Nucleic boiling and critical heat flux (ht.boiling_nucleic)

ht.boiling_nucleic.Bier(P, Pc, Te=None, q=None)[source]

Calculates heat transfer coefficient for a evaporator operating in the nucleate boiling regime according to [1] .

Either heat flux or excess temperature is required.

With Te specified:

\[h = \left(0.00417P_c^{0.69} \Delta Te^{0.7}\left[0.7 + 2P_r\left(4 + \frac{1}{1-P_r}\right) \right]\right)^{1/0.3} \]

With q specified:

\[h = 0.00417P_c^{0.69} \Delta q^{0.7}\left[0.7 + 2P_r\left(4 + \frac{1}{1-P_r}\right) \right] \]
Parameters
Pfloat

Saturation pressure of fluid, [Pa]

Pcfloat

Critical pressure of fluid, [Pa]

Tefloat, optional

Excess wall temperature, [K]

qfloat, optional

Heat flux, [W/m^2]

Returns
hfloat

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

Notes

No examples of this are known. Seems to give very different results than other correlations.

References

1(1,2)

Rohsenow, Warren and James Hartnett and Young Cho. Handbook of Heat Transfer, 3E. New York: McGraw-Hill, 1998.

Examples

Water boiling at 1 atm, with excess temperature of 4.3 K from [1].

>>> Bier(101325., 22048321.0, Te=4.3)
1290.5349471503353
ht.boiling_nucleic.Cooper(P, Pc, MW, Te=None, q=None, Rp=1e-06)[source]

Calculates heat transfer coefficient for a evaporator operating in the nucleate boiling regime according to [2] as presented in [1].

Either heat flux or excess temperature is required.

With Te specified:

\[h = \left(55\Delta Te^{0.67} \frac{P}{P_c}^{(0.12 - 0.2\log_{10} R_p)} (-\log_{10} \frac{P}{P_c})^{-0.55} MW^{-0.5}\right)^{1/0.33} \]

With q specified:

\[h = 55q^{0.67} \frac{P}{P_c}^{(0.12 - 0.2\log_{10} R_p)}(-\log_{10} \frac{P}{P_c})^{-0.55} MW^{-0.5} \]
Parameters
Pfloat

Saturation pressure of fluid, [Pa]

Pcfloat

Critical pressure of fluid, [Pa]

MWfloat

Molecular weight of fluid, [g/mol]

Tefloat, optional

Excess wall temperature, [K]

qfloat, optional

Heat flux, [W/m^2]

Rpfloat, optional

Roughness parameter of the surface (1 micrometer default) used by Cooper method, [m]

Returns
hfloat

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

Notes

Examples 1 and 2 are for water and benzene, from [1]. Roughness parameter is with an old definition. Accordingly, it is not used by the h function. If unchanged, the roughness parameter’s logarithm gives a value of 0.12 as an exponent of reduced pressure.

References

1(1,2,3)

Rohsenow, Warren and James Hartnett and Young Cho. Handbook of Heat Transfer, 3E. New York: McGraw-Hill, 1998.

2

M. G. Cooper, “Saturation and Nucleate Pool Boiling: A Simple Correlation,” Inst. Chem. Eng. Syrup. Ser. (86/2): 785, 1984.

3

Serth, R. W., Process Heat Transfer: Principles, Applications and Rules of Thumb. 2E. Amsterdam: Academic Press, 2014.

Examples

Water boiling at 1 atm, with excess temperature of 4.3 K from [1].

>>> Cooper(P=101325., Pc=22048321.0, MW=18.02, Te=4.3)
1558.1435442153575
ht.boiling_nucleic.Forster_Zuber(rhol, rhog, mul, kl, Cpl, Hvap, sigma, dPsat, Te=None, q=None)[source]

Calculates heat transfer coefficient for a evaporator operating in the nucleate boiling regime according to [2] as presented in [1].

Either heat flux or excess temperature is required.

