def Elamvaluthi_Srinivas(m, x, D, rhol, rhog, Cpl, kl, mug, mu_b, mu_w=None):
r'''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]_.
.. math::
\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}
.. math::
Re_M = \frac{D V_L \rho_L}{\mu_L} + \frac{D V_g \rho_g}{\mu_g}
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]
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 air-water and
air-aqueous glycerine solutions. The tube inner diameter was 1 cm, and the
L/D ratio was 86.
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
References
----------
.. [1] 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] 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.
'''
Vg = m * x / (rhog * pi / 4 * D**2)
Vl = m * (1 - x) / (rhol * pi / 4 * D**2)
Prl = Prandtl(Cp=Cpl, mu=mu_b, k=kl)
ReM = D * Vl * rhol / mu_b + D * Vg * rhog / mug
Nu_TP = 0.5 * (mug / mu_b)**0.25 * ReM**0.7 * Prl**(1 / 3.)
if mu_w:
Nu_TP *= (mu_b / mu_w)**0.14
return Nu_TP * kl / D
def Ravipudi_Godbold(m, x, D, rhol, rhog, Cpl, kl, mug, mu_b, mu_w=None):
r'''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]_.
.. math::
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]
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
1-90, in the froth regime, and for fluid mixtures of air and water,
toluene, benzene, and methanol.
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
References
----------
.. [1] 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] 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.
'''
Vgs = m * x / (rhog * pi / 4 * D**2)
Vls = m * (1 - x) / (rhol * pi / 4 * D**2)
Prl = Prandtl(Cp=Cpl, mu=mu_b, k=kl)
Rels = D * Vls * rhol / mu_b
Nu = 0.56 * (Vgs / Vls)**0.3 * (mug / mu_b)**0.2 * Rels**0.6 * Prl**(1 /
3.)
if mu_w is not None:
Nu *= (mu_b / mu_w)**0.14
return Nu * kl / D
def Aggour(m,
x,
alpha,
D,
rhol,
Cpl,
kl,
mu_b,
mu_w=None,
L=None,
turbulent=None):
r'''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:
.. math::
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:
.. math::
h_{TP} = 0.0155\frac{k_l}{D} Pr_l^{0.5} Re_l^{0.83}
.. math::
Re_l = \frac{\rho_l v_l D}{\mu_l}
.. math::
V_l = \frac{V_{ls}}{1-\alpha}
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
Returns
-------
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.
Examples
--------
>>> Aggour(m=1, x=.9, D=.3, alpha=.9, rhol=1000, Cpl=2300, kl=.6, mu_b=1E-3)
420.9347146885667
References
----------
.. [1] 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] 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.
'''
Vls = m * (1 - x) / (rhol * pi / 4 * D**2)
Vl = Vls / (1. - alpha)
Prl = Prandtl(Cp=Cpl, k=kl, mu=mu_b)
Rel = Reynolds(V=Vl, D=D, rho=rhol, mu=mu_b)
if turbulent or (Rel > 2000.0 and turbulent is None):
hl = 0.0155 * (kl / D) * Rel**0.83 * Prl**0.5
return hl * (1 - alpha)**-0.83
else:
hl = 1.615 * (kl / D) * (Rel * Prl * D / L)**(1 / 3.)
if mu_w:
hl *= (mu_b / mu_w)**0.14
return hl * (1.0 - alpha)**(-1 / 3.)
def Kudirka_Grosh_McFadden(m, x, D, rhol, rhog, Cpl, kl, mug, mu_b, mu_w=None):
r'''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]_.
.. math::
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]
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 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.
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
References
----------
.. [1] 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] 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.
'''
Vgs = m * x / (rhog * pi / 4 * D**2)
Vls = m * (1 - x) / (rhol * pi / 4 * D**2)
Prl = Prandtl(Cp=Cpl, mu=mu_b, k=kl)
Rels = D * Vls * rhol / mu_b
Nu = 125 * (Vgs / Vls)**0.125 * (mug / mu_b)**0.6 * Rels**0.25 * Prl**(1 /
3.)
if mu_w:
Nu *= (mu_b / mu_w)**0.14
return Nu * kl / D
def Martin_Sims(m,
x,
D,
rhol,
rhog,
hl=None,
Cpl=None,
kl=None,
mu_b=None,
mu_w=None,
L=None):
r'''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]_.
.. math::
\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, optional
Liquid-phase heat transfer coefficient as described below, [W/m^2/K]
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]
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
No specific 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`.
