Flow boiling (ht.boiling_flow)

ht.boiling_flow.Thome(m, x, D, rhol, rhog, mul, mug, kl, kg, Cpl, Cpg, Hvap, sigma, Psat, Pc, q=None, Te=None)[source]

Calculates heat transfer coefficient for film boiling of saturated fluid in any orientation of flow. Correlation is as developed in [R325] and [R425], and also reviewed [R525]. This is a complicated model, but expected to have more accuracy as a result.

Either the heat flux or excess temperature is required for the calculation of heat transfer coefficient. The solution for a specified excess temperature is solved numerically, making it slow.

\[ \begin{align}\begin{aligned}h(z) = \frac{t_l}{\tau} h_l(z) +\frac{t_{film}}{\tau} h_{film}(z) + \frac{t_{dry}}{\tau} h_{g}(z) \\h_{l/g}(z) = (Nu_{lam}^4 + Nu_{trans}^4)^{1/4} k/D\\Nu_{laminar} = 0.91 {Pr}^{1/3} \sqrt{ReD/L(z)}\\Nu_{trans} = \frac{ (f/8) (Re-1000)Pr}{1+12.7 (f/8)^{1/2} (Pr^{2/3}-1)} \left[ 1 + \left( \frac{D}{L(z)}\right)^{2/3}\right]\\f = (1.82 \log_{10} Re - 1.64 )^{-2}\\L_l = \frac{\tau G_{tp}}{\rho_l}(1-x)\\L_{dry} = v_p t_{dry}\\t_l = \frac{\tau}{1 + \frac{\rho_l}{\rho_g}\frac{x}{1-x}}\\t_v = \frac{\tau}{1 + \frac{\rho_g}{\rho_l}\frac{1-x}{x}}\\\tau = \frac{1}{f_{opt}}\\f_{opt} = \left(\frac{q}{q_{ref}}\right)^{n_f}\\q_{ref} = 3328\left(\frac{P_{sat}}{P_c}\right)^{-0.5}\\t_{dry,film} = \frac{\rho_l \Delta H_{vap}}{q}[\delta_0(z) - \delta_{min}]\\\frac{\delta_0}{D} = C_{\delta 0}\left(3\sqrt{\frac{\nu_l}{v_p D}} \right)^{0.84}\left[(0.07Bo^{0.41})^{-8} + 0.1^{-8}\right]^{-1/8}\\Bo = \frac{\rho_l D}{\sigma} v_p^2\\v_p = G_{tp} \left[\frac{x}{\rho_g} + \frac{1-x}{\rho_l}\right]\\h_{film}(z) = \frac{2 k_l}{\delta_0(z) + \delta_{min}(z)}\\\delta_{min} = 0.3\cdot 10^{-6} \text{m}\\C_{\delta,0} = 0.29\\n_f = 1.74\end{aligned}\end{align} \]

if t dry film > tv:

\[ \begin{align}\begin{aligned}\delta_{end}(x) = \delta(z, t_v)\\t_{film} = t_v\\t_{dry} = 0\end{aligned}\end{align} \]

Otherwise:

\[ \begin{align}\begin{aligned}\delta_{end}(z) = \delta_{min}\\t_{film} = t_{dry,film}\\t_{dry} = t_v - t_{film}\end{aligned}\end{align} \]
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]

kg : float

Thermal conductivity of gas [W/m/K]

Cpl : float

Heat capacity of liquid [J/kg/K]

Cpg : float

Heat capacity of gas [J/kg/K]

Hvap : float

Heat of vaporization of liquid [J/kg]

sigma : float

Surface tension of liquid [N/m]

Psat : float

Vapor pressure of fluid, [Pa]

Pc : float

Critical pressure of fluid, [Pa]

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

[R325] and [R425] have been reviewed, and are accurately reproduced in [R525].

[R325] used data from 7 studies, covering 7 fluids and Dh from 0.7-3.1 mm, heat flux from 0.5-17.8 W/cm^2, x from 0.01-0.99, and G from 50-564 kg/m^2/s.

Liquid and/or gas slugs are both considered, and are hydrodynamically developing. Ll is the calculated length of liquid slugs, and L_dry is the same for vapor slugs.

Because of the complexity of the model and that there is some logic in this function, Te as an input may lead to a different solution that the calculated q will in return.

References

[R325](1, 2, 3, 4) Thome, J. R., V. Dupont, and A. M. Jacobi. “Heat Transfer Model for Evaporation in Microchannels. Part I: Presentation of the Model.” International Journal of Heat and Mass Transfer 47, no. 14-16 (July 2004): 3375-85. doi:10.1016/j.ijheatmasstransfer.2004.01.006.
[R425](1, 2, 3) Dupont, V., J. R. Thome, and A. M. Jacobi. “Heat Transfer Model for Evaporation in Microchannels. Part II: Comparison with the Database.” International Journal of Heat and Mass Transfer 47, no. 14-16 (July 2004): 3387-3401. doi:10.1016/j.ijheatmasstransfer.2004.01.007.
[R525](1, 2, 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.

