Flow boiling (ht.boiling_flow)¶
- 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 [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.
$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]
- m
- Returns
- h
float
Heat transfer coefficient [W/m^2/K]
- h
See also
Chen_Edelstein
turbulent_Dittus_Boelter
Forster_Zuber
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.
References
- 1(1,2)
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(1,2)
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(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
>>> 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.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 [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.
$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]
- m
- Returns
- h
float
Heat transfer coefficient [W/m^2/K]
- h
See also
turbulent_Dittus_Boelter
Forster_Zuber
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.
References
- 1(1,2)
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(1,2)
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(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
>>> 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.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 [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.
$h_{tp} = 30 Re_{lo}^{0.857} Bg^{0.714} \frac{k_l}{D}$$Re_{lo} = \frac{G_{tp}D}{\mu_l}$- Parameters
- Returns
- h
float
Heat transfer coefficient [W/m^2/K]
- h
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.
References
- 1(1,2)
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(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.
- 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
>>> 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 [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.
$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}$- 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]
- m
- Returns
- h
float
Heat transfer coefficient [W/m^2/K]
- h
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.
References
- 1(1,2,3)
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.
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
- 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 [1], also reviewed in [2] and [3].
Excess wall temperature is required to use this correlation.
$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]
- m
- Returns
- h
float
Heat transfer coefficient [W/m^2/K]
- h
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.
References
- 1(1,2,3)
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(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
>>> 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.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 [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.
$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}$- 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]
- m
- Returns
- h
float
Heat transfer coefficient [W/m^2/K]
- h
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.
References
- 1(1,2,3)
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.
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.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 [1] and [2], and also reviewed [3]. 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.
$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$if t dry film > tv:
$\delta_{end}(x) = \delta(z, t_v)$$t_{film} = t_v$$t_{dry} = 0$Otherwise:
$\delta_{end}(z) = \delta_{min}$$t_{film} = t_{dry,film}$$t_{dry} = t_v - t_{film}$- 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]
- m
- Returns
- h
float
Heat transfer coefficient [W/m^2/K]
- h
Notes
[1] and [2] have been reviewed, and are accurately reproduced in [3].
[1] 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
- 1(1,2,3)
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.
- 2(1,2)
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.
- 3(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
>>> 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.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 [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.
$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}$- 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]
- m
- Returns
- h
float
Heat transfer coefficient [W/m^2/K]
- h
Notes
[1] has been reviewed.
References
- 1(1,2)
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.
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