# Boiling in plate and frame exchangers (ht.boiling_plate)¶

ht.boiling_plate.h_boiling_Amalfi(m, x, Dh, rhol, rhog, mul, mug, kl, Hvap, sigma, q, A_channel_flow, chevron_angle=45)[source]

Calculates the two-phase boiling heat transfer coefficient of a liquid and gas flowing inside a plate and frame heat exchanger, as developed in [R117134] from a wide range of existing correlations and data sets. Expected to be the most accurate correlation currently available.

For Bond number < 4 (tiny channel case):

$h= 982 \left(\frac{k_l}{D_h}\right)\left(\frac{\beta}{\beta_{max}}\right)^{1.101} \left(\frac{G^2 D_h}{\rho_m \sigma}\right)^{0.315} \left(\frac{\rho_l}{\rho_g}\right)^{-0.224} Bo^{0.320}$

For Bond number >= 4:

$h = 18.495 \left(\frac{k_l}{D_h}\right) \left(\frac{\beta}{\beta_{max}} \right)^{0.248}\left(Re_g\right)^{0.135}\left(Re_{lo}\right)^{0.351} \left(\frac{\rho_l}{\rho_g}\right)^{-0.223} Bd^{0.235} Bo^{0.198}$

In the above equations, beta max is 45 degrees; Bo is Boiling number; and Bd is Bond number.

Note that this model depends on the specific heat flux involved.

Parameters: m : float Mass flow rate [kg/s] x : float Quality at the specific point in the plate exchanger [] Dh : float Hydraulic diameter of the plate, $$D_h = \frac{4\lambda}{\phi}$$ [m] rhol : float Density of the liquid [kg/m^3] rhog : float Density of the gas [kg/m^3] mul : float Viscosity of the liquid [Pa*s] mug : float Viscosity of the gas [Pa*s] kl : float Thermal conductivity of liquid [W/m/K] Hvap : float Heat of vaporization of the fluid at the system pressure, [J/kg] sigma : float Surface tension of liquid [N/m] q : float Heat flux, [W/m^2] A_channel_flow : float The flow area for the fluid, calculated as $$A_{ch} = 2\cdot \text{width} \cdot \text{amplitude}$$ [m] chevron_angle : float, optional Angle of the plate corrugations with respect to the vertical axis (the direction of flow if the plates were straight), between 0 and 90. For exchangers with two angles, use the average value. [degrees] h : float Boiling heat transfer coefficient [W/m^2/K]

Notes

Heat transfer correlation developed from 1903 datum. Fluids included R134a, ammonia, R236fa, R600a, R290, R1270, R1234yf, R410A, R507A, ammonia/water, and air/water mixtures. Wide range of operating conditions, plate geometries.

References

 [R117134] (1, 2) Amalfi, Raffaele L., Farzad Vakili-Farahani, and John R. Thome. “Flow Boiling and Frictional Pressure Gradients in Plate Heat Exchangers. Part 2: Comparison of Literature Methods to Database and New Prediction Methods.” International Journal of Refrigeration 61 (January 2016): 185-203. doi:10.1016/j.ijrefrig.2015.07.009.

Examples

>>> h_boiling_Amalfi(m=3E-5, x=.4, Dh=0.00172, rhol=567., rhog=18.09,
... kl=0.086, mul=156E-6, mug=7.11E-6, sigma=0.02, Hvap=9E5, q=1E5,
... A_channel_flow=0.0003)
776.0781179096225

ht.boiling_plate.h_boiling_Lee_Kang_Kim(m, x, D_eq, rhol, rhog, mul, mug, kl, Hvap, q, A_channel_flow)[source]

Calculates the two-phase boiling heat transfer coefficient of a liquid and gas flowing inside a plate and frame heat exchanger, as shown in [R118135] and reviewed in [R119135].

For $$Re_g/Re_l < 9$$:

$h = 98.7 \left(\frac{k_l}{D_h}\right)\left(\frac{Re_g}{Re_l} \right)^{-0.0848}Bo^{-0.0597} X_{tt}^{0.0973}$

For $$Re_g/Re_l \ge 9$$:

$h = 234.9 \left(\frac{k_l}{D_h}\right)\left(\frac{Re_g}{Re_l} \right)^{-0.576} Bo^{-0.275} X_{tt}^{0.66}$
$X_{tt} = \left(\frac{1-x}{x}\right)^{0.875} \left(\frac{\rho_g}{\rho_l} \right)^{0.5}\left(\frac{\mu_l}{\mu_g}\right)^{0.125}$

In the above equations, Bo is Boiling number.