With Te specified:

\[h = 0.00122\left(\frac{k_L^{0.79} C_{p,l}^{0.45}\rho_L^{0.49}} {\sigma^{0.5}\mu_L^{0.29} H_{vap}^{0.24} \rho_V^{0.24}}\right) \Delta T_e^{0.24} \Delta P_{sat}^{0.75} \]

With q specified:

\[h = \left[0.00122\left(\frac{k_L^{0.79} C_{p,l}^{0.45}\rho_L^{0.49}} {\sigma^{0.5}\mu_L^{0.29} H_{vap}^{0.24} \rho_V^{0.24}}\right) \Delta P_{sat}^{0.75} q^{0.24}\right]^{\frac{1}{1.24}} \]
Parameters
rholfloat

Density of the liquid [kg/m^3]

rhogfloat

Density of the produced gas [kg/m^3]

mulfloat

Viscosity of liquid [Pa*s]

klfloat

Thermal conductivity of liquid [W/m/K]

Cplfloat

Heat capacity of liquid [J/kg/K]

Hvapfloat

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

sigmafloat

Surface tension of liquid [N/m]

dPsatfloat

Difference in saturation pressure of the fluid at Te and T, [Pa]

Tefloat, optional

Excess wall temperature, [K]

qfloat, optional

Heat flux, [W/m^2]

Returns
hfloat

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

Notes

Examples have been found in [1] and [3] and match exactly.

References

1(1,2,3)

Cao, Eduardo. Heat Transfer in Process Engineering. McGraw Hill Professional, 2009.

2

Forster, H. K., and N. Zuber. “Dynamics of Vapor Bubbles and Boiling Heat Transfer.” AIChE Journal 1, no. 4 (December 1, 1955): 531-35. doi:10.1002/aic.690010425.

3

Serth, R. W., Process Heat Transfer: Principles, Applications and Rules of Thumb. 2E. Amsterdam: Academic Press, 2014.

Examples

Water boiling, with excess temperature of 4.3K from [1].

>>> Forster_Zuber(Te=4.3, dPsat=3906*4.3, Cpl=4180., kl=0.688,
... mul=0.275E-3, sigma=0.0588, Hvap=2.25E6, rhol=958., rhog=0.597)
3519.9239897462644
ht.boiling_nucleic.Gorenflo(P, Pc, q=None, Te=None, CASRN=None, h0=None, Ra=4e-07)[source]

Calculates heat transfer coefficient for a pool boiling according to [1] and also presented in [2]. Calculation is based on the corresponding states law, with a single regression constant per fluid. P and Pc are always required.

Either q or Te may be specified. Either CASRN or h0 may be specified as well. If CASRN is specified and the fluid is not in the list of those studied, an error is raises.

\[\frac{h}{h_0} = C_W F(p^*) \left(\frac{q}{q_0}\right)^n \]
\[C_W = \left(\frac{R_a}{R_{ao}}\right)^{0.133} \]
\[q_0 = 20 \;000 \frac{\text{W}}{\text{m}^{2}} \]
\[R_{ao} = 0.4 \mu\text{m} \]

For fluids other than water:

\[n = 0.9 - 0.3 p^{*0.3} \]
\[f(p^*) = 1.2p^{*0.27} + \left(2.5 + \frac{1}{1-p^*}\right)p^* \]

For water:

\[n = 0.9 - 0.3 p^{*0.15} \]
\[f(p^*) = 1.73p^{*0.27} + \left(6.1 + \frac{0.68}{1-p^*}\right)p^2 \]
Parameters
Pfloat

Saturation pressure of fluid, [Pa]

Pcfloat

Critical pressure of fluid, [Pa]

qfloat, optional

Heat flux, [W/m^2]

Tefloat, optional

Excess wall temperature, [K]

CASRNstr, optional

CASRN of fluid

h0float

Reference heat transfer coefficient for Gorenflo method, [W/m^2/K]

Rafloat, optional

Roughness parameter of the surface (0.4 micrometer default) for Gorenflo method, [m]

Returns
hfloat

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

Notes

A more recent set of reference heat fluxes is available. Where a range of values was listed for reference heat fluxes in [1], values from the second edition of [1] were used instead. 44 values are available, all listed in the dictionary h0_Gorenflow_1993. Values range from 2000 to 24000 W/m^2/K.

References

1(1,2,3)

Schlunder, Ernst U, VDI. VDI Heat Atlas. Dusseldorf: V.D.I. Verlag, 1993. http://digital.ub.uni-paderborn.de/hs/download/pdf/41898?originalFilename=true

2

Bertsch, Stefan S., Eckhard A. Groll, and Suresh V. Garimella. “Review and Comparative Analysis of Studies on Saturated Flow Boiling in Small Channels.” Nanoscale and Microscale Thermophysical Engineering 12, no. 3 (September 4, 2008): 187-227. doi:10.1080/15567260802317357.

