Non boiling and non condensing twophase heat transfer (ht.conv_two_phase)¶

ht.conv_two_phase.
Davis_David
(m, x, D, rhol, rhog, Cpl, kl, mul)[source]¶ Calculates the twophase nonboiling heat transfer coefficient of a liquid and gas flowing inside a tube of any inclination, as in [1] and reviewed in [2].
\[\frac{h_{TP} D}{k_l} = 0.060\left(\frac{\rho_L}{\rho_G}\right)^{0.28} \left(\frac{DG_{TP} x}{\mu_L}\right)^{0.87} \left(\frac{C_{p,L} \mu_L}{k_L}\right)^{0.4}\]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]
 Cpl : float
Constantpressure heat capacity of liquid [J/kg/K]
 kl : float
Thermal conductivity of liquid [W/m/K]
 mul : float
Viscosity of liquid [Pa*s]
Returns:  h : float
Heat transfer coefficient [W/m^2/K]
Notes
Developed for both vertical and horizontal flow, and flow patters of annular or mist annular flow. Steamwater and airwater were the only considered fluid combinations. Quality ranged from 0.1 to 1 in their data. [1] claimed an AAE of 17%.
References
[1] (1, 2, 3) Davis, E. J., and M. M. David. “TwoPhase GasLiquid Convection Heat Transfer. A Correlation.” Industrial & Engineering Chemistry Fundamentals 3, no. 2 (May 1, 1964): 11118. doi:10.1021/i160010a005. [2] (1, 2) Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L. Dougherty. “Comparison of 20 TwoPhase Heat Transfer Correlations with Seven Sets of Experimental Data, Including Flow Pattern and Tube Inclination Effects.” Heat Transfer Engineering 20, no. 1 (February 1, 1999): 1540. doi:10.1080/014576399271691. Examples
>>> Davis_David(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300, kl=.6, ... mul=1E3) 1437.3282869955121

ht.conv_two_phase.
Elamvaluthi_Srinivas
(m, x, D, rhol, rhog, Cpl, kl, mug, mu_b, mu_w=None)[source]¶ Calculates the twophase nonboiling heat transfer coefficient of a liquid and gas flowing inside a tube of any inclination, as in [1] and reviewed in [2].
\[ \begin{align}\begin{aligned}\frac{h_{TP} D}{k_L} = 0.5\left(\frac{\mu_G}{\mu_L}\right)^{0.25} Re_M^{0.7} Pr^{1/3}_L (\mu_b/\mu_w)^{0.14}\\Re_M = \frac{D V_L \rho_L}{\mu_L} + \frac{D V_g \rho_g}{\mu_g}\end{aligned}\end{align} \]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]
 Cpl : float
Constantpressure heat capacity of liquid [J/kg/K]
 kl : float
Thermal conductivity of liquid [W/m/K]
 mug : float
Viscosity of gas [Pa*s]
 mu_b : float
Viscosity of liquid at bulk conditions (average of inlet/outlet temperature) [Pa*s]
 mu_w : float, optional
Viscosity of liquid at wall temperature [Pa*s]
Returns:  h : float
Heat transfer coefficient [W/m^2/K]
Notes
If the viscosity at the wall temperature is not given, the liquid viscosity correction is not applied.
Developed for vertical flow, and flow patters of bubbly and slug. Gas/liquid superficial velocity ratios from 0.3 to 4.6, liquid mass fluxes from 200 to 1600 kg/m^2/s, and the fluids tested were airwater and airaqueous glycerine solutions. The tube inner diameter was 1 cm, and the L/D ratio was 86.
References
[1] (1, 2) Elamvaluthi, G., and N. S. Srinivas. “TwoPhase Heat Transfer in Two Component Vertical Flows.” International Journal of Multiphase Flow 10, no. 2 (April 1, 1984): 23742. doi:10.1016/03019322(84)900211. [2] (1, 2) Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L. Dougherty. “Comparison of 20 TwoPhase Heat Transfer Correlations with Seven Sets of Experimental Data, Including Flow Pattern and Tube Inclination Effects.” Heat Transfer Engineering 20, no. 1 (February 1, 1999): 1540. doi:10.1080/014576399271691. Examples
>>> Elamvaluthi_Srinivas(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300, ... kl=.6, mug=1E5, mu_b=1E3, mu_w=1.2E3) 3901.2134471578584