Note that this model depends on the specific heat flux involved. It also uses equivalent diameter, not hydraulic diameter.

Parameters: m : float Mass flow rate [kg/s] x : float Quality at the specific point in the plate exchanger [] D_eq : float Equivalent diameter of the channels, $$D_{eq} = 4a$$ [m] rhol : float Density of the liquid [kg/m^3] rhog : float Density of the gas [kg/m^3] mul : float Viscosity of the liquid [Pa*s] mug : float Viscosity of the gas [Pa*s] kl : float Thermal conductivity of liquid [W/m/K] Hvap : float Heat of vaporization of the fluid at the system pressure, [J/kg] q : float Heat flux, [W/m^2] A_channel_flow : float The flow area for the fluid, calculated as $$A_{ch} = 2\cdot \text{width} \cdot \text{amplitude}$$ [m] h : float Boiling heat transfer coefficient [W/m^2/K]

Notes

This correlation was developed with mass fluxes from 14.5 to 33.6 kg/m^2/s, heat flux from 15 to 30 kW/m^2, qualities from 0.09 to 0.6, 200 < Re < 600, 2.3 < Re_g/Re_l < 32.1, 0.00019 < Bo < 0.001, 0.028 < Xtt < 0.3. Mean average deviation of 4.4%.

References

 [R118135] (1, 2) Lee, Eungchan, Hoon Kang, and Yongchan Kim. “Flow Boiling Heat Transfer and Pressure Drop of Water in a Plate Heat Exchanger with Corrugated Channels at Low Mass Flux Conditions.” International Journal of Heat and Mass Transfer 77 (October 2014): 37-45. doi:10.1016/j.ijheatmasstransfer.2014.05.019.
 [R119135] (1, 2) Amalfi, Raffaele L., Farzad Vakili-Farahani, and John R. Thome. “Flow Boiling and Frictional Pressure Gradients in Plate Heat Exchangers. Part 1: Review and Experimental Database.” International Journal of Refrigeration 61 (January 2016): 166-84. doi:10.1016/j.ijrefrig.2015.07.010.

Examples

>>> h_boiling_Lee_Kang_Kim(m=3E-5, x=.4, D_eq=0.002, rhol=567., rhog=18.09,
... kl=0.086, mul=156E-6, mug=9E-6, Hvap=9E5, q=1E5, A_channel_flow=0.0003)
1229.6271295086806

ht.boiling_plate.h_boiling_Han_Lee_Kim(m, x, Dh, rhol, rhog, mul, kl, Hvap, Cpl, q, A_channel_flow, wavelength, chevron_angle=45)[source]

Calculates the two-phase boiling heat transfer coefficient of a liquid and gas flowing inside a plate and frame heat exchanger, as developed in [R120137] from experiments with three plate exchangers and the working fluids R410A and R22. A well-documented and tested correlation, reviewed in [R121137], [R122137], [R123137], [R124137], and [R125137].

\begin{align}\begin{aligned}h = Ge_1\left(\frac{k_l}{D_h}\right)Re_{eq}^{Ge_2} Pr^{0.4} Bo_{eq}^{0.3}\\Ge_1 = 2.81\left(\frac{\lambda}{D_h}\right)^{-0.041}\left(\frac{\pi}{2} -\beta\right)^{-2.83}\\Ge_2 = 0.746\left(\frac{\lambda}{D_h}\right)^{-0.082}\left(\frac{\pi} {2}-\beta\right)^{0.61}\\Re_{eq} = \frac{G_{eq} D_h}{\mu_l}\\Bo_{eq} = \frac{q}{G_{eq} H_{vap}}\\G_{eq} = \frac{m}{A_{flow}}\left[1 - x + x\left(\frac{\rho_l}{\rho_g} \right)^{1/2}\right]\end{aligned}\end{align}

In the above equations, lambda is the wavelength of the corrugations, and the flow area is specified to be (twice the corrugation amplitude times the width of the plate. The mass flow is that per channel. Radians is used in degrees, and the formulas are for the inclination angle not the chevron angle (it is converted internally). Note that this model depends on the specific heat flux involved.

