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')