Examples

>>> Thome(m=1, x=0.4, D=0.3, rhol=567., rhog=18.09, kl=0.086, kg=0.2,
... mul=156E-6, mug=1E-5, Cpl=2300, Cpg=1400, sigma=0.02, Hvap=9E5, 
... Psat=1E5, Pc=22E6, q=1E5)
1633.008836502032
ht.boiling_flow.Liu_Winterton(m, x, D, rhol, rhog, mul, kl, Cpl, MW, P, Pc, Te)[source]

Calculates heat transfer coefficient for film boiling of saturated fluid in any orientation of flow. Correlation is as developed in [R628], also reviewed in [R728] and [R828].

Excess wall temperature is required to use this correlation.

\[ \begin{align}\begin{aligned}h_{tp} = \sqrt{ (F\cdot h_l)^2 + (S\cdot h_{nb})^2} \\S = \left( 1+0.055F^{0.1} Re_{L}^{0.16}\right)^{-1}\\h_{l} = 0.023 Re_L^{0.8} Pr_l^{0.4} k_l/D\\Re_L = \frac{GD}{\mu_l}\\F = \left[ 1+ xPr_{l}(\rho_l/\rho_g-1)\right]^{0.35}\\h_{nb} = \left(55\Delta Te^{0.67} \frac{P}{P_c}^{(0.12 - 0.2\log_{10} R_p)}(-\log_{10} \frac{P}{P_c})^{-0.55} MW^{-0.5}\right)^{1/0.33}\end{aligned}\end{align} \]
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

[R628] has been reviewed, and is accurately reproduced in [R828].

Uses the Cooper and turbulent_Dittus_Boelter correlations.

A correction for horizontal flow at low Froude numbers is available in [R628] but has not been implemented and is not recommended in several sources.

References

[R628](1, 2, 3, 4) 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.
[R728](1, 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.
[R828](1, 2, 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.

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
ht.boiling_flow.Chen_Edelstein(m, x, D, rhol, rhog, mul, mug, kl, Cpl, Hvap, sigma, dPsat, Te)[source]

Calculates heat transfer coefficient for film boiling of saturated fluid in any orientation of flow. Correlation is developed in [R931] and [R1031], and reviewed in [R1131]. 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.

\[ \begin{align}\begin{aligned}h_{tp} = S\cdot h_{nb} + F \cdot h_{sp,l}\\h_{sp,l} = 0.023 Re_l^{0.8} Pr_l^{0.4} k_l/D\\Re_l = \frac{DG(1-x)}{\mu_l}\\h_{nb} = 0.00122\left( \frac{\lambda_l^{0.79} c_{p,l}^{0.45} \rho_l^{0.49}}{\sigma^{0.5} \mu^{0.29} H_{vap}^{0.24} \rho_g^{0.24}} \right)\Delta T_{sat}^{0.24} \Delta p_{sat}^{0.75}\\F = (1 + X_{tt}^{-0.5})^{1.78}\\X_{tt} = \left( \frac{1-x}{x}\right)^{0.9} \left(\frac{\rho_g}{\rho_l} \right)^{0.5}\left( \frac{\mu_l}{\mu_g}\right)^{0.1}\\S = 0.9622 - 0.5822\left(\tan^{-1}\left(\frac{Re_L\cdot F^{1.25}} {6.18\cdot 10^4}\right)\right)\end{aligned}\end{align} \]
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]

See also

turbulent_Dittus_Boelter, Forster_Zuber

Notes

[R931] and [R1031] have been reviewed, but the model is only put together in the review of [R1131]. Many other forms of this equation exist with different functions for F and S.

References

[R931](1, 2, 3) 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.
[R1031](1, 2, 3) 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.
[R1131](1, 2, 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.

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
ht.boiling_flow.Chen_Bennett(m, x, D, rhol, rhog, mul, mug, kl, Cpl, Hvap, sigma, dPsat, Te)[source]

Calculates heat transfer coefficient for film boiling of saturated fluid in any orientation of flow. Correlation is developed in [R1234] and [R1334], and reviewed in [R1434]. 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.

