Unified correlation for heat transfer during boiling in plain mini/micro and conventional channels

A correlation is presented for predicting heat transfer coefficients during saturated boiling prior to critical heat flux in mini/micro channels as well as channels of conventional sizes in horizontal and vertical upward flow. The correlation is verified with a database that includes channels of various shapes (round, rectangle, triangle), fully or partially heated, horizontal and vertical downflow, diameters 0.38 to 27.1 mm, 30 fluids (water, CO₂, ammonia, halocarbon refrigerants, organics, cryogens), reduced pressure 0.0046 to 0.787, and mass flux 15 to 2437 kg m⁻²s⁻¹. The new correlation predicts the 4852 data points from 137 data sets from 81 sources with a mean absolute deviation of 18.6 %. Several other correlations were also compared with the same database; all had significantly higher deviations.     

A correlation for heat transfer during boiling on bundles of horizontal plain and enhanced tubes

A dimensionless correlation is presented for calculation of local heat transfer coefficients during saturated boiling in bundles of plain and enhanced tubes. It has been verified with a wide range of data that include 12 fluids (water, ammonia, halocarbon refrigerants, and hydrocarbons), plain and a variety of enhanced tubes of many materials, inline and staggered arrangements, pitch to diameter ratios 1.17 to 2.0, reduced pressures from 0.005 to 0.2866, mass flux from 0.17 to 1391 kgm⁻²s⁻¹, heat flux from 1 to 1000 kWm⁻², and vapor quality from 0 to 0.98. A total of 2173 data points from 51 data sets from 28 sources are predicted with mean absolute deviation of 15.2%.     

A new model for flow boiling heat transfer coefficient inside horizontal tubes with twisted-tape inserts

This paper presents a new method to predict the heat transfer coefficient during flow boiling inside horizontal tubes containing twisted tape inserts. The method was developed based on the database presented by Kanizawa et al. This database comprises flow boiling results for horizontal tubes with internal diameters of 12.7 and 15.9 mm, twisted-tape ratios of 3, 4, 9 and 14, mass velocities ranging from 75 to 200 kg m⁻² s⁻¹, heat fluxes of 5 and 10 kW m⁻² and saturation temperatures of 5 and 15 °C. The method is flow-pattern based and considers flow boiling, dryout and mist flow regions. The predictive method also takes into account the physical picture of the swirl flow phenomenon by considering swirl flow effects promoted by the twisted tape insert. The proposed method provides satisfactory predictions and captures the main heat transfer trends of the data of Kanizawa et al. and also of independent data from literature.     

Experimental correlation of falling film absorption heat transfer on micro-scale hatched tubes

The objectives of this paper are to investigate the effect of surface roughness of micro-hatching tubes on the absorption performance and to develop an experimental correlation of Nusselt number as a function of the roughness. Two different micro-scale hatched tubes and a bare tube are tested to quantify the effect of the surface roughness on the absorption performance. The roughness of the micro-scale hatched tubes ranges 0.386–11.359 μm. The working fluid is H₂O/LiBr solution with inlet concentration of 55, 58 and 61 wt.% of LiBr. The absorber heat exchanger consists of 24 horizontal tubes in a column, liquid distributor at the liquid inlet and the liquid reservoir at the bottom of the absorber. It was found that absorption performance of micro-hatching tubes was improved up to two times compared with the bare tube. An experimental correlation of Nusselt number was developed as a function of the film Reynolds number and the roughness with an error band of ±25%.     

Experimental correlation of pool boiling heat transfer for HFC134a on enhanced tubes: Turbo-E

The objectives of this paper are to study the heat transfer characteristics for enhanced surface tubes in the pool boiling and to provide a guideline for the design conditions for the evaporator using HFC134a. The shape of tube surfaces, the wall superheat, and the saturation temperature are considered as the key parameters. Copper tubes (d_o = 19.05 mm) are treated with different helix angles and the saturation temperatures are controlled from 3 to 16 °C. It is found that the pool boiling heat transfer coefficient decreases with increasing the wall superheat. It is also found that boiling heat transfer coefficients for Turbo-II and Turbo-III are 1.5–3.0 times and 1.2–2.0 times higher than that for Turbo-I without the helix angle, respectively. The higher heat transfer performance from Turbo-II and Turbo-III can be explained by the “bubble detention” phenomenon on the surface without the helix angle for the Turbo-I. The experimental correlations for the pool boiling heat transfer on the present enhanced tubes without (Type I) and with the helix angle (Type II and Type III) are developed with the error bands of ±30%, respectively.     

