def Liu_Winterton(m, x, D, rhol, rhog, mul, kl, Cpl, MW, P, Pc, Te):
r'''Calculates heat transfer coefficient for film boiling of saturated
fluid in any orientation of flow. Correlation
is as developed in [1]_, also reviewed in [2]_ and [3]_.
Excess wall temperature is required to use this correlation.
.. math::
h_{tp} = \sqrt{ (F\cdot h_l)^2 + (S\cdot h_{nb})^2}
.. math::
S = \left( 1+0.055F^{0.1} Re_{L}^{0.16}\right)^{-1}
.. math::
h_{l} = 0.023 Re_L^{0.8} Pr_l^{0.4} k_l/D
.. math::
Re_L = \frac{GD}{\mu_l}
.. math::
F = \left[ 1+ xPr_{l}(\rho_l/\rho_g-1)\right]^{0.35}
.. math::
h_{nb} = \left(55\Delta Te^{0.67} \frac{P}{P_c}^{(0.12 - 0.2\log_{10}
R_p)}(-\log_{10} \frac{P}{P_c})^{-0.55} MW^{-0.5}\right)^{1/0.33}
Parameters
----------
m : float
Mass flow rate [kg/s]
x : float
Quality at the specific tube interval []
D : float
Diameter of the tube [m]
rhol : float
Density of the liquid [kg/m^3]
rhog : float
Density of the gas [kg/m^3]
mul : float
Viscosity of liquid [Pa*s]
kl : float
Thermal conductivity of liquid [W/m/K]
Cpl : float
Heat capacity of liquid [J/kg/K]
MW : float
Molecular weight of the fluid, [g/mol]
P : float
Pressure of fluid, [Pa]
Pc : float
Critical pressure of fluid, [Pa]
Te : float, optional
Excess temperature of wall, [K]
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
[1]_ has been reviewed, and is accurately reproduced in [3]_.
Uses the `Cooper` and `turbulent_Dittus_Boelter` correlations.
A correction for horizontal flow at low Froude numbers is available in
[1]_ but has not been implemented and is not recommended in several
sources.
Examples
--------
>>> Liu_Winterton(m=1, x=0.4, D=0.3, rhol=567., rhog=18.09, kl=0.086,
... mul=156E-6, Cpl=2300, P=1E6, Pc=22E6, MW=44.02, Te=7)
4747.749477190532
References
----------
.. [1] Liu, Z., and R. H. S. Winterton. "A General Correlation for
Saturated and Subcooled Flow Boiling in Tubes and Annuli, Based on a
Nucleate Pool Boiling Equation." International Journal of Heat and Mass
Transfer 34, no. 11 (November 1991): 2759-66.
doi:10.1016/0017-9310(91)90234-6.
.. [2] Fang, Xiande, Zhanru Zhou, and Dingkun Li. "Review of Correlations
of Flow Boiling Heat Transfer Coefficients for Carbon Dioxide."
International Journal of Refrigeration 36, no. 8 (December 2013):
2017-39. doi:10.1016/j.ijrefrig.2013.05.015.
.. [3] Bertsch, Stefan S., Eckhard A. Groll, and Suresh V. Garimella.
"Review and Comparative Analysis of Studies on Saturated Flow Boiling in
Small Channels." Nanoscale and Microscale Thermophysical Engineering 12,
no. 3 (September 4, 2008): 187-227. doi:10.1080/15567260802317357.
'''
G = m/(pi/4*D**2)
ReL = D*G/mul
Prl = Prandtl(Cp=Cpl, mu=mul, k=kl)
hl = turbulent_Dittus_Boelter(Re=ReL, Pr=Prl)*kl/D
F = (1 + x*Prl*(rhol/rhog - 1))**0.35
S = (1 + 0.055*F**0.1*ReL**0.16)**-1
# if horizontal:
# Fr = Froude(V=G/rhol, L=D, squared=True)
# if Fr < 0.05:
# ef = Fr**(0.1 - 2*Fr)
# es = Fr**0.5
# F *= ef
# S *= es
h_nb = Cooper(Te=Te, P=P, Pc=Pc, MW=MW)
return ((F*hl)**2 + (S*h_nb)**2)**0.5
def Chen_Edelstein(m, x, D, rhol, rhog, mul, mug, kl, Cpl, Hvap, sigma,
dPsat, Te):
r'''Calculates heat transfer coefficient for film boiling of saturated
fluid in any orientation of flow. Correlation
is developed in [1]_ and [2]_, and reviewed in [3]_. This model is one of
the most often used. It uses the Dittus-Boelter correlation for turbulent
convection and the Forster-Zuber correlation for pool boiling, and
combines them with two factors `F` and `S`.