\[ \begin{align}\begin{aligned}h_{tp} = S\cdot h_{nb} + F \cdot h_{sp,l}\\h_{sp,l} = 0.023 Re_l^{0.8} Pr_l^{0.4} k_l/D\\Re_l = \frac{DG(1-x)}{\mu_l}\\h_{nb} = 0.00122\left( \frac{\lambda_l^{0.79} c_{p,l}^{0.45} \rho_l^{0.49}}{\sigma^{0.5} \mu^{0.29} H_{vap}^{0.24} \rho_g^{0.24}} \right)\Delta T_{sat}^{0.24} \Delta p_{sat}^{0.75}\\F = \left(\frac{Pr_1+1}{2}\right)^{0.444}\cdot (1+X_{tt}^{-0.5})^{1.78}\\S = \frac{1-\exp(-F\cdot h_{conv} \cdot X_0/k_l)} {F\cdot h_{conv}\cdot X_0/k_l}\\X_{tt} = \left( \frac{1-x}{x}\right)^{0.9} \left(\frac{\rho_g}{\rho_l} \right)^{0.5}\left( \frac{\mu_l}{\mu_g}\right)^{0.1}\\X_0 = 0.041 \left(\frac{\sigma}{g \cdot (\rho_l-\rho_v)}\right)^{0.5} \end{aligned}\end{align} \]
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]

See also

Chen_Edelstein, turbulent_Dittus_Boelter, Forster_Zuber

Notes

[R1234] and [R1334] have been reviewed, but the model is only put together in the review of [R1434]. Many other forms of this equation exist with different functions for F and S.

References

[R1234](1, 2, 3) 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.
[R1334](1, 2, 3) 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.
[R1434](1, 2, 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.

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
ht.boiling_flow.Lazarek_Black(m, D, mul, kl, Hvap, q=None, Te=None)[source]

Calculates heat transfer coefficient for film boiling of saturated fluid in vertical tubes for either upward or downward flow. Correlation is as shown in [R1537], and also reviewed in [R1637] and [R1737].

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.

\[ \begin{align}\begin{aligned}h_{tp} = 30 Re_{lo}^{0.857} Bg^{0.714} \frac{k_l}{D}\\Re_{lo} = \frac{G_{tp}D}{\mu_l}\end{aligned}\end{align} \]
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

[R1537] has been reviewed.

[R1637] 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.

References

[R1537](1, 2, 3) 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.
[R1637](1, 2, 3) 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.
[R1737](1, 2) 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.

Examples

>>> Lazarek_Black(m=10, D=0.3, mul=1E-3, kl=0.6, Hvap=2E6, Te=100)
9501.932636079293
ht.boiling_flow.Li_Wu(m, x, D, rhol, rhog, mul, kl, Hvap, sigma, q=None, Te=None)[source]

Calculates heat transfer coefficient for film boiling of saturated fluid in any orientation of flow. Correlation is as shown in [R1840], and also reviewed in [R1940] and [R2040].

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.

\[ \begin{align}\begin{aligned}h_{tp} = 334 Bg^{0.3}(Bo\cdot Re_l^{0.36})^{0.4}\frac{k_l}{D}\\Re_{l} = \frac{G(1-x)D}{\mu_l}\end{aligned}\end{align} \]
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

[R1840] has been reviewed.

[R1840] used 18 sets of experimental data to derive the results, covering hydraulic diameters from 0.19 to 3.1 mm and 12 different fluids.

References

[R1840](1, 2, 3, 4) 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.
[R1940](1, 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.
[R2040](1, 2) 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.

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)
5345.409399239493
ht.boiling_flow.Sun_Mishima(m, D, rhol, rhog, mul, kl, Hvap, sigma, q=None, Te=None)[source]

Calculates heat transfer coefficient for film boiling of saturated fluid in any orientation of flow. Correlation is as shown in [R2143], and also reviewed in [R2243] and [3]_.

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.

\[ \begin{align}\begin{aligned}h_{tp} = \frac{ 6 Re_{lo}^{1.05} Bg^{0.54}} {We_l^{0.191}(\rho_l/\rho_g)^{0.142}}\frac{k_l}{D}\\Re_{lo} = \frac{G_{tp}D}{\mu_l}\end{aligned}\end{align} \]
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

[R2143] has been reviewed.

[R2143] used 2501 data points to derive the results, covering hydraulic diameters from 0.21 to 6.05 mm and 11 different fluids.

References

[R2143](1, 2, 3, 4) 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.
[R2243](1, 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.

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
ht.boiling_flow.Yun_Heo_Kim(m, x, D, rhol, mul, Hvap, sigma, q=None, Te=None)[source]

Calculates heat transfer coefficient for film boiling of saturated fluid in any orientation of flow. Correlation is as shown in [R2345] and [R2445], and also reviewed in [R2545].

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.

\[ \begin{align}\begin{aligned}h_{tp} = 136876(Bg\cdot We_l)^{0.1993} Re_l^{-0.1626}\\Re_l = \frac{G D (1-x)}{\mu_l}\\We_l = \frac{G^2 D}{\rho_l \sigma}\end{aligned}\end{align} \]
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

[R2345] has been reviewed.

References

[R2345](1, 2, 3) 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.
[R2445](1, 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.
[R2545](1, 2) 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.

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