ht.conv_two_phase.
Groothuis_Hendal
(m, x, D, rhol, rhog, Cpl, kl, mug, mu_b, mu_w=None, water=False)[source]¶ Calculates the twophase nonboiling heat transfer coefficient of a liquid and gas flowing inside a tube of any inclination, as in [1] and reviewed in [2].
\[Re_M = \frac{D V_{ls} \rho_l}{\mu_l} + \frac{D V_{gs} \rho_g}{\mu_g}\]For the airwater system:
\[\frac{h_{TP} D}{k_L} = 0.029 Re_M^{0.87}Pr^{1/3}_l (\mu_b/\mu_w)^{0.14}\]For gas/airoil systems (default):
\[\frac{h_{TP} D}{k_L} = 2.6 Re_M^{0.39}Pr^{1/3}_l (\mu_b/\mu_w)^{0.14}\]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]
 Cpl : float
Constantpressure heat capacity of liquid [J/kg/K]
 kl : float
Thermal conductivity of liquid [W/m/K]
 mug : float
Viscosity of gas [Pa*s]
 mu_b : float
Viscosity of liquid at bulk conditions (average of inlet/outlet temperature) [Pa*s]
 mu_w : float, optional
Viscosity of liquid at wall temperature [Pa*s]
 water : bool, optional
Whether to use the waterair correlation or the gas/airoil correlation
Returns:  h : float
Heat transfer coefficient [W/m^2/K]
Notes
If the viscosity at the wall temperature is not given, the liquid viscosity correction is not applied.
Developed for vertical pipes, with superficial velocity ratios of 0.6250. Tested fluids were airwater, and gas/airoil.
References
[1] (1, 2) Groothuis, H., and W. P. Hendal. “Heat Transfer in TwoPhase Flow.: Chemical Engineering Science 11, no. 3 (November 1, 1959): 21220. doi:10.1016/00092509(59)800890. [2] (1, 2) Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L. Dougherty. “Comparison of 20 TwoPhase Heat Transfer Correlations with Seven Sets of Experimental Data, Including Flow Pattern and Tube Inclination Effects.” Heat Transfer Engineering 20, no. 1 (February 1, 1999): 1540. doi:10.1080/014576399271691. Examples
>>> Groothuis_Hendal(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300, kl=.6, ... mug=1E5, mu_b=1E3, mu_w=1.2E3) 1192.9543445455754

ht.conv_two_phase.
Hughmark
(m, x, alpha, D, L, Cpl, kl, mu_b=None, mu_w=None)[source]¶ Calculates the twophase nonboiling laminar heat transfer coefficient of a liquid and gas flowing inside a tube of any inclination, as in [1] and reviewed in [2].
\[\frac{h_{TP} D}{k_l} = 1.75(1\alpha)^{0.5}\left(\frac{m_l C_{p,l}} {(1\alpha)k_l L}\right)^{1/3}\left(\frac{\mu_b}{\mu_w}\right)^{0.14}\]Parameters:  m : float
Mass flow rate [kg/s]
 x : float
Quality at the specific tube interval []
 alpha : float
Void fraction in the tube, []
 D : float
Diameter of the tube [m]
 L : float
Length of the tube, [m]
 Cpl : float
Constantpressure heat capacity of liquid [J/kg/K]
 kl : float
Thermal conductivity of liquid [W/m/K]
 mu_b : float
Viscosity of liquid at bulk conditions (average of inlet/outlet temperature) [Pa*s]
 mu_w : float, optional
Viscosity of liquid at wall temperature [Pa*s]
Returns:  h : float
Heat transfer coefficient [W/m^2/K]
Notes
This model is based on a laminar entry length correlation  for a sufficiently long tube, this will predict unrealistically low heat transfer coefficients.
If the viscosity at the wall temperature is not given, the liquid viscosity correction is not applied.
Developed for horizontal pipes in laminar slug flow. Data consisted of the systems airwater, airSAE 10 oil, gasoil, airdiethylene glycol, and airaqueous glycerine.
References
[1] (1, 2) Hughmark, G. A. “Holdup and Heat Transfer in Horizontal Slug Gas Liquid Flow.” Chemical Engineering Science 20, no. 12 (December 1, 1965): 100710. doi:10.1016/00092509(65)801014. [2] (1, 2) Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L. Dougherty. “Comparison of 20 TwoPhase Heat Transfer Correlations with Seven Sets of Experimental Data, Including Flow Pattern and Tube Inclination Effects.” Heat Transfer Engineering 20, no. 1 (February 1, 1999): 1540. doi:10.1080/014576399271691. Examples
>>> Hughmark(m=1, x=.9, alpha=.9, D=.3, L=.5, Cpl=2300, kl=0.6, mu_b=1E3, ... mu_w=1.2E3) 212.7411636127175