Examples
--------
>>> Martin_Sims(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, hl=141.2)
5563.280000000001
>>> Martin_Sims(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=24)
5977.505465781747
References
----------
.. [1] 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] 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.
'''
Vgs = m * x / (rhog * pi / 4 * D**2)
Vls = m * (1 - x) / (rhol * pi / 4 * D**2)
if hl is None:
V = Vgs + Vls # Net velocity
Re = Reynolds(V=V, D=D, rho=rhol, mu=mu_b)
Pr = Prandtl(Cp=Cpl, k=kl, mu=mu_b)
Nul = laminar_entry_Seider_Tate(Re=Re,
Pr=Pr,
L=L,
Di=D,
mu=mu_b,
mu_w=mu_w)
hl = Nul * kl / D
return hl * (1.0 + 0.64 * (Vgs / Vls)**0.5)
def Knott(m,
x,
D,
rhol,
rhog,
Cpl=None,
kl=None,
mu_b=None,
mu_w=None,
L=None,
hl=None):
r'''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`.
.. math::
\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]
Returns
-------
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.
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
References
----------
.. [1] 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] 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.
'''
Vgs = m * x / (rhog * pi / 4 * D**2)
Vls = m * (1 - x) / (rhol * pi / 4 * D**2)
if not hl:
V = Vgs + Vls # Net velocity
Re = Reynolds(V=V, D=D, rho=rhol, mu=mu_b)
Pr = Prandtl(Cp=Cpl, k=kl, mu=mu_b)
Nul = laminar_entry_Seider_Tate(Re=Re,
Pr=Pr,
L=L,
Di=D,
mu=mu_b,
mu_w=mu_w)
hl = Nul * kl / D
return hl * (1 + Vgs / Vls)**(1 / 3.)
def Davis_David(m, x, D, rhol, rhog, Cpl, kl, mul):
r'''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]_.
.. math::
\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]
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. 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%.
Examples
--------
>>> Davis_David(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300, kl=.6,
... mul=1E-3)
1437.3282869955121
References
----------
.. [1] 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] 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.
'''
G = m / (pi / 4 * D**2)
Prl = Prandtl(Cp=Cpl, mu=mul, k=kl)
Nu_TP = 0.060 * (rhol / rhog)**0.28 * (D * G * x / mul)**0.87 * Prl**0.4
return Nu_TP * kl / D
def Groothuis_Hendal(m,
x,
D,
rhol,
rhog,
Cpl,
kl,
mug,
mu_b,
mu_w=None,
water=False):
r'''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]_.
.. math::
Re_M = \frac{D V_{ls} \rho_l}{\mu_l} + \frac{D V_{gs} \rho_g}{\mu_g}
For the air-water system:
.. math::
\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):
.. math::
\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
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 0.6-250.
Tested fluids were air-water, and gas/air-oil.
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
References
----------
.. [1] 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] 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.
'''
Vg = m * x / (rhog * pi / 4 * D**2)
Vl = m * (1 - x) / (rhol * pi / 4 * D**2)
Prl = Prandtl(Cp=Cpl, mu=mu_b, k=kl)
ReM = D * Vl * rhol / mu_b + D * Vg * rhog / mug
if water:
Nu_TP = 0.029 * (ReM)**0.87 * (Prl)**(1 / 3.)
else:
Nu_TP = 2.6 * ReM**0.39 * Prl**(1 / 3.)
if mu_w:
Nu_TP *= (mu_b / mu_w)**0.14
return Nu_TP * kl / D
def Shah(m, x, D, rhol, mul, kl, Cpl, P, Pc):
r'''Calculates heat transfer coefficient for condensation
of a fluid inside a tube, as presented in [1]_ and again by the same
author in [2]_; also given in [3]_. Requires no properties of the gas.
Uses the Dittus-Boelter correlation for single phase heat transfer
coefficient, with a Reynolds number assuming all the flow is liquid.
.. math::
h_{TP} = h_L\left[(1-x)^{0.8} +\frac{3.8x^{0.76}(1-x)^{0.04}}
{P_r^{0.38}}\right]
Parameters
----------
m : float
Mass flow rate [kg/s]
x : float
Quality at the specific interval []
D : float
Diameter of the channel [m]
rhol : float
Density of the liquid [kg/m^3]
mul : float
Viscosity of liquid [Pa*s]
kl : float
Thermal conductivity of liquid [W/m/K]
Cpl : float
Constant-pressure heat capacity of liquid [J/kg/K]
P : float
Pressure of the fluid, [Pa]
Pc : float
Critical pressure of the fluid, [Pa]
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
[1]_ is well written an unambiguous as to how to apply this equation.