.. math::
h_{tp} = S\cdot h_{nb} + F \cdot h_{sp,l}
.. math::
h_{sp,l} = 0.023 Re_l^{0.8} Pr_l^{0.4} k_l/D
.. math::
Re_l = \frac{DG(1-x)}{\mu_l}
.. math::
h_{nb} = 0.00122\left( \frac{\lambda_l^{0.79} c_{p,l}^{0.45}
\rho_l^{0.49}}{\sigma^{0.5} \mu^{0.29} H_{vap}^{0.24} \rho_g^{0.24}}
\right)\Delta T_{sat}^{0.24} \Delta p_{sat}^{0.75}
.. math::
F = (1 + X_{tt}^{-0.5})^{1.78}
.. math::
X_{tt} = \left( \frac{1-x}{x}\right)^{0.9} \left(\frac{\rho_g}{\rho_l}
\right)^{0.5}\left( \frac{\mu_l}{\mu_g}\right)^{0.1}
.. math::
S = 0.9622 - 0.5822\left(\tan^{-1}\left(\frac{Re_L\cdot F^{1.25}}
{6.18\cdot 10^4}\right)\right)
Parameters
----------
m : float
Mass flow rate [kg/s]
x : float
Quality at the specific tube interval []
D : float
Diameter of the tube [m]
rhol : float
Density of the liquid [kg/m^3]
rhog : float
Density of the gas [kg/m^3]
mul : float
Viscosity of liquid [Pa*s]
mug : float
Viscosity of gas [Pa*s]
kl : float
Thermal conductivity of liquid [W/m/K]
Cpl : float
Heat capacity of liquid [J/kg/K]
Hvap : float
Heat of vaporization of liquid [J/kg]
sigma : float
Surface tension of liquid [N/m]
dPsat : float
Difference in Saturation pressure of fluid at Te and T, [Pa]
Te : float
Excess temperature of wall, [K]
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
[1]_ and [2]_ have been reviewed, but the model is only put together in
the review of [3]_. Many other forms of this equation exist with different
functions for `F` and `S`.
Examples
--------
>>> Chen_Edelstein(m=0.106, x=0.2, D=0.0212, rhol=567, rhog=18.09,
... mul=156E-6, mug=7.11E-6, kl=0.086, Cpl=2730, Hvap=2E5, sigma=0.02,
... dPsat=1E5, Te=3)
3289.058731974052
See Also
--------
turbulent_Dittus_Boelter
Forster_Zuber
References
----------
.. [1] Chen, J. C. "Correlation for Boiling Heat Transfer to Saturated
Fluids in Convective Flow." Industrial & Engineering Chemistry Process
Design and Development 5, no. 3 (July 1, 1966): 322-29.
doi:10.1021/i260019a023.
.. [2] Edelstein, Sergio, A. J. Pérez, and J. C. Chen. "Analytic
Representation of Convective Boiling Functions." AIChE Journal 30, no.
5 (September 1, 1984): 840-41. doi:10.1002/aic.690300528.
.. [3] Bertsch, Stefan S., Eckhard A. Groll, and Suresh V. Garimella.
"Review and Comparative Analysis of Studies on Saturated Flow Boiling in
Small Channels." Nanoscale and Microscale Thermophysical Engineering 12,
no. 3 (September 4, 2008): 187-227. doi:10.1080/15567260802317357.
