Condensation (ht.condensation)

ht.condensation.Akers_Deans_Crosser(m, rhog, rhol, kl, mul, Cpl, D, x)

Calculates heat transfer coefficient for condensation of a pure chemical inside a vertical tube or tube bundle, as presented in [2] according to [1].

$$Nu = \frac{hD_i}{k_l} = C Re_e^n Pr_l^{1/3}$$

$$C = 0.0265, n=0.8 \text{ for } Re_e > 5\times10^4$$

$$C = 5.03, n=\frac{1}{3} \text{ for } Re_e < 5\times10^4$$

$$Re_e = \frac{D_i G_e}{\mu_l}$$

$$G_e = G\left[(1-x)+x(\rho_l/\rho_g)^{0.5}\right]$$

Parameters

mfloat

Mass flow rate [kg/s]

rhogfloat

Density of the gas [kg/m^3]

rholfloat

Density of the liquid [kg/m^3]

klfloat

Thermal conductivity of liquid [W/m/K]

mulfloat

Viscosity of liquid [Pa*s]

Cplfloat

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

Dfloat

Diameter of the tubing [m]

xfloat

Quality at the specific interval [-]

Returns

hfloat

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

References

1

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).

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.Boyko_Kruzhilin(m, rhog, rhol, kl, mul, Cpl, D, x)

Calculates heat transfer coefficient for condensation of a pure chemical inside a vertical tube or tube bundle, as presented in [2] according to [1].

$$h_f = h_{LO}\left[1 + x\left(\frac{\rho_L}{\rho_G} - 1\right)\right]^{0.5}$$

$$h_{LO} = 0.021 \frac{k_L}{L} Re_{LO}^{0.8} Pr^{0.43}$$

Parameters

mfloat

Mass flow rate [kg/s]

rhogfloat

Density of the gas [kg/m^3]

rholfloat

Density of the liquid [kg/m^3]

klfloat

Thermal conductivity of liquid [W/m/K]

mulfloat

Viscosity of liquid [Pa*s]

Cplfloat

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

Dfloat

Diameter of the tubing [m]

xfloat

Quality at the specific interval [-]

Returns

hfloat

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

1

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.

2(1,2)

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 [2], 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.Cavallini_Smith_Zecchin(m, x, D, rhol, rhog, mul, mug, kl, Cpl)

Calculates heat transfer coefficient for condensation of a fluid inside a tube, as presented in [1], also given in [2] and [3].

$$Nu = \frac{hD_i}{k_l} = 0.05 Re_e^{0.8} Pr_l^{0.33}$$

$$Re_{eq} = Re_g(\mu_g/\mu_l)(\rho_l/\rho_g)^{0.5} + Re_l$$

$$v_{gs} = \frac{mx}{\rho_g \frac{\pi}{4}D^2}$$

$$v_{ls} = \frac{m(1-x)}{\rho_l \frac{\pi}{4}D^2}$$

Parameters

mfloat

Mass flow rate [kg/s]

xfloat

Quality at the specific interval [-]

Dfloat

Diameter of the channel [m]

rholfloat

Density of the liquid [kg/m^3]

rhogfloat

Density of the gas [kg/m^3]

mulfloat

Viscosity of liquid [Pa*s]

mugfloat

Viscosity of gas [Pa*s]

klfloat

Thermal conductivity of liquid [W/m/K]

Cplfloat

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

Returns

hfloat

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

References

1

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.

2

Kakaç, Sadik, ed. Boilers, Evaporators, and Condensers. 1st. Wiley-Interscience, 1991.

3

Balcilar, Muhammet, Ahmet Selim Dalkiliç, 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.Nusselt_laminar(Tsat, Tw, rhog, rhol, kl, mul, Hvap, L, angle=90.0)

Calculates heat transfer coefficient for laminar film condensation of a pure chemical on a flat plate, as presented in [1] 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

Tsatfloat

Saturation temperature at operating pressure [Pa]

Twfloat

Wall temperature, [K]

rhogfloat

Density of the gas [kg/m^3]

rholfloat

Density of the liquid [kg/m^3]

klfloat

Thermal conductivity of liquid [W/m/K]

mulfloat

Viscosity of liquid [Pa*s]

Hvapfloat

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

Lfloat

Length of the plate [m]

anglefloat, optional

Angle of inclination of the plate [degrees]

Returns

hfloat

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

1(1,2)

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

16. 578 in [1], 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.Shah(m, x, D, rhol, mul, kl, Cpl, P, Pc)

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.

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

Parameters

mfloat

Mass flow rate [kg/s]

xfloat

Quality at the specific interval [-]

Dfloat

Diameter of the channel [m]

rholfloat

Density of the liquid [kg/m^3]

mulfloat

Viscosity of liquid [Pa*s]

klfloat

Thermal conductivity of liquid [W/m/K]

Cplfloat

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

Pfloat

Pressure of the fluid, [Pa]

Pcfloat

Critical pressure of the fluid, [Pa]

Returns

hfloat

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

Notes

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

References

1(1,2)

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.

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

ht.condensation.h_kinetic(T, P, MW, Hvap, f=1.0)

Calculates heat transfer coefficient for condensation of a pure chemical inside a vertical tube or tube bundle, as presented in [2] according to [1].

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

Parameters

Tfloat

Vapor temperature, [K]

Pfloat

Vapor pressure, [Pa]

MWfloat

Molecular weight of the gas, [g/mol]

Hvapfloat

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

ffloat

Correction factor, [-]

Returns

hfloat

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

1

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.

2

Kakaç, Sadik, ed. Boilers, Evaporators, and Condensers. 1 edition. Wiley-Interscience, 1991.

3

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)
30788829.908851154