Parameters: m : float Mass flow rate [kg/s] x : float Quality at the specific point in the plate exchanger [] Dh : float Hydraulic diameter of the plate, $$D_h = \frac{4\lambda}{\phi}$$ [m] rhol : float Density of the liquid [kg/m^3] rhog : float Density of the gas [kg/m^3] mul : float Viscosity of the liquid [Pa*s] kl : float Thermal conductivity of liquid [W/m/K] Hvap : float Heat of vaporization of the fluid at the system pressure, [J/kg] Cpl : float Heat capacity of liquid [J/kg/K] q : float Heat flux, [W/m^2] A_channel_flow : float The flow area for the fluid, calculated as $$A_{ch} = 2\cdot \text{width} \cdot \text{amplitude}$$ [m] wavelength : float Distance between the bottoms of two of the ridges (sometimes called pitch), [m] chevron_angle : float, optional Angle of the plate corrugations with respect to the vertical axis (the direction of flow if the plates were straight), between 0 and 90. For exchangers with two angles, use the average value. [degrees] h : float Boiling heat transfer coefficient [W/m^2/K]

Notes

Date regression was with the log mean temperature difference, uncorrected for geometry. Developed with three plate heat exchangers with angles of 45, 35, and 20 degrees. Mass fluxes ranged from 13 to 34 kg/m^2/s; evaporating temperatures of 5, 10, and 15 degrees, vapor quality 0.9 to 0.15, heat fluxes of 2.5-8.5 kW/m^2.

References

 [R120137] (1, 2) Han, Dong-Hyouck, Kyu-Jung Lee, and Yoon-Ho Kim. “Experiments on the Characteristics of Evaporation of R410A in Brazed Plate Heat Exchangers with Different Geometric Configurations.” Applied Thermal Engineering 23, no. 10 (July 2003): 1209-25. doi:10.1016/S1359-4311(03)00061-9.
 [R121137] (1, 2) Amalfi, Raffaele L., Farzad Vakili-Farahani, and John R. Thome. “Flow Boiling and Frictional Pressure Gradients in Plate Heat Exchangers. Part 1: Review and Experimental Database.” International Journal of Refrigeration 61 (January 2016): 166-84. doi:10.1016/j.ijrefrig.2015.07.010.
 [R122137] (1, 2) Eldeeb, Radia, Vikrant Aute, and Reinhard Radermacher. “A Survey of Correlations for Heat Transfer and Pressure Drop for Evaporation and Condensation in Plate Heat Exchangers.” International Journal of Refrigeration 65 (May 2016): 12-26. doi:10.1016/j.ijrefrig.2015.11.013.
 [R123137] (1, 2) Solotych, Valentin, Donghyeon Lee, Jungho Kim, Raffaele L. Amalfi, and John R. Thome. “Boiling Heat Transfer and Two-Phase Pressure Drops within Compact Plate Heat Exchangers: Experiments and Flow Visualizations.” International Journal of Heat and Mass Transfer 94 (March 2016): 239-253. doi:10.1016/j.ijheatmasstransfer.2015.11.037.
 [R124137] (1, 2) García-Cascales, J. R., F. Vera-García, J. M. Corberán-Salvador, and J. Gonzálvez-Maciá. “Assessment of Boiling and Condensation Heat Transfer Correlations in the Modelling of Plate Heat Exchangers.” International Journal of Refrigeration 30, no. 6 (September 2007): 1029-41. doi:10.1016/j.ijrefrig.2007.01.004.
 [R125137] (1, 2) Huang, Jianchang. “Performance Analysis of Plate Heat Exchangers Used as Refrigerant Evaporators,” 2011. Thesis. http://wiredspace.wits.ac.za/handle/10539/9779

Examples

>>> h_boiling_Han_Lee_Kim(m=3E-5, x=.4, Dh=0.002, rhol=567., rhog=18.09,
... kl=0.086, mul=156E-6,  Hvap=9E5, Cpl=2200, q=1E5, A_channel_flow=0.0003,
... wavelength=3.7E-3, chevron_angle=45)
675.7322255419421

ht.boiling_plate.h_boiling_Huang_Sheer(rhol, rhog, mul, kl, Hvap, sigma, Cpl, q, Tsat, angle=35.0)[source]