ht.conv_two_phase.
Knott
(m, x, D, rhol, rhog, Cpl=None, kl=None, mu_b=None, mu_w=None, L=None, hl=None)[source]¶ Calculates the twophase nonboiling heat transfer coefficient of a liquid and gas flowing inside a tube of any inclination, as in [1] and reviewed in [2].
Either a specified hl is required, or Cpl, kl, mu_b, mu_w and L are required to calculate hl.
\[\frac{h_{TP}}{h_l} = \left(1 + \frac{V_{gs}}{V_{ls}}\right)^{1/3}\]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]
 Cpl : float, optional
Constantpressure heat capacity of liquid [J/kg/K]
 kl : float, optional
Thermal conductivity of liquid [W/m/K]
 mu_b : float, optional
Viscosity of liquid at bulk conditions (average of inlet/outlet temperature) [Pa*s]
 mu_w : float, optional
Viscosity of liquid at wall temperature [Pa*s]
 L : float, optional
Length of the tube [m]
 hl : float, optional
Liquidphase heat transfer coefficient as described below, [W/m^2/K]
Returns:  h : float
Heat transfer coefficient [W/m^2/K]
Notes
The liquidonly heat transfer coefficient will be calculated with the laminar_entry_Seider_Tate correlation, should it not be provided as an input. Many of the arguments to this function are optional and are only used if hl is not provided.
hl should be calculated with a velocity equal to that determined with a combined volumetric flow of both the liquid and the gas. All other parameters used in calculating the heat transfer coefficient are those of the liquid. If the viscosity at the wall temperature is not given, the liquid viscosity correction in laminar_entry_Seider_Tate is not applied.
References
[1] (1, 2) Knott, R. F., R. N. Anderson, Andreas. Acrivos, and E. E. Petersen. “An Experimental Study of Heat Transfer to NitrogenOil Mixtures.” Industrial & Engineering Chemistry 51, no. 11 (November 1, 1959): 136972. doi:10.1021/ie50599a032. [2] (1, 2) Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L. Dougherty. “Comparison of 20 TwoPhase Heat Transfer Correlations with Seven Sets of Experimental Data, Including Flow Pattern and Tube Inclination Effects.” Heat Transfer Engineering 20, no. 1 (February 1, 1999): 1540. doi:10.1080/014576399271691. Examples
>>> Knott(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300, kl=.6, mu_b=1E3, ... mu_w=1.2E3, L=4) 4225.536758045839