'''
G = m/(pi/4*D**2)
Rel = D*G*(1-x)/mul
Prl = Prandtl(Cp=Cpl, mu=mul, k=kl)
hl = turbulent_Dittus_Boelter(Re=Rel, Pr=Prl)*kl/D
Xtt = Lockhart_Martinelli_Xtt(x=x, rhol=rhol, rhog=rhog, mul=mul, mug=mug)
F = (1 + Xtt**-0.5)**1.78
Re = Rel*F**1.25
S = 0.9622 - 0.5822*atan(Re/6.18E4)
hnb = Forster_Zuber(Te=Te, dPsat=dPsat, Cpl=Cpl, kl=kl, mul=mul, sigma=sigma,
Hvap=Hvap, rhol=rhol, rhog=rhog)
return hnb*S + hl*F
def Chen_Bennett(m, x, D, rhol, rhog, mul, mug, kl, Cpl, Hvap, sigma,
dPsat, Te):
r'''Calculates heat transfer coefficient for film boiling of saturated
fluid in any orientation of flow. Correlation
is developed in [1]_ and [2]_, and reviewed in [3]_. This model is one of
the most often used, and replaces the `Chen_Edelstein` correlation. It uses
the Dittus-Boelter correlation for turbulent convection and the
Forster-Zuber correlation for pool boiling, and combines them with two
factors `F` and `S`.
.. math::
h_{tp} = S\cdot h_{nb} + F \cdot h_{sp,l}
.. math::
h_{sp,l} = 0.023 Re_l^{0.8} Pr_l^{0.4} k_l/D
.. math::
Re_l = \frac{DG(1-x)}{\mu_l}
.. math::
h_{nb} = 0.00122\left( \frac{\lambda_l^{0.79} c_{p,l}^{0.45}
\rho_l^{0.49}}{\sigma^{0.5} \mu^{0.29} H_{vap}^{0.24} \rho_g^{0.24}}
\right)\Delta T_{sat}^{0.24} \Delta p_{sat}^{0.75}
.. math::
F = \left(\frac{Pr_1+1}{2}\right)^{0.444}\cdot (1+X_{tt}^{-0.5})^{1.78}
.. math::
S = \frac{1-\exp(-F\cdot h_{conv} \cdot X_0/k_l)}
{F\cdot h_{conv}\cdot X_0/k_l}
.. math::
X_{tt} = \left( \frac{1-x}{x}\right)^{0.9} \left(\frac{\rho_g}{\rho_l}
\right)^{0.5}\left( \frac{\mu_l}{\mu_g}\right)^{0.1}
.. math::
X_0 = 0.041 \left(\frac{\sigma}{g \cdot (\rho_l-\rho_v)}\right)^{0.5}
Parameters
----------
m : float
Mass flow rate [kg/s]
x : float
Quality at the specific tube interval []
D : float
Diameter of the tube [m]
rhol : float
Density of the liquid [kg/m^3]
rhog : float
Density of the gas [kg/m^3]
mul : float
Viscosity of liquid [Pa*s]
mug : float
Viscosity of gas [Pa*s]
kl : float
Thermal conductivity of liquid [W/m/K]
Cpl : float
Heat capacity of liquid [J/kg/K]
Hvap : float
Heat of vaporization of liquid [J/kg]
sigma : float
Surface tension of liquid [N/m]
dPsat : float
Difference in Saturation pressure of fluid at Te and T, [Pa]
Te : float
Excess temperature of wall, [K]
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
[1]_ and [2]_ have been reviewed, but the model is only put together in
the review of [3]_. Many other forms of this equation exist with different
functions for `F` and `S`.
Examples
--------
>>> Chen_Bennett(m=0.106, x=0.2, D=0.0212, rhol=567, rhog=18.09,
... mul=156E-6, mug=7.11E-6, kl=0.086, Cpl=2730, Hvap=2E5, sigma=0.02,
... dPsat=1E5, Te=3)
4938.275351219369
See Also
--------
Chen_Edelstein
turbulent_Dittus_Boelter
Forster_Zuber
References
----------
.. [1] Bennett, Douglas L., and John C. Chen. "Forced Convective Boiling in
Vertical Tubes for Saturated Pure Components and Binary Mixtures."
