Heat transfer engineering an international journal, tập 31, số 12, 2010

Heat Transfer Engineering, 31(12):963–964, 2010 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457631003638903 editorial Advances in Heat Transfer Engineering PRADEEP BANSAL Department of Mechanical Engineering, The University of Auckland, Auckland, New Zealand It gives me a great pleasure to present this special issue on “Advances in Heat Transfer Engineering” that contains some selected papers that were presented at the 4th International Conference on Cooling and Heating Technologies, held in Jinhae, Korea, during October 28–31, 2008 The conference was hosted in the “green” and environmentally friendly Jinhae City of Korea, with Professor Hanshik Chung as the chairperson and local host The conference provided an excellent platform for researchers from over 10 countries to present more than 80 papers covering a range of topics on “heat transfer engineering” leading to sustainable environment The conference specifically emphasized the need for international cooperation on the global warming issues leading to innovations in low carbon industry and environmentally sustainable development This special issue of Heat Transfer Engineering includes seven articles that cover a number of topics, ranging from uncovering the physics of frost formation on a flat plate to subcooled flow boiling of CO2 at low temperatures The first article is by Shinhyuk Yoon, Gaku Hayase, and Keumnam Cho This article presents the details of an experimental apparatus that was used to collect novel data on the frost formation on a flat plate, and correlations that were developed for the local and average frost thickness, frost density, and frost mass The second article is by Di Wu, Zhen Wang, Gui Lu, and Xiaofeng Peng from the Department of Thermal Engineering, Tsinghua University (China) The article introduced a new idea to design high-performance air-cooling condensers to automatAddress correspondence to Professor Pradeep Bansal, Department of Mechanical Engineering, The University of Auckland, Private Bag–92019, Auckland, New Zealand E-mail: p.bansal@auckland.ac.nz ically separate liquid from gas and to let condensation to occur in the droplet and unsteady thin film mode, resulting in a high average heat transfer coefficient The third contribution is by Xiaofeng Peng, Chen Fang, and Fen Wang from the Department of Thermal Engineering, Tsinghua University (China) The article presents mathematical treatment for better understanding of the vapor bubble transport in two-phase flow in bead-packed structures Gyu-Jin Shim, M M A Sarker, Choon-Geun Moon, HoSaeng Lee, and Jung-In Yoon, in the fourth article present experimental performance of a closed wet cooling tower (CWCT) with multiple paths having a rated capacity of kW The study concluded that a CWCT operating with two paths has higher heat and mass transfer coefficients than that with single path The fifth article in this group is from Yifu Zhang, Weizhong Li, and Shenglin Quan from the School of Energy and Power Engineering, Dalian University of Technology (China) The article presents a numerical method using a combination of the level-set approach and finite-volume framework to simulate two-dimensional laminar incompressible two-phase flows The method leads to the fluid properties (such as density, viscosity, etc.) being smoothed as continuous properties Yong Yang, Shengqiang Shen, Taewoo Kong, and Kun Zhang, also from the School of Energy and Power Engineering, Dalian University of Technology (China), in the sixth article describe a two-dimensional compressible numerical model to evaluate steam properties by the Virial equation The article studies the difference between condensation shock and aerodynamic shock, and the influence of aerodynamic shock on the nonequilibrium phase change is revealed The final article in this volume is from Xiumin Zhao and Pradeep Bansal from the Department of Mechanical Engineering of the University of Auckland (New Zealand) This article 963 964 P BANSAL presents an experimental investigation on the subcooled flow boiling heat transfer characteristics of CO2 in a horizontal tube below –30◦ C The article develops a new empirical correlation that agrees to within ±30% with the current CO2 experimental data It is expected that the data presented in this study would be beneficial to industry and designers of compact heat exchangers for CO2 at low temperatures I am extremely thankful to the conference organizers, specifically Professor Hanshik Chung for inviting me as a keynote speaker and providing me the opportunity to be involved in this conference, and to these authors, who worked diligently in meeting the review schedule and responding to reviewers’ comments in a timely manner My special thanks to all the reviewers, who have done an excellent job in improving the quality of the papers Finally, I am also thankful to Professor Afshin Ghajar for allowing me to publish this special volume of Heat Transfer Engineering heat transfer engineering Pradeep Bansal holds a personal chair in the Department of Mechanical Engineering at the University of Auckland (New Zealand) Currently he is also serving as the Postgraduate Associate Dean in the Faculty of Engineering, and the Director of the Energy & Fuels Research Unit at the University of Auckland