# Non boiling and non condensing two-phase heat transfer (ht.conv_two_phase)¶

ht.conv_two_phase.Davis_David(m, x, D, rhol, rhog, Cpl, kl, mul)[source]

Calculates the two-phase non-boiling 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 Constant-pressure heat capacity of liquid [J/kg/K] kl : float Thermal conductivity of liquid [W/m/K] mul : float Viscosity of liquid [Pa*s] 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. Steam-water and air-water 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. “Two-Phase Gas-Liquid Convection Heat Transfer. A Correlation.” Industrial & Engineering Chemistry Fundamentals 3, no. 2 (May 1, 1964): 111-18. doi:10.1021/i160010a005.
 [2] (1, 2) Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L. Dougherty. “Comparison of 20 Two-Phase 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): 15-40. doi:10.1080/014576399271691.

Examples

>>> Davis_David(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300, kl=.6,
... mul=1E-3)
1437.3282869955121

ht.conv_two_phase.Elamvaluthi_Srinivas(m, x, D, rhol, rhog, Cpl, kl, mug, mu_b, mu_w=None)[source]

Calculates the two-phase non-boiling 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 Constant-pressure 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] 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 air-water and air-aqueous 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. “Two-Phase Heat Transfer in Two Component Vertical Flows.” International Journal of Multiphase Flow 10, no. 2 (April 1, 1984): 237-42. doi:10.1016/0301-9322(84)90021-1.
 [2] (1, 2) Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L. Dougherty. “Comparison of 20 Two-Phase 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): 15-40. doi:10.1080/014576399271691.

Examples

>>> Elamvaluthi_Srinivas(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300,
... kl=.6, mug=1E-5, mu_b=1E-3, mu_w=1.2E-3)
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 two-phase non-boiling 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 air-water 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/air-oil 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 Constant-pressure 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 water-air correlation or the gas/air-oil correlation 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 0.6-250. Tested fluids were air-water, and gas/air-oil.

References

 [1] (1, 2) Groothuis, H., and W. P. Hendal. “Heat Transfer in Two-Phase Flow.: Chemical Engineering Science 11, no. 3 (November 1, 1959): 212-20. doi:10.1016/0009-2509(59)80089-0.
 [2] (1, 2) Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L. Dougherty. “Comparison of 20 Two-Phase 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): 15-40. doi:10.1080/014576399271691.

Examples

>>> Groothuis_Hendal(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300, kl=.6,
... mug=1E-5, mu_b=1E-3, mu_w=1.2E-3)
1192.9543445455754

ht.conv_two_phase.Hughmark(m, x, alpha, D, L, Cpl, kl, mu_b=None, mu_w=None)[source]

Calculates the two-phase non-boiling 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 Constant-pressure 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] 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 air-water, air-SAE 10 oil, gas-oil, air-diethylene glycol, and air-aqueous 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): 1007-10. doi:10.1016/0009-2509(65)80101-4.
 [2] (1, 2) Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L. Dougherty. “Comparison of 20 Two-Phase 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): 15-40. doi:10.1080/014576399271691.

Examples

>>> Hughmark(m=1, x=.9, alpha=.9, D=.3, L=.5, Cpl=2300, kl=0.6, mu_b=1E-3,
... mu_w=1.2E-3)
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 two-phase non-boiling 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 Constant-pressure 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 Liquid-phase heat transfer coefficient as described below, [W/m^2/K] h : float Heat transfer coefficient [W/m^2/K]

Notes

The liquid-only 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 Nitrogen-Oil Mixtures.” Industrial & Engineering Chemistry 51, no. 11 (November 1, 1959): 1369-72. doi:10.1021/ie50599a032.
 [2] (1, 2) Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L. Dougherty. “Comparison of 20 Two-Phase 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): 15-40. doi:10.1080/014576399271691.

Examples

>>> Knott(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300, kl=.6, mu_b=1E-3,
... mu_w=1.2E-3, 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 two-phase non-boiling 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 Constant-pressure 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] 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 air-water and air-ethylene glycol systems with a L/D of 17.6 and at low gas-liquid 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 Two-Phase Flow of Gas-Liquid Mixtures.” Industrial & Engineering Chemistry Fundamentals 4, no. 3 (August 1, 1965): 339-44. doi:10.1021/i160015a018.
 [2] (1, 2) Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L. Dougherty. “Comparison of 20 Two-Phase 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): 15-40. doi:10.1080/014576399271691.

Examples

>>> Kudirka_Grosh_McFadden(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300,
... kl=.6, mug=1E-5, mu_b=1E-3, mu_w=1.2E-3)
303.9941255903587

ht.conv_two_phase.Martin_Sims(m, x, D, rhol, rhog, hl)[source]

Calculates the two-phase non-boiling 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 Liquid-phase heat transfer coefficient as described below, [W/m^2/K] h : float Heat transfer coefficient [W/m^2/K]

Notes

No suggestion for how to calculate the liquid-phase 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): 1115-34. doi:10.1016/0017-9310(71)90208-0.
 [2] (1, 2, 3) Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L. Dougherty. “Comparison of 20 Two-Phase 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): 15-40. 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 two-phase non-boiling 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 Constant-pressure 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] 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 1-90, 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 Two-Phase Flow in a Vertical Pipe, Proceedings 6th International Heat Transfer Conference, Toronto, V. 1, p. 505-510, 1978.
 [2] (1, 2) Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L. Dougherty. “Comparison of 20 Two-Phase 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): 15-40. doi:10.1080/014576399271691.

Examples

>>> Ravipudi_Godbold(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300, kl=.6, mug=1E-5, mu_b=1E-3, mu_w=1.2E-3)
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 two-phase non-boiling 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 Constant-pressure 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 h : float Heat transfer coefficient [W/m^2/K]

Notes

Developed with mixtures of air-water, helium-water, and freon-12-water and vertical tests. Studied flow patterns were bubbly, slug, annular, bubbly-slug, and slug-annular 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 Two-Phase Two-Component 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 Two-Phase 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): 15-40. doi:10.1080/014576399271691.

Examples

>>> Aggour(m=1, x=.9, D=.3, alpha=.9, rhol=1000, Cpl=2300, kl=.6, mu_b=1E-3)
420.9347146885667