AIChE Journal 26, no. 3 (May 1, 1980): 454-61. doi:10.1002/aic.690260317.
.. [2] Bennett, Douglas L., M.W. Davies and B.L. Hertzler, The Suppression
of Saturated Nucleate Boiling by Forced Convective Flow, American
Institute of Chemical Engineers Symposium Series, vol. 76, no. 199.
91-103, 1980.
.. [3] Bertsch, Stefan S., Eckhard A. Groll, and Suresh V. Garimella.
"Review and Comparative Analysis of Studies on Saturated Flow Boiling in
Small Channels." Nanoscale and Microscale Thermophysical Engineering 12,
no. 3 (September 4, 2008): 187-227. doi:10.1080/15567260802317357.
'''
G = m/(pi/4*D**2)
Rel = D*G*(1-x)/mul
Prl = Prandtl(Cp=Cpl, mu=mul, k=kl)
hl = turbulent_Dittus_Boelter(Re=Rel, Pr=Prl)*kl/D
Xtt = Lockhart_Martinelli_Xtt(x=x, rhol=rhol, rhog=rhog, mul=mul, mug=mug)
F = ((Prl+1)/2.)**0.444*(1 + Xtt**-0.5)**1.78
X0 = 0.041*(sigma/(g*(rhol-rhog)))**0.5
S = (1 - exp(-F*hl*X0/kl))/(F*hl*X0/kl)
hnb = Forster_Zuber(Te=Te, dPsat=dPsat, Cpl=Cpl, kl=kl, mul=mul, sigma=sigma,
Hvap=Hvap, rhol=rhol, rhog=rhog)
return hnb*S + hl*F
def Shah(m, x, D, rhol, mul, kl, Cpl, P, Pc):
r'''Calculates heat transfer coefficient for condensation
of a fluid inside a tube, as presented in [1]_ and again by the same
author in [2]_; also given in [3]_. Requires no properties of the gas.
Uses the Dittus-Boelter correlation for single phase heat transfer
coefficient, with a Reynolds number assuming all the flow is liquid.
.. math::
h_{TP} = h_L\left[(1-x)^{0.8} +\frac{3.8x^{0.76}(1-x)^{0.04}}
{P_r^{0.38}}\right]
Parameters
----------
m : float
Mass flow rate [kg/s]
x : float
Quality at the specific interval []
D : float
Diameter of the channel [m]
rhol : float
Density of the liquid [kg/m^3]
mul : float
Viscosity of liquid [Pa*s]
kl : float
Thermal conductivity of liquid [W/m/K]
Cpl : float
Constant-pressure heat capacity of liquid [J/kg/K]
P : float
Pressure of the fluid, [Pa]
Pc : float
Critical pressure of the fluid, [Pa]
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
[1]_ is well written an unambiguous as to how to apply this equation.
Examples
--------
>>> Shah(m=1, x=0.4, D=.3, rhol=800, mul=1E-5, kl=0.6, Cpl=2300, P=1E6, Pc=2E7)
2561.2593415479214
References
----------
.. [1] Shah, M. M. "A General Correlation for Heat Transfer during Film
Condensation inside Pipes." International Journal of Heat and Mass
Transfer 22, no. 4 (April 1, 1979): 547-56.
doi:10.1016/0017-9310(79)90058-9.
.. [2] Shah, M. M., Heat Transfer During Film Condensation in Tubes and
Annuli: A Review of the Literature, ASHRAE Transactions, vol. 87, no.
3, pp. 1086-1100, 1981.
.. [3] Kakaç, Sadik, ed. Boilers, Evaporators, and Condensers. 1st.
Wiley-Interscience, 1991.
'''
VL = m/(rhol*pi/4*D**2)
ReL = Reynolds(V=VL, D=D, rho=rhol, mu=mul)
Prl = Prandtl(Cp=Cpl, k=kl, mu=mul)
hL = turbulent_Dittus_Boelter(ReL, Prl)*kl/D
Pr = P/Pc
h_TP = hL*((1-x)**0.8 + 3.8*x**0.76*(1-x)**0.04/Pr**0.38)
return h_TP
def Shah(m, x, D, rhol, mul, kl, Cpl, P, Pc):
r'''Calculates heat transfer coefficient for condensation
of a fluid inside a tube, as presented in [1]_ and again by the same
author in [2]_; also given in [3]_. Requires no properties of the gas.