Examples

Water boiling at 3 bar and a heat flux of 2E4 W/m^2/K.

>>> Gorenflo(3E5, 22048320., q=2E4, CASRN='7732-18-5')
3043.344595525422
ht.boiling_nucleic.HEDH_Montinsky(P, Pc)[source]

Calculates critical heat flux in the nucleate boiling regime according to [3] as presented in [1], using an expression modified from [2].

\[q_c = 367 P_cP_r^{0.35}(1-P_r)^{0.9} \]
Parameters
Pfloat

Saturation pressure of fluid, [Pa]

Pcfloat

Critical pressure of fluid, [Pa]

Returns
qfloat

Critical heat flux [W/m^2]

Notes

No further work is required. Units of Pc are kPa internally.

References

1

Schlünder, Ernst U, and International Center for Heat and Mass Transfer. Heat Exchanger Design Handbook. Washington: Hemisphere Pub. Corp., 1987.

2

Mostinsky I. L.: “Application of the rule of corresponding states for the calculation of heat transfer and critical heat flux,” Teploenergetika 4:66, 1963 English Abstr. Br Chem Eng 8(8):586, 1963

3(1,2)

Serth, R. W., Process Heat Transfer: Principles, Applications and Rules of Thumb. 2E. Amsterdam: Academic Press, 2014.

Examples

Example is from [3] and matches to within the error of the algebraic manipulation rounding.

>>> HEDH_Montinsky(P=310.3E3, Pc=2550E3)
398405.66545181436
ht.boiling_nucleic.HEDH_Taborek(P, Pc, Te=None, q=None)[source]

Calculates heat transfer coefficient for a evaporator operating in the nucleate boiling regime according to Taborek (1986) as described in [1] and as presented in [2]. Modification of [3].

Either heat flux or excess temperature is required.

With Te specified:

\[h = \left(0.00417P_c^{0.69} \Delta Te^{0.7}\left[2.1P_r^{0.27} + \left(9 + (1-Pr^2)^{-1}\right)P_r^2 \right]\right)^{1/0.3} \]

With q specified:

\[h = 0.00417P_c^{0.69} q^{0.7}\left[2.1P_r^{0.27} + \left(9 + (1-Pr^2 )^{-1}\right)P_r^2\right] \]
Parameters
Pfloat

Saturation pressure of fluid, [Pa]

Pcfloat

Critical pressure of fluid, [Pa]

Tefloat, optional

Excess wall temperature, [K]

qfloat, optional

Heat flux, [W/m^2]

Returns
hfloat

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

Notes

Example is from [3] and matches to within the error of the algebraic manipulation rounding.

References

1

Schlünder, Ernst U, and International Center for Heat and Mass Transfer. Heat Exchanger Design Handbook. Washington: Hemisphere Pub. Corp., 1987.

2

Mostinsky I. L.: “Application of the rule of corresponding states for the calculation of heat transfer and critical heat flux,” Teploenergetika 4:66, 1963 English Abstr. Br Chem Eng 8(8):586, 1963

3(1,2)

Serth, R. W., Process Heat Transfer: Principles, Applications and Rules of Thumb. 2E. Amsterdam: Academic Press, 2014.

Examples

>>> HEDH_Taborek(Te=16.2, P=310.3E3, Pc=2550E3)
1397.272486525486
ht.boiling_nucleic.McNelly(rhol, rhog, kl, Cpl, Hvap, sigma, P, Te=None, q=None)[source]

Calculates heat transfer coefficient for a evaporator operating in the nucleate boiling regime according to [2] as presented in [1].

Either heat flux or excess temperature is required.