He is a fellow of the American Society of Heating, Refrigerating, and Air-Conditioning Engineers (ASHRAE) and of the Institute of Refrigerating, Heating, and AirConditioning Engineers (IRHRAE) of New Zealand He is also the chair of an ASHRAE Technical Committee (TC10.4) on “Ultra low cryogenic temperatures,” as well as a member of its Handbook Committee, and a member of various other committees, including TC8.02, TC8.08, TC8.09, TC10.6, TC10.7, and TC8.09 He serves on numerous national and international committees, has collaborated with various international institutions, has supervised more than 50 graduate student theses, and has published more than 200 technical papers, including books His research domain comprises fundamental heat transfer studies on natural refrigerants, development of simulation models, and design and development of energy-efficient thermal systems vol 31 no 12 2010 Heat Transfer Engineering, 31(12):965–972, 2010 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457631003638911 Measurements of Frost Thickness and Frost Mass on a Flat Plate under Heat Pump Condition SHINHYUK YOON,1 GAKU HAYASE,2 and KEUMNAM CHO3 Graduate School, Sungkyunkwan University, Suwon, Korea System Appliances Division, Samsung Electronics Co., Ltd, Suwon, Korea School of Mechanical Engineering, Sungkyunkwan University, Suwon, Korea This study measured the frost thickness and frost mass on a flat plate to propose the correlation equations for the local and average frost thickness, frost density, and frost mass Key parameters were the cooling surface temperature of the flat plate from 258.2 to 268.2 K, absolute humidity of air from 2.98 to 4.16 g/kgDA , air temperature from 273.5 to 280.2 K, and air velocity from 1.0 to 2.5 m/s A 50% ethylene glycol aqueous solution was used as a coolant The sensitivity analysis of the parameters such as air temperature, air humidity, air velocity, and surface temperature on the frost thickness and frost mass were experimentally investigated under the heat pump condition Correlation equations for the local and average frost thickness and frost mass under the heat pump condition were proposed The values predicted by the correlation equations under the freezer condition were larger by a maximum of 30–50% than the values predicted by the present correlation equations under the heat pump condition The proposed correlation equations might be applied to the part of the freezer condition INTRODUCTION The use of air-source heat pumps for residential applications has steadily increased It has an advantage of using affluent heat sources from the surrounding atmosphere When the air temperature in winter is below the freezing temperature of water, porous frost begins to form The frost layer on the evaporator of the heat pump acts as a resistance to heat transfer and reduces air flow rate Frost thickness, frost density, etc are required to be investigated to understand frost formation Even though the finned-tube evaporator for the heat pump mostly uses louvered fins and slit fins instead of plate fins, the fin might be simplified as a flat plate There are lots of studies on frost on a flat plate in the open literature Most of them reported the frost pattern under freezer conditions instead of heat pump conditions Frost formations under heat pump conditions might be different from those under freezer conditions due to different frost properties, even This work was supported by SFARC at Sungkyunkwan University, and Brain Korea 21 Project in Korea The authors appreciate Samsung Electronics Co for providing test samples and advice Address correspondence to Professor Keumnam Cho, School of Mechanical Engineering, Sungkyunkwan University, 300 Chunchun-dong, Jangan-gu, Suwon 440-746, Korea E-mail: keumnamcho@skku.edu though they show similar trends Most of the following studies are based on the freezer condition Trammel et al [1] studied the frost layer on the flat plate They found that the frost density increases as the dew point and air velocity increase Brian et al [2] provided measured frost density graphically Frost density was increased as the air temperature was increased Sanders [3] reported that the frost density was increased as wall and air temperatures were increased They also reported that higher air humidity makes lower frost density O’Neal and Tree [4] found that the frost density increases as time passes, due to vapor diffusion Na and Webb [5] investigated fundamental phenomena related to frost deposition and growth They found that water vapor pressure at the frost surface is supersaturated, by applying laminar concentration boundary layer analysis A couple of other studies [6–8] modeled the frost formation process employing a semi-empirical transient model for a flat plate under forced convection condition Mao et al [9, 10], Yang and Lee [11], and Lee and Ro [12] proposed their own correlation equations for the frost density and the frost thickness None of them were developed by considering heat pump conditions There are few studies under heat pump conditions so far Kwon et al [13] investigated the frost formation on a flat plate with local cooling Our previous study, Shin et al [14], 965 966 S YOON ET AL reported that the pressure drop through the slit-fin-and-tube heat exchanger under frosting condition at low velocity was higher than that