Uses the Dittus-Boelter correlation for single phase heat transfer
coefficient, with a Reynolds number assuming all the flow is liquid.
.. math::
h_{TP} = h_L\left[(1-x)^{0.8} +\frac{3.8x^{0.76}(1-x)^{0.04}}
{P_r^{0.38}}\right]
Parameters
----------
m : float
Mass flow rate [kg/s]
x : float
Quality at the specific interval []
D : float
Diameter of the channel [m]
rhol : float
Density of the liquid [kg/m^3]
mul : float
Viscosity of liquid [Pa*s]
kl : float
Thermal conductivity of liquid [W/m/K]
Cpl : float
Constant-pressure heat capacity of liquid [J/kg/K]
P : float
Pressure of the fluid, [Pa]
Pc : float
Critical pressure of the fluid, [Pa]
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
[1]_ is well written an unambiguous as to how to apply this equation.
Examples
--------
>>> Shah(m=1, x=0.4, D=.3, rhol=800, mul=1E-5, kl=0.6, Cpl=2300, P=1E6, Pc=2E7)
2561.2593415479214
References
----------
.. [1] Shah, M. M. "A General Correlation for Heat Transfer during Film
Condensation inside Pipes." International Journal of Heat and Mass
Transfer 22, no. 4 (April 1, 1979): 547-56.
doi:10.1016/0017-9310(79)90058-9.
.. [2] Shah, M. M., Heat Transfer During Film Condensation in Tubes and
Annuli: A Review of the Literature, ASHRAE Transactions, vol. 87, no.
3, pp. 1086-1100, 1981.
.. [3] Kakaç, Sadik, ed. Boilers, Evaporators, and Condensers. 1st.
Wiley-Interscience, 1991.
'''
VL = m / (rhol * pi / 4 * D**2)
ReL = Reynolds(V=VL, D=D, rho=rhol, mu=mul)
Prl = Prandtl(Cp=Cpl, k=kl, mu=mul)
hL = turbulent_Dittus_Boelter(ReL, Prl) * kl / D
Pr = P / Pc
h_TP = hL * ((1 - x)**0.8 + 3.8 * x**0.76 * (1 - x)**0.04 / Pr**0.38)
return h_TP
def Liu_Winterton(m, x, D, rhol, rhog, mul, kl, Cpl, MW, P, Pc, Te):
r"""Calculates heat transfer coefficient for film boiling of saturated
fluid in any orientation of flow. Correlation
is as developed in [1]_, also reviewed in [2]_ and [3]_.
Excess wall temperature is required to use this correlation.
.. math::
h_{tp} = \sqrt{ (F\cdot h_l)^2 + (S\cdot h_{nb})^2}
S = \left( 1+0.055F^{0.1} Re_{L}^{0.16}\right)^{-1}
h_{l} = 0.023 Re_L^{0.8} Pr_l^{0.4} k_l/D
Re_L = \frac{GD}{\mu_l}
F = \left[ 1+ xPr_{l}(\rho_l/\rho_g-1)\right]^{0.35}
h_{nb} = \left(55\Delta Te^{0.67} \frac{P}{P_c}^{(0.12 - 0.2\log_{10}
R_p)}(-\log_{10} \frac{P}{P_c})^{-0.55} MW^{-0.5}\right)^{1/0.33}
Parameters
----------
m : float
Mass flow rate [kg/s]
x : float
Quality at the specific tube interval []
D : float
Diameter of the tube [m]
rhol : float
Density of the liquid [kg/m^3]
rhog : float
Density of the gas [kg/m^3]
mul : float
Viscosity of liquid [Pa*s]
kl : float
Thermal conductivity of liquid [W/m/K]
Cpl : float
Heat capacity of liquid [J/kg/K]
MW : float
Molecular weight of the fluid, [g/mol]
P : float
Pressure of fluid, [Pa]
Pc : float
Critical pressure of fluid, [Pa]
Te : float, optional
Excess temperature of wall, [K]
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
[1]_ has been reviewed, and is accurately reproduced in [3]_.