ht.conv_two_phase.
Kudirka_Grosh_McFadden
(m, x, D, rhol, rhog, Cpl, kl, mug, mu_b, mu_w=None)[source]¶ Calculates the twophase nonboiling heat transfer coefficient of a liquid and gas flowing inside a tube of any inclination, as in [1] and reviewed in [2].
\[Nu = \frac{h_{TP} D}{k_l} = 125 \left(\frac{V_{gs}}{V_{ls}} \right)^{0.125}\left(\frac{\mu_g}{\mu_l}\right)^{0.6} Re_{ls}^{0.25} Pr_l^{1/3}\left(\frac{\mu_b}{\mu_w}\right)^{0.14}\]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]
 Cpl : float
Constantpressure heat capacity of liquid [J/kg/K]
 kl : float
Thermal conductivity of liquid [W/m/K]
 mug : float
Viscosity of gas [Pa*s]
 mu_b : float
Viscosity of liquid at bulk conditions (average of inlet/outlet temperature) [Pa*s]
 mu_w : float, optional
Viscosity of liquid at wall temperature [Pa*s]
Returns:  h : float
Heat transfer coefficient [W/m^2/K]
Notes
If the viscosity at the wall temperature is not given, the liquid viscosity correction is not applied.
Developed for airwater and airethylene glycol systems with a L/D of 17.6 and at low gasliquid ratios. The flow regimes studied were bubble, slug, and froth flow.
References
[1] (1, 2) Kudirka, A. A., R. J. Grosh, and P. W. McFadden. “Heat Transfer in TwoPhase Flow of GasLiquid Mixtures.” Industrial & Engineering Chemistry Fundamentals 4, no. 3 (August 1, 1965): 33944. doi:10.1021/i160015a018. [2] (1, 2) Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L. Dougherty. “Comparison of 20 TwoPhase Heat Transfer Correlations with Seven Sets of Experimental Data, Including Flow Pattern and Tube Inclination Effects.” Heat Transfer Engineering 20, no. 1 (February 1, 1999): 1540. doi:10.1080/014576399271691. Examples
>>> Kudirka_Grosh_McFadden(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300, ... kl=.6, mug=1E5, mu_b=1E3, mu_w=1.2E3) 303.9941255903587

ht.conv_two_phase.
Martin_Sims
(m, x, D, rhol, rhog, hl)[source]¶ Calculates the twophase nonboiling heat transfer coefficient of a liquid and gas flowing inside a tube of any inclination, as in [1] and reviewed in [2].
\[\frac{h_{TP}}{h_l} = 1 + 0.64\sqrt{\frac{V_{gs}}{V_{ls}}}\]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]
 hl : float
Liquidphase heat transfer coefficient as described below, [W/m^2/K]
Returns:  h : float
Heat transfer coefficient [W/m^2/K]
Notes
No suggestion for how to calculate the liquidphase heat transfer coefficient is given in [1]; [2] suggests to use the same procedure as in Knott, but this has not been implemented.
References
[1] (1, 2, 3) Martin, B. W, and G. E Sims. “Forced Convection Heat Transfer to Water with Air Injection in a Rectangular Duct.” International Journal of Heat and Mass Transfer 14, no. 8 (August 1, 1971): 111534. doi:10.1016/00179310(71)902080. [2] (1, 2, 3) Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L. Dougherty. “Comparison of 20 TwoPhase Heat Transfer Correlations with Seven Sets of Experimental Data, Including Flow Pattern and Tube Inclination Effects.” Heat Transfer Engineering 20, no. 1 (February 1, 1999): 1540. doi:10.1080/014576399271691. Examples
>>> Martin_Sims(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, hl=141.2) 5563.280000000001

