def Yun_Heo_Kim(m, x, D, rhol, mul, Hvap, sigma, q=None, Te=None):
r'''Calculates heat transfer coefficient for film boiling of saturated
fluid in any orientation of flow. Correlation
is as shown in [1]_ and [2]_, and also reviewed in [3]_.
Either the heat flux or excess temperature is required for the calculation
of heat transfer coefficient. Uses liquid Reynolds number, Weber
number, and Boiling number. Weber number is defined in terms of the velocity
if all fluid were liquid.
.. math::
h_{tp} = 136876(Bg\cdot We_l)^{0.1993} Re_l^{-0.1626}
.. math::
Re_l = \frac{G D (1-x)}{\mu_l}
.. math::
We_l = \frac{G^2 D}{\rho_l \sigma}
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]
mul : float
Viscosity of liquid [Pa*s]
Hvap : float
Heat of vaporization of liquid [J/kg]
sigma : float
Surface tension of liquid [N/m]
q : float, optional
Heat flux to wall [W/m^2]
Te : float, optional
Excess temperature of wall, [K]
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
[1]_ has been reviewed.
Examples
--------
>>> Yun_Heo_Kim(m=1, x=0.4, D=0.3, rhol=567., mul=156E-6, sigma=0.02, Hvap=9E5, q=1E4)
9479.313988550184
References
----------
.. [1] Yun, Rin, Jae Hyeok Heo, and Yongchan Kim. "Evaporative Heat
Transfer and Pressure Drop of R410A in Microchannels." International
Journal of Refrigeration 29, no. 1 (January 2006): 92-100.
doi:10.1016/j.ijrefrig.2005.08.005.
.. [2] Yun, Rin, Jae Hyeok Heo, and Yongchan Kim. "Erratum to 'Evaporative
Heat Transfer and Pressure Drop of R410A in Microchannels; [Int. J.
Refrigeration 29 (2006) 92-100]." International Journal of Refrigeration
30, no. 8 (December 2007): 1468. doi:10.1016/j.ijrefrig.2007.08.003.
.. [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)
V = G/rhol
Rel = G*D*(1-x)/mul
We = Weber(V=V, L=D, rho=rhol, sigma=sigma)
if q is not None:
Bg = Boiling(G=G, q=q, Hvap=Hvap)
return 136876*(Bg*We)**0.1993*Rel**-0.1626
elif Te is not None:
A = 136876*(We)**0.1993*Rel**-0.1626*(Te/G/Hvap)**0.1993
return A**(10000/8007.)
else:
raise ValueError('Either q or Te is needed for this correlation')
def Sun_Mishima(m, D, rhol, rhog, mul, kl, Hvap, sigma, q=None, Te=None):
r'''Calculates heat transfer coefficient for film boiling of saturated
fluid in any orientation of flow. Correlation
is as shown in [1]_, and also reviewed in [2]_.
Either the heat flux or excess temperature is required for the calculation
of heat transfer coefficient. Uses liquid-only Reynolds number, Weber
number, and Boiling number. Weber number is defined in terms of the velocity
if all fluid were liquid.
.. math::
h_{tp} = \frac{ 6 Re_{lo}^{1.05} Bg^{0.54}}
{We_l^{0.191}(\rho_l/\rho_g)^{0.142}}\frac{k_l}{D}
.. math::
Re_{lo} = \frac{G_{tp}D}{\mu_l}
Parameters
----------
m : float
Mass flow rate [kg/s]
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]
Hvap : float
Heat of vaporization of liquid [J/kg]
sigma : float
Surface tension of liquid [N/m]
q : float, optional
Heat flux to wall [W/m^2]
Te : float, optional
Excess temperature of wall, [K]
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
[1]_ has been reviewed.
[1]_ used 2501 data points to derive the results, covering
hydraulic diameters from 0.21 to 6.05 mm and 11 different fluids.
Examples
--------
>>> Sun_Mishima(m=1, D=0.3, rhol=567., rhog=18.09, kl=0.086, mul=156E-6, sigma=0.02, Hvap=9E5, Te=10)
507.6709168372167
References
----------
.. [1] Sun, Licheng, and Kaichiro Mishima. "An Evaluation of Prediction
Methods for Saturated Flow Boiling Heat Transfer in Mini-Channels."
International Journal of Heat and Mass Transfer 52, no. 23-24 (November
2009): 5323-29. doi:10.1016/j.ijheatmasstransfer.2009.06.041.
.. [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.
'''
G = m/(pi/4*D**2)
V = G/rhol
Relo = G*D/mul
We = Weber(V=V, L=D, rho=rhol, sigma=sigma)
if q is not None:
Bg = Boiling(G=G, q=q, Hvap=Hvap)
return 6*Relo**1.05*Bg**0.54/(We**0.191*(rhol/rhog)**0.142)*kl/D
elif Te is not None:
A = 6*Relo**1.05/(We**0.191*(rhol/rhog)**0.142)*kl/D
return A**(50/23.)*Te**(27/23.)/(G**(27/23.)*Hvap**(27/23.))
else:
raise ValueError('Either q or Te is needed for this correlation')
def Lazarek_Black(m, D, mul, kl, Hvap, q=None, Te=None):
r'''Calculates heat transfer coefficient for film boiling of saturated
fluid in vertical tubes for either upward or downward flow. Correlation
is as shown in [1]_, and also reviewed in [2]_ and [3]_.