Uses the `Cooper` and `turbulent_Dittus_Boelter` correlations.
A correction for horizontal flow at low Froude numbers is available in
[1]_ but has not been implemented and is not recommended in several
sources.
Examples
--------
>>> Liu_Winterton(m=1, x=0.4, D=0.3, rhol=567., rhog=18.09, kl=0.086,
... mul=156E-6, Cpl=2300, P=1E6, Pc=22E6, MW=44.02, Te=7)
4747.749477190532
References
----------
.. [1] Liu, Z., and R. H. S. Winterton. "A General Correlation for
Saturated and Subcooled Flow Boiling in Tubes and Annuli, Based on a
Nucleate Pool Boiling Equation." International Journal of Heat and Mass
Transfer 34, no. 11 (November 1991): 2759-66.
doi:10.1016/0017-9310(91)90234-6.
.. [2] Fang, Xiande, Zhanru Zhou, and Dingkun Li. "Review of Correlations
of Flow Boiling Heat Transfer Coefficients for Carbon Dioxide."
International Journal of Refrigeration 36, no. 8 (December 2013):
2017-39. doi:10.1016/j.ijrefrig.2013.05.015.
.. [3] Bertsch, Stefan S., Eckhard A. Groll, and Suresh V. Garimella.
"Review and Comparative Analysis of Studies on Saturated Flow Boiling in
Small Channels." Nanoscale and Microscale Thermophysical Engineering 12,
no. 3 (September 4, 2008): 187-227. doi:10.1080/15567260802317357.
"""
G = m / (pi / 4 * D ** 2)
ReL = D * G / mul
Prl = Prandtl(Cp=Cpl, mu=mul, k=kl)
hl = turbulent_Dittus_Boelter(Re=ReL, Pr=Prl) * kl / D
F = (1 + x * Prl * (rhol / rhog - 1)) ** 0.35
S = (1 + 0.055 * F ** 0.1 * ReL ** 0.16) ** -1
# if horizontal:
# Fr = Froude(V=G/rhol, L=D, squared=True)
# if Fr < 0.05:
# ef = Fr**(0.1 - 2*Fr)
# es = Fr**0.5
# F *= ef
# S *= es
h_nb = Cooper(Te=Te, P=P, Pc=Pc, MW=MW)
h_tp = ((F * hl) ** 2 + (S * h_nb) ** 2) ** 0.5
return h_tp
def Chen_Bennett(m, x, D, rhol, rhog, mul, mug, kl, Cpl, Hvap, sigma, dPsat, Te):
r"""Calculates heat transfer coefficient for film boiling of saturated
fluid in any orientation of flow. Correlation
is developed in [1]_ and [2]_, and reviewed in [3]_. This model is one of
the most often used, and replaces the `Chen_Edelstein` correlation. It uses
the Dittus-Boelter correlation for turbulent convection and the
Forster-Zuber correlation for pool boiling, and combines them with two
factors `F` and `S`.