With Te specified:

\[h = \left(0.225\left(\frac{\Delta T_e C_{p,l}}{H_{vap}}\right)^{0.69} \left(\frac{P k_L}{\sigma}\right)^{0.31} \left(\frac{\rho_L}{\rho_V}-1\right)^{0.33}\right)^{1/0.31} \]

With q specified:

\[h = 0.225\left(\frac{q C_{p,l}}{H_{vap}}\right)^{0.69} \left(\frac{P k_L}{\sigma}\right)^{0.31}\left(\frac{\rho_L}{\rho_V}-1\right)^{0.33} \]
Parameters
rholfloat

Density of the liquid [kg/m^3]

rhogfloat

Density of the produced gas [kg/m^3]

klfloat

Thermal conductivity of liquid [W/m/K]

Cplfloat

Heat capacity of liquid [J/kg/K]

Hvapfloat

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

sigmafloat

Surface tension of liquid [N/m]

Pfloat

Saturation pressure of fluid, [Pa]

Tefloat, optional

Excess wall temperature, [K]

qfloat, optional

Heat flux, [W/m^2]

Returns
hfloat

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

Notes

Further examples for this function are desired.

References

1

Cao, Eduardo. Heat Transfer in Process Engineering. McGraw Hill Professional, 2009.

2

McNelly M. J.: “A correlation of the rates of heat transfer to n ucleate boiling liquids,” J. Imp Coll. Chem Eng Soc 7:18, 1953.

Examples

Water boiling, with excess temperature of 4.3 K.

>>> McNelly(Te=4.3, P=101325, Cpl=4180., kl=0.688, sigma=0.0588,
... Hvap=2.25E6, rhol=958., rhog=0.597)
533.8056972951352
ht.boiling_nucleic.Montinsky(P, Pc, Te=None, q=None)[source]

Calculates heat transfer coefficient for a evaporator operating in the nucleate boiling regime according to [2] as presented in [1].

Either heat flux or excess temperature is required.

With Te specified:

\[h = \left(0.00417P_c^{0.69} \Delta Te^{0.7}\left[1.8(P/P_c)^{0.17} + 4(P/P_c)^{1.2} + 10(P/P_c)^{10}\right]\right)^{1/0.3} \]

With q specified:

\[h = 0.00417P_c^{0.69} q^{0.7}\left[1.8(P/P_c)^{0.17} + 4(P/P_c)^{1.2} + 10(P/P_c)^{10}\right] \]
Parameters
Pfloat

Saturation pressure of fluid, [Pa]

Pcfloat

Critical pressure of fluid, [Pa]

Tefloat, optional

Excess wall temperature, [K]

qfloat, optional

Heat flux, [W/m^2]

Returns
hfloat

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

Notes

Formulas has been found consistent in all cited sources. Examples have been found in [1] and [3].

The equation for this function is sometimes given with a constant of 3.7E-5 instead of 0.00417 if critical pressure is not internally converted to kPa. [3] lists a constant of 3.596E-5.

References

1(1,2,3)

Cao, Eduardo. Heat Transfer in Process Engineering. McGraw Hill Professional, 2009.

2

Mostinsky I. L.: “Application of the rule of corresponding states for the calculation of heat transfer and critical heat flux,” Teploenergetika 4:66, 1963 English Abstr. Br Chem Eng 8(8):586, 1963

3(1,2)

Rohsenow, Warren and James Hartnett and Young Cho. Handbook of Heat Transfer, 3E. New York: McGraw-Hill, 1998.

4

Serth, R. W., Process Heat Transfer: Principles, Applications and Rules of Thumb. 2E. Amsterdam: Academic Press, 2014.

Examples

Water boiling at 1 atm, with excess temperature of 4.3K from [1].

>>> Montinsky(P=101325, Pc=22048321, Te=4.3)
1185.0509770292663
ht.boiling_nucleic.Rohsenow(rhol, rhog, mul, kl, Cpl, Hvap, sigma, Te=None, q=None, Csf=0.013, n=1.7)[source]

Calculates heat transfer coefficient for a evaporator operating in the nucleate boiling regime according to [2] as presented in [1].

Either heat flux or excess temperature is required.

With Te specified:

\[h = {{\mu }_{L}} \Delta H_{vap} \left[ \frac{g( \rho_L-\rho_v)} {\sigma } \right]^{0.5}\left[\frac{C_{p,L}\Delta T_e^{2/3}}{C_{sf} \Delta H_{vap} Pr_L^n}\right]^3 \]

With q specified:

\[h = \left({{\mu }_{L}} \Delta H_{vap} \left[ \frac{g( \rho_L-\rho_v)} {\sigma } \right]^{0.5}\left[\frac{C_{p,L}\Delta T_e^{2/3}}{C_{sf} \Delta H_{vap} Pr_L^n}\right]^3\right)^{1/3}q^{2/3} \]
Parameters
rholfloat