Calculates the two-phase boiling heat transfer coefficient of a liquid and gas flowing inside a plate and frame heat exchanger, as developed in [R126143] and again in the thesis [R127143]. Depends on the properties of the fluid and not the heat exchanger’s geometry.

\begin{align}\begin{aligned}h = 1.87\times10^{-3}\left(\frac{k_l}{d_o}\right)\left(\frac{q d_o} {k_l T_{sat}}\right)^{0.56} \left(\frac{H_{vap} d_o^2}{\alpha_l^2}\right)^{0.31} Pr_l^{0.33}\\\begin{split}d_o = 0.0146\theta\left[\frac{2\sigma}{g(\rho_l-\rho_g)}\right]^{0.5}\\ \theta = 35^\circ\end{split}\end{aligned}\end{align}

Note that this model depends on the specific heat flux involved and the saturation temperature of the fluid.

Parameters: rhol : float Density of the liquid [kg/m^3] rhog : float Density of the gas [kg/m^3] mul : float Viscosity of the liquid [Pa*s] kl : float Thermal conductivity of liquid [W/m/K] Hvap : float Heat of vaporization of the fluid at the system pressure, [J/kg] sigma : float Surface tension of liquid [N/m] Cpl : float Heat capacity of liquid [J/kg/K] q : float Heat flux, [W/m^2] Tsat : float Actual saturation temperature of the fluid at the system pressure, [K] angle : float, optional Contact angle of the bubbles with the wall, assumed 35 for refrigerants in the development of the correlation [degrees] h : float Boiling heat transfer coefficient [W/m^2/K]

Notes

Developed with 222 data points for R134a and R507A with only two of them for ammonia and R12. Chevron angles ranged from 28 to 60 degrees, heat fluxes from 1.85 kW/m^2 to 10.75 kW/m^2, mass fluxes 5.6 to 52.25 kg/m^2/s, qualities from 0.21 to 0.95, and saturation temperatures in degrees Celcius of 1.9 to 13.04.

The inclusion of the saturation temperature makes this correlation have limited predictive power for other fluids whose saturation tempratures might be much higher or lower than those used in the development of the correlation. For this reason it should be regarded with caution.

As first published in [R126143] a power of two was missing in the correlation for bubble diameter in the dimensionless group with a power of 0.31. That made the correlation non-dimensional.

A second variant of this correlation was also published in [R127143] but with less accuracy because it was designed to mimick the standard pool boiling curve.

The correlation is reviewed in [R128143], but without the corrected power. It was also changed there to use hydraulic diameter, not bubble diameter. It still ranked as one of the more accurate correlations reviewed. [R129143] also reviewed it without the corrected power but found it predicted the lowest results of those surveyed.

References

 [R126143] (1, 2, 3) Huang, Jianchang, Thomas J. Sheer, and Michael Bailey-McEwan. “Heat Transfer and Pressure Drop in Plate Heat Exchanger Refrigerant Evaporators.” International Journal of Refrigeration 35, no. 2 (March 2012): 325-35. doi:10.1016/j.ijrefrig.2011.11.002.
 [R127143] (1, 2, 3) Huang, Jianchang. “Performance Analysis of Plate Heat Exchangers Used as Refrigerant Evaporators,” 2011. Thesis. http://wiredspace.wits.ac.za/handle/10539/9779
 [R128143] (1, 2) Amalfi, Raffaele L., Farzad Vakili-Farahani, and John R. Thome. “Flow Boiling and Frictional Pressure Gradients in Plate Heat Exchangers. Part 1: Review and Experimental Database.” International Journal of Refrigeration 61 (January 2016): 166-84. doi:10.1016/j.ijrefrig.2015.07.010.
 [R129143] (1, 2) Eldeeb, Radia, Vikrant Aute, and Reinhard Radermacher. “A Survey of Correlations for Heat Transfer and Pressure Drop for Evaporation and Condensation in Plate Heat Exchangers.” International Journal of Refrigeration 65 (May 2016): 12-26. doi:10.1016/j.ijrefrig.2015.11.013.