.. math::
h_{tp} = S\cdot h_{nb} + F \cdot h_{sp,l}
h_{sp,l} = 0.023 Re_l^{0.8} Pr_l^{0.4} k_l/D
Re_l = \frac{DG(1-x)}{\mu_l}
h_{nb} = 0.00122\left( \frac{\lambda_l^{0.79} c_{p,l}^{0.45}
\rho_l^{0.49}}{\sigma^{0.5} \mu^{0.29} H_{vap}^{0.24} \rho_g^{0.24}}
\right)\Delta T_{sat}^{0.24} \Delta p_{sat}^{0.75}
F = \left(\frac{Pr_1+1}{2}\right)^{0.444}\cdot (1+X_{tt}^{-0.5})^{1.78}
S = \frac{1-\exp(-F\cdot h_{conv} \cdot X_0/k_l)}
{F\cdot h_{conv}\cdot X_0/k_l}
X_{tt} = \left( \frac{1-x}{x}\right)^{0.9} \left(\frac{\rho_g}{\rho_l}
\right)^{0.5}\left( \frac{\mu_l}{\mu_g}\right)^{0.1}
X_0 = 0.041 \left(\frac{\sigma}{g \cdot (\rho_l-\rho_v)}\right)^{0.5}
Parameters
----------
m : float
Mass flow rate [kg/s]
x : float
Quality at the specific tube interval []
D : float
Diameter of the tube [m]
rhol : float
Density of the liquid [kg/m^3]
rhog : float
Density of the gas [kg/m^3]
mul : float
Viscosity of liquid [Pa*s]
mug : float
Viscosity of gas [Pa*s]
kl : float
Thermal conductivity of liquid [W/m/K]
Cpl : float
Heat capacity of liquid [J/kg/K]
Hvap : float
Heat of vaporization of liquid [J/kg]
sigma : float
Surface tension of liquid [N/m]
dPsat : float
Difference in Saturation pressure of fluid at Te and T, [Pa]
Te : float
Excess temperature of wall, [K]
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
[1]_ and [2]_ have been reviewed, but the model is only put together in
the review of [3]_. Many other forms of this equation exist with different
functions for `F` and `S`.
Examples
--------
>>> Chen_Bennett(m=0.106, x=0.2, D=0.0212, rhol=567, rhog=18.09,
... mul=156E-6, mug=7.11E-6, kl=0.086, Cpl=2730, Hvap=2E5, sigma=0.02,
... dPsat=1E5, Te=3)
4938.275351219369
See Also
--------
Chen_Edelstein
turbulent_Dittus_Boelter
Forster_Zuber
References
----------
.. [1] Bennett, Douglas L., and John C. Chen. "Forced Convective Boiling in
Vertical Tubes for Saturated Pure Components and Binary Mixtures."
AIChE Journal 26, no. 3 (May 1, 1980): 454-61. doi:10.1002/aic.690260317.
.. [2] Bennett, Douglas L., M.W. Davies and B.L. Hertzler, The Suppression
of Saturated Nucleate Boiling by Forced Convective Flow, American
Institute of Chemical Engineers Symposium Series, vol. 76, no. 199.
91-103, 1980.
.. [3] Bertsch, Stefan S., Eckhard A. Groll, and Suresh V. Garimella.
"Review and Comparative Analysis of Studies on Saturated Flow Boiling in
Small Channels." Nanoscale and Microscale Thermophysical Engineering 12,
no. 3 (September 4, 2008): 187-227. doi:10.1080/15567260802317357.
"""
G = m / (pi / 4 * D ** 2)
Rel = D * G * (1 - x) / mul
Prl = Prandtl(Cp=Cpl, mu=mul, k=kl)
hl = turbulent_Dittus_Boelter(Re=Rel, Pr=Prl) * kl / D
Xtt = Lockhart_Martinelli_Xtt(x=x, rhol=rhol, rhog=rhog, mul=mul, mug=mug)
F = ((Prl + 1) / 2.0) ** 0.444 * (1 + Xtt ** -0.5) ** 1.78
X0 = 0.041 * (sigma / (g * (rhol - rhog))) ** 0.5
S = (1 - exp(-F * hl * X0 / kl)) / (F * hl * X0 / kl)
hnb = Forster_Zuber(Te=Te, dPsat=dPsat, Cpl=Cpl, kl=kl, mul=mul, sigma=sigma, Hvap=Hvap, rhol=rhol, rhog=rhog)
h = hnb * S + hl * F
return h
def Chen_Edelstein(m, x, D, rhol, rhog, mul, mug, kl, Cpl, Hvap, sigma, dPsat, Te):
r"""Calculates heat transfer coefficient for film boiling of saturated
fluid in any orientation of flow. Correlation
is developed in [1]_ and [2]_, and reviewed in [3]_. This model is one of
the most often used. It uses the Dittus-Boelter correlation for turbulent
convection and the Forster-Zuber correlation for pool boiling, and
combines them with two factors `F` and `S`.