Density of the liquid [kg/m^3]

rhogfloat

Density of the produced gas [kg/m^3]

mulfloat

Viscosity of liquid [Pa*s]

klfloat

Thermal conductivity of liquid [W/m/K]

Cplfloat

Heat capacity of liquid [J/kg/K]

Hvapfloat

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

sigmafloat

Surface tension of liquid [N/m]

Tefloat, optional

Excess wall temperature, [K]

qfloat, optional

Heat flux, [W/m^2]

Csffloat

Rohsenow coefficient specific to fluid and metal [-]

nfloat

Constant, 1 for water, 1.7 (default) for other fluids usually [-]

Returns
hfloat

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

Notes

No further work is required on this correlation. Multiple sources confirm its form and rearrangement.

References

1

Cao, Eduardo. Heat Transfer in Process Engineering. McGraw Hill Professional, 2009.

2

Rohsenow, Warren M. “A Method of Correlating Heat Transfer Data for Surface Boiling of Liquids.” Technical Report. Cambridge, Mass. : M.I.T. Division of Industrial Cooporation, 1951

Examples

h for water at atmospheric pressure on oxidized aluminum.

>>> Rohsenow(rhol=957.854, rhog=0.595593, mul=2.79E-4, kl=0.680, Cpl=4217,
... Hvap=2.257E6, sigma=0.0589, Te=4.9, Csf=0.011, n=1.26)
3723.655267067467
ht.boiling_nucleic.Serth_HEDH(D, sigma, Hvap, rhol, rhog)[source]

Calculates critical heat flux for nucleic boiling of a tube bundle according to [2], citing [3], and using [1] as the original form.

\[q_c = KH_{vap} \rho_g^{0.5}\left[\sigma g (\rho_L-\rho_g)\right]^{0.25} \]
\[K = 0.123 (R^*)^{-0.25} \text{ for 0.12 < R* < 1.17} \]
\[K = 0.118 \]
\[R^* = \frac{D}{2} \left[\frac{g(\rho_L-\rho_G)}{\sigma}\right]^{0.5} \]
Parameters
Dfloat

Diameter of tubes [m]

sigmafloat

Surface tension of liquid [N/m]

Hvapfloat

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

rholfloat

Density of the liquid [kg/m^3]

rhogfloat

Density of the produced gas [kg/m^3]

Returns
q: float

Critical heat flux [W/m^2]

Notes

A further source for this would be nice.

References

1

Zuber N. “On the stability of boiling heat transfer”. Trans ASME 1958 80:711-20.

2

Serth, R. W., Process Heat Transfer: Principles, Applications and Rules of Thumb. 2E. Amsterdam: Academic Press, 2014.

3

Schlünder, Ernst U, and International Center for Heat and Mass Transfer. Heat Exchanger Design Handbook. Washington: Hemisphere Pub. Corp., 1987.

Examples

>>> Serth_HEDH(D=0.0127, sigma=8.2E-3, Hvap=272E3, rhol=567, rhog=18.09)
351867.46522901946
ht.boiling_nucleic.Stephan_Abdelsalam(rhol, rhog, mul, kl, Cpl, Hvap, sigma, Tsat, Te=None, q=None, kw=401.0, rhow=8.96, Cpw=384.0, angle=None, correlation='general')[source]

Calculates heat transfer coefficient for a evaporator operating in the nucleate boiling regime according to [2] as presented in [1]. Five variants are possible.

Either heat flux or excess temperature is required. The forms for Te are not shown here, but are similar to those of the other functions.

\[h = 0.23X_1^{0.674} X_2^{0.35} X_3^{0.371} X_5^{0.297} X_8^{-1.73} k_L/d_B \]
\[X1 = \frac{q D_d}{K_L T_{sat}} \]
\[X2 = \frac{\alpha^2 \rho_L}{\sigma D_d} \]
\[X3 = \frac{C_{p,L} T_{sat} D_d^2}{\alpha^2} \]
\[X4 = \frac{H_{vap} D_d^2}{\alpha^2} \]
\[X5 = \frac{\rho_V}{\rho_L} \]
\[X6 = \frac{C_{p,l} \mu_L}{k_L} \]
\[X7 = \frac{\rho_W C_{p,W} k_W}{\rho_L C_{p,L} k_L} \]
\[X8 = \frac{\rho_L-\rho_V}{\rho_L} \]
\[D_b = 0.0146\theta\sqrt{\frac{2\sigma}{g(\rho_L-\rho_g)}} \]