Either the heat flux or excess temperature is required for the calculation
of heat transfer coefficient.
Quality independent. Requires no properties of the gas.
Uses a Reynolds number assuming all the flow is liquid.
.. math::
h_{tp} = 30 Re_{lo}^{0.857} Bg^{0.714} \frac{k_l}{D}
.. math::
Re_{lo} = \frac{G_{tp}D}{\mu_l}
Parameters
----------
m : float
Mass flow rate [kg/s]
D : float
Diameter of the channel [m]
mul : float
Viscosity of liquid [Pa*s]
kl : float
Thermal conductivity of liquid [W/m/K]
Hvap : float
Heat of vaporization of liquid [J/kg]
q : float, optional
Heat flux to wall [W/m^2]
Te : float, optional
Excess temperature of wall, [K]
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
[1]_ has been reviewed.
[2]_ claims it was developed for a range of quality 0-0.6,
Relo 860-5500, mass flux 125-750 kg/m^2/s, q of 1.4-38 W/cm^2, and with a
pipe diameter of 3.1 mm. Developed with data for R113 only.
Examples
--------
>>> Lazarek_Black(m=10, D=0.3, mul=1E-3, kl=0.6, Hvap=2E6, Te=100)
9501.932636079293
References
----------
.. [1] Lazarek, G. M., and S. H. Black. "Evaporative Heat Transfer,
Pressure Drop and Critical Heat Flux in a Small Vertical Tube with
R-113." International Journal of Heat and Mass Transfer 25, no. 7 (July
1982): 945-60. doi:10.1016/0017-9310(82)90070-9.
.. [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)
Relo = G*D/mul
if q is not None:
Bg = Boiling(G=G, q=q, Hvap=Hvap)
return 30*Relo**0.857*Bg**0.714*kl/D
elif Te is not None:
# Solved with sympy
return 27000*30**(71/143)*(1./(G*Hvap))**(357/143)*Relo**(857/286)*Te**(357/143)*kl**(500/143)/D**(500/143)
else:
raise ValueError('Either q or Te is needed for this correlation')
def Li_Wu(m, x, D, rhol, rhog, mul, kl, Hvap, sigma, q=None, Te=None):
r'''Calculates heat transfer coefficient for film boiling of saturated
fluid in any orientation of flow. Correlation
is as shown in [1]_, and also reviewed in [2]_ and [3]_.
Either the heat flux or excess temperature is required for the calculation
of heat transfer coefficient. Uses liquid Reynolds number, Bond number,
and Boiling number.
.. math::
h_{tp} = 334 Bg^{0.3}(Bo\cdot Re_l^{0.36})^{0.4}\frac{k_l}{D}
.. math::
Re_{l} = \frac{G(1-x)D}{\mu_l}
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]
Hvap : float
Heat of vaporization of liquid [J/kg]
sigma : float
Surface tension of liquid [N/m]
q : float, optional
Heat flux to wall [W/m^2]
Te : float, optional
Excess temperature of wall, [K]
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
[1]_ has been reviewed.
[1]_ used 18 sets of experimental data to derive the results, covering
hydraulic diameters from 0.19 to 3.1 mm and 12 different fluids.
Examples
--------
>>> Li_Wu(m=1, x=0.2, D=0.3, rhol=567., rhog=18.09, kl=0.086, mul=156E-6, sigma=0.02, Hvap=9E5, q=1E5)
5345.409399239492
References
----------
.. [1] Li, Wei, and Zan Wu. "A General Correlation for Evaporative Heat
Transfer in Micro/mini-Channels." International Journal of Heat and Mass
Transfer 53, no. 9-10 (April 2010): 1778-87.
doi:10.1016/j.ijheatmasstransfer.2010.01.012.
.. [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] Kim, Sung-Min, and Issam Mudawar. "Review of Databases and
Predictive Methods for Pressure Drop in Adiabatic, Condensing and
Boiling Mini/micro-Channel Flows." International Journal of Heat and
Mass Transfer 77 (October 2014): 74-97.
doi:10.1016/j.ijheatmasstransfer.2014.04.035.
'''
G = m/(pi/4*D**2)
Rel = G*D*(1-x)/mul
Bo = Bond(rhol=rhol, rhog=rhog, sigma=sigma, L=D)
if q is not None:
Bg = Boiling(G=G, q=q, Hvap=Hvap)
return 334*Bg**0.3*(Bo*Rel**0.36)**0.4*kl/D
elif Te is not None:
A = 334*(Bo*Rel**0.36)**0.4*kl/D
return A**(10/7.)*Te**(3/7.)/(G**(3/7.)*Hvap**(3/7.))
else:
raise ValueError('Either q or Te is needed for this correlation')