Examples
--------
>>> Shah(m=1, x=0.4, D=.3, rhol=800, mul=1E-5, kl=0.6, Cpl=2300, P=1E6, Pc=2E7)
2561.2593415479214
References
----------
.. [1] Shah, M. M. "A General Correlation for Heat Transfer during Film
Condensation inside Pipes." International Journal of Heat and Mass
Transfer 22, no. 4 (April 1, 1979): 547-56.
doi:10.1016/0017-9310(79)90058-9.
.. [2] Shah, M. M., Heat Transfer During Film Condensation in Tubes and
Annuli: A Review of the Literature, ASHRAE Transactions, vol. 87, no.
3, pp. 1086-1100, 1981.
.. [3] Kakaç, Sadik, ed. Boilers, Evaporators, and Condensers. 1st.
Wiley-Interscience, 1991.
'''
VL = m / (rhol * pi / 4 * D**2)
ReL = Reynolds(V=VL, D=D, rho=rhol, mu=mul)
Prl = Prandtl(Cp=Cpl, k=kl, mu=mul)
hL = turbulent_Dittus_Boelter(ReL, Prl) * kl / D
Pr = P / Pc
h_TP = hL * ((1 - x)**0.8 + 3.8 * x**0.76 * (1 - x)**0.04 / Pr**0.38)
return h_TP
def Cavallini_Smith_Zecchin(m, x, D, rhol, rhog, mul, mug, kl, Cpl):
r'''Calculates heat transfer coefficient for condensation
of a fluid inside a tube, as presented in
[1]_, also given in [2]_ and [3]_.
.. math::
Nu = \frac{hD_i}{k_l} = 0.05 Re_e^{0.8} Pr_l^{0.33}
Re_{eq} = Re_g(\mu_g/\mu_l)(\rho_l/\rho_g)^{0.5} + Re_l
v_{gs} = \frac{mx}{\rho_g \frac{\pi}{4}D^2}
v_{ls} = \frac{m(1-x)}{\rho_l \frac{\pi}{4}D^2}
Parameters
----------
m : float
Mass flow rate [kg/s]
x : float
Quality at the specific interval []
D : float
Diameter of the channel [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
Constant-pressure heat capacity of liquid [J/kg/K]
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
Examples
--------
>>> Cavallini_Smith_Zecchin(m=1, x=0.4, D=.3, rhol=800, rhog=2.5, mul=1E-5, mug=1E-3, kl=0.6, Cpl=2300)
5578.218369177804
References
----------
.. [1] A. Cavallini, J. R. Smith and R. Zecchin, A dimensionless correlation
for heat transfer in forced convection condensa- tion, 6th International
Heat Transfer Conference., Tokyo, Japan (1974) 309-313.
http://www.ibrarian.net/navon/paper/A_Dimensionless_Correlation_for_Heat_Transfer_in_.pdf?paperid=4413524
.. [2] Kakaç, Sadik, ed. Boilers, Evaporators, and Condensers. 1st.
Wiley-Interscience, 1991.
.. [3] Balcılar, Muhammet, Ahmet Selim Dalkılıç, Berna Bolat, and Somchai
Wongwises. "Investigation of Empirical Correlations on the Determination
of Condensation Heat Transfer Characteristics during Downward Annular
Flow of R134a inside a Vertical Smooth Tube Using Artificial
Intelligence Algorithms." Journal of Mechanical Science and Technology
25, no. 10 (October 12, 2011): 2683-2701. doi:10.1007/s12206-011-0618-2.
'''
Prl = Prandtl(Cp=Cpl, mu=mul, k=kl)
Vl = m * (1 - x) / (rhol * pi / 4 * D**2)
Vg = m * x / (rhog * pi / 4 * D**2)
Rel = Reynolds(V=Vl, D=D, rho=rhol, mu=mul)
Reg = Reynolds(V=Vg, D=D, rho=rhog, mu=mug)
'''The following was coded, and may be used instead of the above lines,
to check that the definitions of parameters here provide the same results
as those defined in [1]_.
G = m/(pi/4*D**2)
Re = G*D/mul
Rel = Re*(1-x)
Reg = Re*x/(mug/mul)'''
Reeq = Reg * (mug / mul) * (rhol / rhog)**0.5 + Rel
Nul = 0.05 * Reeq**0.8 * Prl**0.33
h = Nul * kl / D # confirmed to be with respect to the liquid
return h