Respectively, the following four correlations are for water, hydrocarbons, cryogenic fluids, and refrigerants.

\[h = 0.246\times 10^7 X1^{0.673} X4^{-1.58} X3^{1.26}X8^{5.22}k_L/d_B \]
\[h = 0.0546 X5^{0.335} X1^{0.67} X8^{-4.33} X4^{0.248}k_L/d_B \]
\[h = 4.82 X1^{0.624} X7^{0.117} X3^{0.374} X4^{-0.329}X5^{0.257} k_L/d_B \]
\[h = 207 X1^{0.745} X5^{0.581} X6^{0.533} k_L/d_B \]
Parameters
rholfloat

Density of the liquid [kg/m^3]

rhogfloat

Density of the produced gas [kg/m^3]

mulfloat

Viscosity of liquid [Pa*s]

klfloat

Thermal conductivity of liquid [W/m/K]

Cplfloat

Heat capacity of liquid [J/kg/K]

Hvapfloat

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

sigmafloat

Surface tension of liquid [N/m]

Tsatfloat

Saturation temperature at operating pressure [Pa]

Tefloat, optional

Excess wall temperature, [K]

qfloat, optional

Heat flux, [W/m^2]

kwfloat, optional

Thermal conductivity of wall (only for cryogenics) [W/m/K]

rhowfloat, optional

Density of the wall (only for cryogenics) [kg/m^3]

Cpwfloat, optional

Heat capacity of wall (only for cryogenics) [J/kg/K]

anglefloat, optional

Contact angle of bubble with wall [degrees]

correlationstr, optional

Any of ‘general’, ‘water’, ‘hydrocarbon’, ‘cryogenic’, or ‘refrigerant’

Returns
hfloat

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

Notes

If cryogenic correlation is selected, metal properties are used. Default values are the properties of copper at STP.

The angle is selected automatically if a correlation is selected; if angle is provided anyway, the automatic selection is ignored. A IndexError exception is raised if the correlation is not in the dictionary _angles_Stephan_Abdelsalam.

References

1

Cao, Eduardo. Heat Transfer in Process Engineering. McGraw Hill Professional, 2009.

2

Stephan, K., and M. Abdelsalam. “Heat-Transfer Correlations for Natural Convection Boiling.” International Journal of Heat and Mass Transfer 23, no. 1 (January 1980): 73-87. doi:10.1016/0017-9310(80)90140-4.

3

Serth, R. W., Process Heat Transfer: Principles, Applications and Rules of Thumb. 2E. Amsterdam: Academic Press, 2014.

Examples

Example is from [3] and matches.

>>> Stephan_Abdelsalam(Te=16.2, Tsat=437.5, Cpl=2730., kl=0.086, mul=156E-6,
... sigma=0.0082, Hvap=272E3, rhol=567, rhog=18.09, angle=35)
26722.441071108373
ht.boiling_nucleic.Zuber(sigma, Hvap, rhol, rhog, K=0.18)[source]

Calculates critical heat flux for nucleic boiling of a flat plate or other shape as presented in various sources. K = pi/24 is believed to be the original [1] value for K, but 0.149 is now more widely used, a value claimed to be from [2] according to [5]. Cao [4] lists a value of 0.18 for K. The Wolverine Tube data book also lists a value of 0.18, and so it is the default.

\[q_c = {KH}_{vap} \rho_g^{0.5}\left[\sigma g (\rho_L-\rho_g)\right]^{0.25} \]
Parameters
sigmafloat

Surface tension of liquid [N/m]

Hvapfloat

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

rholfloat

Density of the liquid [kg/m^3]

rhogfloat

Density of the produced gas [kg/m^3]

Kfloat

Constant []

Returns
q: float

Critical heat flux [W/m^2]

Notes

No further work is required on this correlation. Multiple sources confirm its form.

References

1

Zuber N. “On the stability of boiling heat transfer”. Trans ASME 1958 80:711-20.

2

Lienhard, J.H., and Dhir, V.K., 1973, Extended Hydrodynamic Theory of the Peak and Minimum Heat Fluxes, NASA CR-2270.

