricAnnular Ducts. Heat Transfer Eng. 30(6) (2009) 431-436

[8]

Stephan, K.; Wärmeübergang bei turbulenter und bei laminarer Strömung in Ringspalten. Chem. Ing. Techn. 34(3) (1962) 207-212

[9]

Dirker, J., Meyer, J.P.; Convective Heat Transfer Coefficients in Concentric Annuli. Heat Transfer Eng. 26(2) (2005) 38-44

[10]

Stein, R.P., Begell, W.; Heat Transfer to Water in Turbulent Flow in Internally Heated Annuli. AIChE Journal 4(2) (1958) 127-131

[11]

Crookston, R.B., Rothfus, R.R., Kermode, R.I.; Turbulent Heat Transfer in Annuli with Small Cores. Int. J. Heat Mass Transfer 11(3) (1968) 415-426