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 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.)