3

Serth, R. W., Process Heat Transfer: Principles, Applications and Rules of Thumb. 2E. Amsterdam: Academic Press, 2014.

4

Cao, Eduardo. Heat Transfer in Process Engineering. McGraw Hill Professional, 2009.

5

Kreith, Frank, Raj Manglik, and Mark Bohn. Principles of Heat Transfer, 7E.Mason, OH: Cengage Learning, 2010.

Examples

Example from [3]

>>> Zuber(sigma=8.2E-3, Hvap=272E3, rhol=567, rhog=18.09, K=0.149)
444307.22304342285
>>> Zuber(sigma=8.2E-3, Hvap=272E3, rhol=567, rhog=18.09, K=0.18)
536746.9808578263
ht.boiling_nucleic.h_nucleic(Te=None, q=None, Tsat=None, P=None, dPsat=None, Cpl=None, kl=None, mul=None, rhol=None, sigma=None, Hvap=None, rhog=None, MW=None, Pc=None, Csf=0.013, n=1.7, kw=401.0, rhow=8.96, Cpw=384.0, angle=35.0, Rp=1e-06, Ra=4e-07, h0=None, CAS=None, Method=None)[source]

This function handles the calculation of nucleate boiling heat flux and chooses the best method for performing the calculation based on the provided information.

One of Te and q are always required.

Parameters
Tefloat, optional

Excess wall temperature, [K]

qfloat, optional

Heat flux, [W/m^2]

Tsatfloat, optional

Saturation temperature at operating pressure [Pa]

Pfloat, optional

Saturation pressure of fluid, [Pa]

dPsatfloat, optional

Difference in saturation pressure of the fluid at Te and T, [Pa]

Cplfloat, optional

Heat capacity of liquid [J/kg/K]

klfloat, optional

Thermal conductivity of liquid [W/m/K]

mulfloat, optional

Viscosity of liquid [Pa*s]

rholfloat, optional

Density of the liquid [kg/m^3]

sigmafloat, optional

Surface tension of liquid [N/m]

Hvapfloat, optional

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

rhogfloat, optional

Density of the produced gas [kg/m^3]

MWfloat, optional

Molecular weight of fluid, [g/mol]

Pcfloat, optional

Critical pressure of fluid, [Pa]

Csffloat, optional

Rohsenow coefficient specific to fluid and metal [-]

nfloat, optional

Rohsenow constant, 1 for water, 1.7 (default) for other fluids usually [-]

kwfloat, optional

Thermal conductivity of wall (only for cryogenics) [W/m/K]

rhowfloat, optional

Density of the wall (only for cryogenics) [kg/m^3]

Cpwfloat, optional

Heat capacity of wall (only for cryogenics) [J/kg/K]

anglefloat, optional

Contact angle of bubble with wall [degrees]

Rpfloat, optional

Roughness parameter of the surface (1 micrometer default) used by Cooper method, [m]

Rafloat, optional

Roughness parameter of the surface (0.4 micrometer default) for Gorenflo method, [m]

h0float

Reference heat transfer coefficient for Gorenflo method, [W/m^2/K]

CASstr, optional

CAS of fluid

Returns
hfloat

Nucleate boiling heat flux [W/m^2]

Other Parameters
Methodstring, optional

The name of the method to use; one of [‘Gorenflo (1993)’, ‘Stephan-Abdelsalam water’, ‘Stephan-Abdelsalam cryogenic’, ‘Stephan-Abdelsalam’, ‘HEDH-Taborek’, ‘Forster-Zuber’, ‘Rohsenow’, ‘Cooper’, ‘Bier’, ‘Montinsky’, ‘McNelly’]

Notes

The methods Stephan-Abdelsalam, Cooper, and Gorenflo all take other arguments as well such as surface roughness or the thermal properties of the wall material. See them for their documentation. These parameters can also be passed as keyword arguments.

>>> h_nucleic(P=3E5, Pc=22048320., q=2E4, CAS='7732-18-5', Ra=1E-6)
3437.7726419934147

Examples

Water boiling at 3 bar and a heat flux of 2E4 W/m^2/K.

