Condensation (ht.condensation)

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

Calculates heat transfer coefficient for condensation of a pure chemical inside a vertical tube or tube bundle, as presented in [R154166] according to [R153166].

\[ \begin{align}\begin{aligned}h_f = h_{LO}\left[1 + x\left(\frac{\rho_L}{\rho_G} - 1\right)\right]^{0.5}\\h_{LO} = 0.021 \frac{k_L}{L} Re_{LO}^{0.8} Pr^{0.43}\end{aligned}\end{align} \]
Parameters:

m : float

Mass flow rate [kg/s]

rhog : float

Density of the gas [kg/m^3]

rhol : float

Density of the liquid [kg/m^3]

kl : float

Thermal conductivity of liquid [W/m/K]

mul : float

Viscosity of liquid [Pa*s]

Cpl : float

Constant-pressure heat capacity of liquid [J/kg/K]

D : float

Diameter of the tubing [m]

x : float

Quality at the specific interval [-]

Returns:

h : float

Heat transfer coefficient [W/m^2/K]

Notes

To calculate overall heat transfer coefficient during condensation, simply average values at x = 1 and x = 0.

References

[R153166](1, 2) Boyko, L. D., and G. N. Kruzhilin. “Heat Transfer and Hydraulic Resistance during Condensation of Steam in a Horizontal Tube and in a Bundle of Tubes.” International Journal of Heat and Mass Transfer 10, no. 3 (March 1, 1967): 361-73. doi:10.1016/0017-9310(67)90152-4.
[R154166](1, 2, 3) Hewitt, G. L. Shires T. Reg Bott G. F., George L. Shires, and T. R. Bott. Process Heat Transfer. 1E. Boca Raton: CRC Press, 1994.

Examples

Page 589 in [R154166], matches exactly.

>>> Boyko_Kruzhilin(m=500*pi/4*.03**2, rhog=6.36, rhol=582.9, kl=0.098,
... mul=159E-6, Cpl=2520., D=0.03, x=0.85)
10598.657227479956
ht.condensation.Nusselt_laminar(Tsat, Tw, rhog, rhol, kl, mul, Hvap, L, angle=90)[source]

Calculates heat transfer coefficient for laminar film condensation of a pure chemical on a flat plate, as presented in [R155168] according to an analysis performed by Nusselt in 1916.

\[h=0.943\left[\frac{g\sin(\theta)\rho_{liq}(\rho_l-\rho_v)k_{l}^3 \Delta H_{vap}}{\mu_l(T_{sat}-T_w)L}\right]^{0.25}\]
Parameters:

Tsat : float

Saturation temperature at operating pressure [Pa]

Tw : float

Wall temperature, [K]

rhog : float

Density of the gas [kg/m^3]

rhol : float

Density of the liquid [kg/m^3]

kl : float

Thermal conductivity of liquid [W/m/K]

mul : float

Viscosity of liquid [Pa*s]

Hvap : float

Heat of vaporization of the fluid at P, [J/kg]

L : float

Length of the plate [m]

angle : float, optional

Angle of inclination of the plate [degrees]

Returns:

h : float

Heat transfer coefficient [W/m^2/K]

Notes

Optionally, the plate may be inclined. The constant 0.943 is actually:

\[2\sqrt{2}/3\]

References

[R155168](1, 2, 3) Hewitt, G. L. Shires T. Reg Bott G. F., George L. Shires, and T. R. Bott. Process Heat Transfer. 1E. Boca Raton: CRC Press, 1994.

Examples

  1. 578 in [R155168], matches exactly.
>>> Nusselt_laminar(Tsat=370, Tw=350, rhog=7.0, rhol=585., kl=0.091,
... mul=158.9E-6, Hvap=776900, L=0.1)
1482.206403453679
ht.condensation.h_kinetic(T, P, MW, Hvap, f=1)[source]

Calculates heat transfer coefficient for condensation of a pure chemical inside a vertical tube or tube bundle, as presented in [R157169] according to [R156169].

\[h = \left(\frac{2f}{2-f}\right)\left(\frac{MW}{1000\cdot 2\pi R T} \right)^{0.5}\left(\frac{H_{vap}^2 P \cdot MW}{1000\cdot RT^2}\right)\]
Parameters:

T : float

Vapor temperature, [K]

P : float

Vapor pressure, [Pa]

MW : float

Molecular weight of the gas, [g/mol]

Hvap : float

Heat of vaporization of the fluid at P, [J/kg]

f : float

Correction factor, [-]

Returns:

h : float

Heat transfer coefficient [W/m^2/K]

Notes

f is a correction factor for how the removal of gas particles affects the behavior of the ideal gas in diffusing to the condensing surface. It is quite close to one, and has not been well explored in the literature due to the rarity of the importance of the kinetic resistance.