Examples

>>> h_boiling_Huang_Sheer(rhol=567., rhog=18.09, kl=0.086, mul=156E-6,
... Hvap=9E5, sigma=0.02, Cpl=2200, q=1E4, Tsat=279.15)
4401.055635078054

ht.boiling_plate.h_boiling_Yan_Lin(m, x, Dh, rhol, rhog, mul, kl, Hvap, Cpl, q, A_channel_flow)[source]

Calculates the two-phase boiling heat transfer coefficient of a liquid and gas flowing inside a plate and frame heat exchanger, as developed in [R130147]. Reviewed in [R131147], [R132147], [R133147], and [R134147].

\begin{align}\begin{aligned}h = 1.926\left(\frac{k_l}{D_h}\right) Re_{eq} Pr_l^{1/3} Bo_{eq}^{0.3} Re^{-0.5}\\Re_{eq} = \frac{G_{eq} D_h}{\mu_l}\\Bo_{eq} = \frac{q}{G_{eq} H_{vap}}\\G_{eq} = \frac{m}{A_{flow}}\left[1 - x + x\left(\frac{\rho_l}{\rho_g} \right)^{1/2}\right]\\Re = \frac{G D_h}{\mu_l}\end{aligned}\end{align}

Claimed to be valid for $$2000 < Re_{eq} < 10000$$.

Parameters: m : float Mass flow rate [kg/s] x : float Quality at the specific point in the plate exchanger [] Dh : float Hydraulic diameter of the plate, $$D_h = \frac{4\lambda}{\phi}$$ [m] rhol : float Density of the liquid [kg/m^3] rhog : float Density of the gas [kg/m^3] mul : float Viscosity of the liquid [Pa*s] kl : float Thermal conductivity of liquid [W/m/K] Hvap : float Heat of vaporization of the fluid at the system pressure, [J/kg] Cpl : float Heat capacity of liquid [J/kg/K] q : float Heat flux, [W/m^2] A_channel_flow : float The flow area for the fluid, calculated as $$A_{ch} = 2\cdot \text{width} \cdot \text{amplitude}$$ [m] h : float Boiling heat transfer coefficient [W/m^2/K]

Notes

Developed with R134a as the refrigerant in a PHD with 2 channels, chevron angle 60 degrees, quality from 0.1 to 0.8, heat flux 11-15 kW/m^2, and mass fluxes of 55 and 70 kg/m^2/s.

References

 [R130147] (1, 2) Yan, Y.-Y., and T.-F. Lin. “Evaporation Heat Transfer and Pressure Drop of Refrigerant R-134a in a Plate Heat Exchanger.” Journal of Heat Transfer 121, no. 1 (February 1, 1999): 118-27. doi:10.1115/1.2825924.
 [R131147] (1, 2) Amalfi, Raffaele L., Farzad Vakili-Farahani, and John R. Thome. “Flow Boiling and Frictional Pressure Gradients in Plate Heat Exchangers. Part 1: Review and Experimental Database.” International Journal of Refrigeration 61 (January 2016): 166-84. doi:10.1016/j.ijrefrig.2015.07.010.
 [R132147] (1, 2) Eldeeb, Radia, Vikrant Aute, and Reinhard Radermacher. “A Survey of Correlations for Heat Transfer and Pressure Drop for Evaporation and Condensation in Plate Heat Exchangers.” International Journal of Refrigeration 65 (May 2016): 12-26. doi:10.1016/j.ijrefrig.2015.11.013.
 [R133147] (1, 2) García-Cascales, J. R., F. Vera-García, J. M. Corberán-Salvador, and J. Gonzálvez-Maciá. “Assessment of Boiling and Condensation Heat Transfer Correlations in the Modelling of Plate Heat Exchangers.” International Journal of Refrigeration 30, no. 6 (September 2007): 1029-41. doi:10.1016/j.ijrefrig.2007.01.004.
 [R134147] (1, 2) Huang, Jianchang. “Performance Analysis of Plate Heat Exchangers Used as Refrigerant Evaporators,” 2011. Thesis. http://wiredspace.wits.ac.za/handle/10539/9779

Examples

>>> h_boiling_Yan_Lin(m=3E-5, x=.4, Dh=0.002, rhol=567., rhog=18.09,
... kl=0.086, Cpl=2200, mul=156E-6, Hvap=9E5, q=1E5, A_channel_flow=0.0003)
318.7228565961241