A note on the Chen correlation of saturated flow boiling heat transfer

The Chen (Ind. Eng. Chem. Process Des. Dev., 1966, 5(3): 322–329) correlation of saturated flow boiling heat transfer is one of the most influential flow boiling heat transfer correlations. It adopted the additive concept and incorporated the Reynolds number factor F and the suppression factor S. Chen presented F and S as the best-fit curves without any parametric equation. However, the parametric equations of F and S were widely used in citing the Chen work, among which some were not accurate, and some had typos in the original sources and then used by others. The objective of this paper is to point out the incorrect and inaccurate equations in the literature. For this purpose, the existing expressions of F and S in the available literature are presented and compared with the Chen best-fit curves. The work provides a reference for the correct use of the Chen correlation.     

A mathematical model of heat transfer for forced-convective film boiling

A mathematical model of film boiling with forced convection of the liquid is discussed. A solution is obtained on a computer and is represented in the form of nomographs and approximation relations. The computed results are compared with experimental data.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 5, pp. 822–827, November, 1977.     

Numerical model of a parallel flow minichannel evaporator with new flow boiling heat transfer correlation

In this paper, a distributed parameter (DP) numerical model with the new proposed flow boiling heat transfer correlation was established for parallel flow minichannel (PFMC) evaporator. DP model validation was made by comparing the measured values obtained on experimental studies, which were conducted under refrigerant mass flow rate range of 34.6–245.6 kg h⁻¹ and evaporation pressure of 200–500 kPa. The effects of four different flow boiling heat transfer correlations on DP model performance were investigated. Results showed that the new correlation predicted 99% of experimental data in ± 30% error bands. Moreover, the DP model with the new correlation yielded the mean absolute error (MAE) of 1.5%, 9.1%, 18.8%, 14.2% and 19.8% in prediction of cooling capacity, outlet air temperature, refrigerant superheat, air side and refrigerant side pressure drop, respectively. The presented DP model can be implemented to evaluate the performance of PFMC evaporator, and therefore can save efforts on component and system design and optimization.     

Certain peculiarities of heat transfer in nucleate boiling in capillary tubes

Boiling cryogenic fluids in capillary tubes of varying geometry are used to study heat transfer. It was found that nucleate boiling in a capillary channel, when the heat flux density on the wall is increased, is followed by slug boiling. The optimal cross section for the system is also calculated.     

Refrigerant boiling at low heat flux in vertical tubes with heat transfer enhancing fittings

The paper presents the results of thermal and flow analyses of the boiling process in vertical tubes with heat transfer enhancing inserts. Tests were performed for three different geometrical shapes of the inserts: a spiral tape with a core rod, a rib insert and a spring insert. Experimental measurements were performed for R507, R410A and R407C refrigerants at low heat flux. The obtained results indicate the increase ratio of heat transfer and flow resistance coefficients in tubes with inserts, as opposed to a plain one. Finally, the paper presents the dimensionless relationships which enable the calculation of heat transfer coefficients and pressure drops during boiling in vertical tubes with the studied heat transfer enhancing inserts.     

Liquid film and droplet flow behaviour and heat transfer characteristics of herringbone microfin tubes

Cross-sectional liquid flow rate distribution of vapour liquid two phase flow of R123 in different herringbone microfin tubes has been measured. Droplet and liquid film flow rates are calculated with the measured data and assumptions for droplet distribution and slip ratio. Heat transfer coefficients of evaporation and condensation in herringbone microfin tubes have been measured using R22. Heat transfer enhancement mechanism by the herringbone microfins is discussed by using the measured data and numerically obtained cross-sectional flow field of a single phase flow. Flow rate of thin liquid film flowing on tube sides is affected by the helix angle and fin height. Larger helix angle and higher fin give thinner film. Liquid film flow rates in tube top and bottom are higher than tube sides. Droplet flow rate is increased with increase of helix angle and fin height, although the effect of fin height is not as pronounced as helix angle. Droplet radial mass velocity to tube side walls is increased with helix angle.     