References

[R156169](1, 2) Berman, L. D. “On the Effect of Molecular-Kinetic Resistance upon Heat Transfer with Condensation.” International Journal of Heat and Mass Transfer 10, no. 10 (October 1, 1967): 1463. doi:10.1016/0017-9310(67)90033-6.
[R157169](1, 2) Kakaç, Sadik, ed. Boilers, Evaporators, and Condensers. 1 edition. Wiley-Interscience, 1991.
[R158169]Stephan, Karl. Heat Transfer in Condensation and Boiling. Translated by C. V. Green. Softcover reprint of the original 1st ed. 1992 edition. Berlin; New York: Springer, 2013.

Examples

Water at 1 bar and 300 K:

>>> h_kinetic(300, 1E5, 18.02, 2441674)
30788845.562480535
ht.condensation.Akers_Deans_Crosser(m, rhog, rhol, kl, mul, Cpl, D, x)[source]

Calculates heat transfer coefficient for condensation of a pure chemical inside a vertical tube or tube bundle, as presented in [R160172] according to [R159172].

\[ \begin{align}\begin{aligned}Nu = \frac{hD_i}{k_l} = C Re_e^n Pr_l^{1/3}\\C = 0.0265, n=0.8 \text{ for } Re_e > 5\times10^4\\C = 5.03, n=\frac{1}{3} \text{ for } Re_e < 5\times10^4\\Re_e = \frac{D_i G_e}{\mu_l}\\G_e = G\left[(1-x)+x(\rho_l/\rho_g)^{0.5}\right]\end{aligned}\end{align} \]
Parameters:

m : float

Mass flow rate [kg/s]

rhog : float

Density of the gas [kg/m^3]

rhol : float

Density of the liquid [kg/m^3]

kl : float

Thermal conductivity of liquid [W/m/K]

mul : float

Viscosity of liquid [Pa*s]

Cpl : float

Constant-pressure heat capacity of liquid [J/kg/K]

D : float

Diameter of the tubing [m]

x : float

Quality at the specific interval [-]

Returns:

h : float

Heat transfer coefficient [W/m^2/K]

References

[R159172](1, 2) Akers, W. W., H. A. Deans, and O. K. Crosser. “Condensing Heat Transfer Within Horizontal Tubes.” Chem. Eng. Progr. Vol: 55, Symposium Ser. No. 29 (January 1, 1959).
[R160172](1, 2) Kakaç, Sadik, ed. Boilers, Evaporators, and Condensers. 1st. Wiley-Interscience, 1991.

Examples

>>> Akers_Deans_Crosser(m=0.35, rhog=6.36, rhol=582.9, kl=0.098, 
... mul=159E-6, Cpl=2520., D=0.03, x=0.85)
7117.24177265201
ht.condensation.Cavallini_Smith_Zecchin(m, x, D, rhol, rhog, mul, mug, kl, Cpl)[source]

Calculates heat transfer coefficient for condensation of a fluid inside a tube, as presented in [R161174], also given in [R162174] and [R163174].

\[ \begin{align}\begin{aligned}Nu = \frac{hD_i}{k_l} = 0.05 Re_e^{0.8} Pr_l^{0.33}\\Re_{eq} = Re_g(\mu_g/\mu_l)(\rho_l/\rho_g)^{0.5} + Re_l\\v_{gs} = \frac{mx}{\rho_g \frac{\pi}{4}D^2}\\v_{ls} = \frac{m(1-x)}{\rho_l \frac{\pi}{4}D^2}\end{aligned}\end{align} \]
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]

References

[R161174](1, 2) A. Cavallini, J. R. Smith and R. Zecchin, A dimensionless correlation for heat transfer in forced convection condensation, 6th International Heat Transfer Conference., Tokyo, Japan (1974) 309-313.
[R162174](1, 2) Kakaç, Sadik, ed. Boilers, Evaporators, and Condensers. 1st. Wiley-Interscience, 1991.
[R163174](1, 2) 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.

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
ht.condensation.Shah(m, x, D, rhol, mul, kl, Cpl, P, Pc)[source]

Calculates heat transfer coefficient for condensation of a fluid inside a tube, as presented in [R164177] and again by the same author in [R165177]; also given in [R166177]. 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.

\[h_{TP} = h_L\left[(1-x)^{0.8} +\frac{3.8x^{0.76}(1-x)^{0.04}} {P_r^{0.38}}\right]\]
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

[R164177] is well written an unambiguous as to how to apply this equation.

References

[R164177](1, 2, 3) 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.
[R165177](1, 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.
[R166177](1, 2) Kakaç, Sadik, ed. Boilers, Evaporators, and Condensers. 1st. Wiley-Interscience, 1991.

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