ht.conv_two_phase.
Ravipudi_Godbold
(m, x, D, rhol, rhog, Cpl, kl, mug, mu_b, mu_w=None)[source]¶ Calculates the twophase nonboiling heat transfer coefficient of a liquid and gas flowing inside a tube of any inclination, as in [1] and reviewed in [2].
\[Nu = \frac{h_{TP} D}{k_l} = 0.56 \left(\frac{V_{gs}}{V_{ls}} \right)^{0.3}\left(\frac{\mu_g}{\mu_l}\right)^{0.2} Re_{ls}^{0.6} Pr_l^{1/3}\left(\frac{\mu_b}{\mu_w}\right)^{0.14}\]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]
 Cpl : float
Constantpressure heat capacity of liquid [J/kg/K]
 kl : float
Thermal conductivity of liquid [W/m/K]
 mug : float
Viscosity of gas [Pa*s]
 mu_b : float
Viscosity of liquid at bulk conditions (average of inlet/outlet temperature) [Pa*s]
 mu_w : float, optional
Viscosity of liquid at wall temperature [Pa*s]
Returns:  h : float
Heat transfer coefficient [W/m^2/K]
Notes
If the viscosity at the wall temperature is not given, the liquid viscosity correction is not applied.
Developed with a vertical pipe, superficial gas/liquid velocity ratios of 190, in the froth regime, and for fluid mixtures of air and water, toluene, benzene, and methanol.
References
[1] (1, 2) Ravipudi, S., and Godbold, T., The Effect of Mass Transfer on Heat Transfer Rates for TwoPhase Flow in a Vertical Pipe, Proceedings 6th International Heat Transfer Conference, Toronto, V. 1, p. 505510, 1978. [2] (1, 2) Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L. Dougherty. “Comparison of 20 TwoPhase Heat Transfer Correlations with Seven Sets of Experimental Data, Including Flow Pattern and Tube Inclination Effects.” Heat Transfer Engineering 20, no. 1 (February 1, 1999): 1540. doi:10.1080/014576399271691. Examples
>>> Ravipudi_Godbold(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300, kl=.6, mug=1E5, mu_b=1E3, mu_w=1.2E3) 299.3796286459285

ht.conv_two_phase.
Aggour
(m, x, alpha, D, rhol, Cpl, kl, mu_b, mu_w=None, L=None, turbulent=None)[source]¶ Calculates the twophase nonboiling laminar heat transfer coefficient of a liquid and gas flowing inside a tube of any inclination, as in [1] and reviewed in [2].
Laminar for Rel <= 2000:
\[h_{TP} = 1.615\frac{k_l}{D}\left(\frac{Re_l Pr_l D}{L}\right)^{1/3} \left(\frac{\mu_b}{\mu_w}\right)^{0.14}\]Turbulent for Rel > 2000:
\[ \begin{align}\begin{aligned}h_{TP} = 0.0155\frac{k_l}{D} Pr_l^{0.5} Re_l^{0.83}\\Re_l = \frac{\rho_l v_l D}{\mu_l}\\V_l = \frac{V_{ls}}{1\alpha}\end{aligned}\end{align} \]Parameters:  m : float
Mass flow rate [kg/s]
 x : float
Quality at the specific tube interval []
 alpha : float
Void fraction in the tube, []
 D : float
Diameter of the tube [m]
 rhol : float
Density of the liquid [kg/m^3]
 Cpl : float
Constantpressure heat capacity of liquid [J/kg/K]
 kl : float
Thermal conductivity of liquid [W/m/K]
 mu_b : float
Viscosity of liquid at bulk conditions (average of inlet/outlet temperature) [Pa*s]
 mu_w : float, optional
Viscosity of liquid at wall temperature [Pa*s]
 L : float, optional
Length of the tube, [m]
 turbulent : bool or None, optional
Whether or not to force the correlation to return the turbulent result; will return the laminar regime if False
Returns:  h : float
Heat transfer coefficient [W/m^2/K]
Notes
Developed with mixtures of airwater, heliumwater, and freon12water and vertical tests. Studied flow patterns were bubbly, slug, annular, bubblyslug, and slugannular regimes. Superficial velocity ratios ranged from 0.02 to 470.
A viscosity correction is only suggested for the laminar regime. If the viscosity at the wall temperature is not given, the liquid viscosity correction is not applied.
References
[1] (1, 2) Aggour, Mohamed A. Hydrodynamics and Heat Transfer in TwoPhase TwoComponent Flows, Ph.D. Thesis, University of Manutoba, Canada (1978). http://mspace.lib.umanitoba.ca/xmlui/handle/1993/14171. [2] (1, 2) Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L. Dougherty. “Comparison of 20 TwoPhase Heat Transfer Correlations with Seven Sets of Experimental Data, Including Flow Pattern and Tube Inclination Effects.” Heat Transfer Engineering 20, no. 1 (February 1, 1999): 1540. doi:10.1080/014576399271691. Examples
>>> Aggour(m=1, x=.9, D=.3, alpha=.9, rhol=1000, Cpl=2300, kl=.6, mu_b=1E3) 420.9347146885667