>>> h_nucleic(P=3E5, Pc=22048320., q=2E4, CAS='7732-18-5')
3043.344595525422

Water, known excess temperature of 4.9 K, Rohsenow method

>>> h_nucleic(rhol=957.854, rhog=0.595593, mul=2.79E-4, kl=0.680, Cpl=4217,
... Hvap=2.257E6, sigma=0.0589, Te=4.9, Csf=0.011, n=1.26,
... Method='Rohsenow')
3723.655267067467
ht.boiling_nucleic.h_nucleic_methods(Te=None, Tsat=None, P=None, dPsat=None, Cpl=None, kl=None, mul=None, rhol=None, sigma=None, Hvap=None, rhog=None, MW=None, Pc=None, CAS=None, check_ranges=False)[source]

This function returns the names of correlations for nucleate boiling heat flux.

Parameters
Tefloat, optional

Excess wall temperature, [K]

Tsatfloat, optional

Saturation temperature at operating pressure [Pa]

Pfloat, optional

Saturation pressure of fluid, [Pa]

dPsatfloat, optional

Difference in saturation pressure of the fluid at Te and T, [Pa]

Cplfloat, optional

Heat capacity of liquid [J/kg/K]

klfloat, optional

Thermal conductivity of liquid [W/m/K]

mulfloat, optional

Viscosity of liquid [Pa*s]

rholfloat, optional

Density of the liquid [kg/m^3]

sigmafloat, optional

Surface tension of liquid [N/m]

Hvapfloat, optional

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

rhogfloat, optional

Density of the produced gas [kg/m^3]

MWfloat, optional

Molecular weight of fluid, [g/mol]

Pcfloat, optional

Critical pressure of fluid, [Pa]

CASstr, optional

CAS of fluid

check_rangesbool, optional

Whether or not to return only correlations suitable for the provided data, [-]

Returns
methodslist[str]

List of methods which can be used to calculate h with the given inputs

Examples

>>> h_nucleic_methods(P=3E5, Pc=22048320., Te=4.0, CAS='7732-18-5')
['Gorenflo (1993)', 'HEDH-Taborek', 'Bier', 'Montinsky']
ht.boiling_nucleic.qmax_boiling(rhol=None, rhog=None, sigma=None, Hvap=None, D=None, P=None, Pc=None, Method=None)[source]

This function handles the calculation of nucleate boiling critical heat flux and chooses the best method for performing the calculation.

Preferred methods are ‘Serth-HEDH’ when a tube diameter is specified, and ‘Zuber’ otherwise.

Parameters
rholfloat, optional

Density of the liquid [kg/m^3]

rhogfloat, optional

Density of the produced gas [kg/m^3]

sigmafloat, optional

Surface tension of liquid [N/m]

Hvapfloat, optional

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

Dfloat, optional

Diameter of tubes [m]

Pfloat, optional

Saturation pressure of fluid, [Pa]

Pcfloat, optional

Critical pressure of fluid, [Pa]

Returns
qfloat

Nucleate boiling critical heat flux [W/m^2]

Other Parameters
Methodstring, optional

A string of the function name to use; one of (‘Serth-HEDH’, ‘Zuber’, or ‘HEDH-Montinsky’)

Examples

>>> qmax_boiling(D=0.0127, sigma=8.2E-3, Hvap=272E3, rhol=567, rhog=18.09)
351867.46522901946
ht.boiling_nucleic.qmax_boiling_methods(rhol=None, rhog=None, sigma=None, Hvap=None, D=None, P=None, Pc=None, check_ranges=False)[source]

This function returns a list of methods names which can be used to calculate nucleate boiling critical heat flux. Preferred methods are ‘Serth-HEDH’ when a tube diameter is specified, and ‘Zuber’ otherwise.

Parameters
rholfloat, optional

Density of the liquid [kg/m^3]

rhogfloat, optional

Density of the produced gas [kg/m^3]

sigmafloat, optional

Surface tension of liquid [N/m]

Hvapfloat, optional

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

Dfloat, optional

Diameter of tubes [m]

Pfloat, optional

Saturation pressure of fluid, [Pa]

Pcfloat, optional

Critical pressure of fluid, [Pa]

check_rangesbool, optional

Added for Future use only

Returns
methodslist

List of methods which can be used to calculate qmax with the given inputs

Examples

>>> qmax_boiling_methods(D=0.0127, sigma=8.2E-3, Hvap=272E3, rhol=567, rhog=18.09)
['Serth-HEDH', 'Zuber']