Prediction of heat transfer during boiling of cryogenic fluids flowing in tubes

Data from eleven sources for nitrogen, neon, helium, and argon boiling in horizontal and vertical tubes were compared with the correlations of Shah and Klimenko as well as the superposition correlation of Rohsenow. Best agreement was found with the Shah correlation which agrees with nine of the data sets. Each of the other two correlations gives satisfactory agreement with only four of the twelve data sets. The results of data analysis are presented and discussed.     

Simplified film model of a heat transfer crisis in tubes

A simplified model is proposed dealing with a heat transfer crisis during forced flow of water in tubes. The formula for the critical heat flow is obtained. The verification showed that this formula with a single empirical coefficient embraces 4745 experimental values of critical heat flows at a mean square error of 0.0691 in a wide range of parametric variations.     

Comprehensive correlations for heat transfer during condensation in conventional and mini/micro channels in all orientations

Two alternative correlations are presented for heat transfer during condensation in plain conventional channels as well as mini/micro channels in all orientations. These have been validated by comparison with a database that includes 33 fluids, diameters 0.10 to 49.0 mm, reduced pressures 0.0008 to 0.946, mass flux from 1.1 to 1400 kgm⁻²s⁻¹, various shapes (round, rectangular, triangular, etc.), all orientations (horizontal, vertical up and down, and angles in between). The data are from 136 data sets from 67 sources. While both correlations predict the 4063 data points with mean absolute deviation (MAD) of about 17%, their accuracy varies somewhat in different ranges. The same data are also compared to other correlations.     

Transient solid-liquid He heat transfer and onset of film boiling

The transient heat transfer between single-crystalline Ge chips and liquid helium is investigated during the application of light pulses with different optical power to the Ge sample. The strong temperature dependence of the electrical conductivity of Ge conveniently serves for monitoring the temporal behaviour of the sample temperature during the input of optical energy. After a certain time interval following the beginning of the light pulse an abrupt rise of the sample temperature is observed. This time interval is much longer than the thermal time constant expected for the sample. This abrupt rise of the sample temperature can be understood in terms of the onset of film boiling. The observed onset time of film boiling and its dependence upon the heat transfer power density agrees reasonably with earlier results by Steward.     

Heat transfer intensity at forced flow boiling of cryogenic liquids in tubes

A generalized correlation for heat transfer with forced flow boiling of cryogenic liquids (nitrogen, hydrogen and neon) in tubes is presented. The correlation describes, with a ± 35% accuracy, all known experimental data for vertical and horizontal channels (without stratified regimes) in the pressure range 0.9 – 22 bar, mass flow rates from 20 to 2200 kg m^?2 S^?1, and heat fluxes from 400 to 210 000 W m^?2. The boundary line between channels of a large and a small diameter has been established; a simple method of taking into account the higher heat transfer intensity in capillaries has been suggested.     

Forced flow boiling heat transfer of liquid hydrogen for superconductor cooling

Heat transfer from inner side of a heated vertical pipe to liquid hydrogen flowing upward was first measured at the pressure of 0.7 MPa for wide ranges of flow rates and liquid temperatures. The heat transfer coefficients in non-boiling regime for each flow velocity were well in agreement with the Dittus–Boelter equation. The heat fluxes at the inception of boiling and the departure from nucleate boiling (DNB) heat fluxes are higher for higher flow velocity and subcooling. It was found that the trend of dependence of the DNB heat flux on flow velocity was expressed by the correlation derived by Hata et al. based on their data for subcooled flow boiling of water, although it has different propensity to subcooling.     

Model of heat transfer associated with the surface boiling of liquid in tubes

A model is proposed for the heat-transfer process associated with the surface boiling of liquid in tubes. An analysis of the various constituents of the heat-transfer mechanism distributed over the thickness of the intermediate boiling layer is presented.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 31, No. 3, pp. 396–401, September, 1976.     

An experimental study of heat transfer during boiling of n-butane in vertical tubes

This article presents the results of an experimental investigation of heat transfer during boiling of n-butane in tubes. We isolated the zones in which the principal parameters (heat flux density and effective liquid velocity) affect the heat transfer rate. Appropriate equations are recommended for calculating the heat transfer constant.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 17, No. 4, pp. 616–621, October, 1969.In conclusion, the authors wish to thank L. S. Sterman for his interest in this work and his helpful comments.