.. math::
h_{tp} = S\cdot h_{nb} + F \cdot h_{sp,l}
h_{sp,l} = 0.023 Re_l^{0.8} Pr_l^{0.4} k_l/D
Re_l = \frac{DG(1-x)}{\mu_l}
h_{nb} = 0.00122\left( \frac{\lambda_l^{0.79} c_{p,l}^{0.45}
\rho_l^{0.49}}{\sigma^{0.5} \mu^{0.29} H_{vap}^{0.24} \rho_g^{0.24}}
\right)\Delta T_{sat}^{0.24} \Delta p_{sat}^{0.75}
F = (1 + X_{tt}^{-0.5})^{1.78}
X_{tt} = \left( \frac{1-x}{x}\right)^{0.9} \left(\frac{\rho_g}{\rho_l}
\right)^{0.5}\left( \frac{\mu_l}{\mu_g}\right)^{0.1}
S = 0.9622 - 0.5822\left(\tan^{-1}\left(\frac{Re_L\cdot F^{1.25}}
{6.18\cdot 10^4}\right)\right)
Parameters
----------
m : float
Mass flow rate [kg/s]
x : float
Quality at the specific tube interval []
D : float
Diameter of the tube [m]
rhol : float
Density of the liquid [kg/m^3]
rhog : float
Density of the gas [kg/m^3]
mul : float
Viscosity of liquid [Pa*s]
mug : float
Viscosity of gas [Pa*s]
kl : float
Thermal conductivity of liquid [W/m/K]
Cpl : float
Heat capacity of liquid [J/kg/K]
Hvap : float
Heat of vaporization of liquid [J/kg]
sigma : float
Surface tension of liquid [N/m]
dPsat : float
Difference in Saturation pressure of fluid at Te and T, [Pa]
Te : float
Excess temperature of wall, [K]
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
[1]_ and [2]_ have been reviewed, but the model is only put together in
the review of [3]_. Many other forms of this equation exist with different
functions for `F` and `S`.
Examples
--------
>>> Chen_Edelstein(m=0.106, x=0.2, D=0.0212, rhol=567, rhog=18.09,
... mul=156E-6, mug=7.11E-6, kl=0.086, Cpl=2730, Hvap=2E5, sigma=0.02,
... dPsat=1E5, Te=3)
3289.058731974052
See Also
--------
turbulent_Dittus_Boelter
Forster_Zuber
References
----------
.. [1] Chen, J. C. "Correlation for Boiling Heat Transfer to Saturated
Fluids in Convective Flow." Industrial & Engineering Chemistry Process
Design and Development 5, no. 3 (July 1, 1966): 322-29.
doi:10.1021/i260019a023.
.. [2] Edelstein, Sergio, A. J. Pérez, and J. C. Chen. "Analytic
Representation of Convective Boiling Functions." AIChE Journal 30, no.
5 (September 1, 1984): 840-41. doi:10.1002/aic.690300528.
.. [3] Bertsch, Stefan S., Eckhard A. Groll, and Suresh V. Garimella.
"Review and Comparative Analysis of Studies on Saturated Flow Boiling in
Small Channels." Nanoscale and Microscale Thermophysical Engineering 12,
no. 3 (September 4, 2008): 187-227. doi:10.1080/15567260802317357.
"""
G = m / (pi / 4 * D ** 2)
Rel = D * G * (1 - x) / mul
Prl = Prandtl(Cp=Cpl, mu=mul, k=kl)
hl = turbulent_Dittus_Boelter(Re=Rel, Pr=Prl) * kl / D
Xtt = Lockhart_Martinelli_Xtt(x=x, rhol=rhol, rhog=rhog, mul=mul, mug=mug)
F = (1 + Xtt ** -0.5) ** 1.78
Re = Rel * F ** 1.25
S = 0.9622 - 0.5822 * atan(Re / 6.18e4)
hnb = Forster_Zuber(Te=Te, dPsat=dPsat, Cpl=Cpl, kl=kl, mul=mul, sigma=sigma, Hvap=Hvap, rhol=rhol, rhog=rhog)
h = hnb * S + hl * F
return h