at high velocity, although the average frost thickness at low velocity was less than that at high velocity Most of frost studies were performed by using the average frost properties, even though they are locally different The objective of the present study is to suggest the correlation equations for the local and average frost thickness and frost mass on the flat plate under heat pump conditions EXPERIMENTAL APPARATUS The schematic diagram of the experimental apparatus is shown in Figure 1a It consists of a psychrometric calorimeter, a refrigerant system, a wind tunnel, a data acquisition system, and a test section The psychrometric calorimeter, which had temperature control range of −10 to 50◦ C and humidity control range of 30 to 95%, provided constant dry- and wetbulb temperature by using an air handling unit The refrigerant system used an ethylene glycol–water mixture for easy control of the inlet temperature of refrigerant Bypass solenoid valves at both inlet and outlet of the test section made the refrigerant not flow into the test section prior to the test The mass flow rate of refrigerant was measured by a Coriolis mass flow meter with an accuracy of ±0.1% of the full scale The inlet and outlet temperatures of refrigerant were measured by the RTD with an accuracy of ±0.15◦ C In the wind tunnel, air was supplied by a 2.2-kW exhaust fan and four nozzles that had different diameters To homogenize the air flow, honeycombs were installed at the inlet and outlet of the test section Insulating material was placed around the test apparatus to minimize the heat loss The wind-tunnel section designed was made of transparent acryl with a width of 300 mm, height of 100 mm, and length of 1000 mm The test section with a width of 200 mm and length of 150 mm was made of copper, and it was flush mounted at the center of the bottom of the acryl wind tunnel Frost mass was measured by using aluminum tape and a balance A piece of thin aluminum tape was used to cover the surface of the flat plate before each test, as shown in Figure 1b Frost mass was determined by measuring the change of the aluminum tape before and after the test Frost mass was measured every 30 by repeating the frost mass measurements at the same test condition, since it was very difficult to measure instantaneous frost mass Four different frost masses were measured every 30 under the same condition since the test period was h The frost surface temperatures on the flat plate were measured by an infrared thermometer and T-type thermocouples Figure 1b shows the positions measured the frost surface temperature Frost thickness was measured by a digital CCD camera positioned properly by a stepping motor, as shown in Figure 2a The CCD camera took pictures of the frost every 10 automatically The flat plate was flush mounted at the bottom cenheat transfer engineering Figure Experimental apparatus ter of the acryl duct to avoid any edge effect of the duct Most commercial three-dimensional scanners are very expensive, and they have a resolution of the order of mm, which is not good enough to measure the frost thickness Since the frost profile was almost symmetrical on the left- and right-hand sides along the flow direction, a two-dimensional frost profile was utilized instead of a three-dimensional profile Frost thickness profiles were measured at four different positions as shown in Figure 2b to verify the two-dimensional frost profile The frost thickness was defined as shown in Figure 2c Figure showed the typical frost thickness profiles at four different positions Frost thickness profiles at the left and right sides showed similar patterns with almost the same values, while the frost thicknesses at front and rear sides were almost constant except for a small part of the front and rear edges This means that the frost thickness profile might be determined by monitoring only the left-hand-side frost thickness Two dry- and wet-bulb thermometers were installed before and after the test section to measure the average temperature and humidity of the moist air The uncertainty of the air temperature measurement was 0.4◦ C, while the uncertainty of the relative humidity was 1% The refrigeration system consisted of a refrigerator and a pump to circulate the refrigerant A 50% ethylene glycol aqueous solution was used as the refrigerant Flow rate of the refrigerant was set to kg/min The test data were recorded every s for 120 Key experimental parameters were cooling surface temperature (Tw ), air humidity (wa ), air temperature (Ta ), and air velocity (Va ) They ranged from 258.2 to 268 K for the cooling vol 31 no 12 2010 S YOON ET AL 967 Figure Comparison of measured and estimated frost masses where δ f,m is the measured frost thickness, W is the length of the flat plate, and ρ f,e is the estimated frost density by using Eq (2) suggested by Hayashi et al [15] In general, high values of density are expected as the frost surface temperature approaches the water triple point, and a curve like the one depicted as the exponential function by Hayashi et al [15] is a good representation of expected results That’s why it is used for the comparison ρ f,e = 650 exp(0.277T f,m ) Figure Frost thickness measurement surface temperature, from 2.98 to 4.16 g/kgDA for the air humidity, from 273.5 to 280.2 K for the air temperature, and from 1.0 to 2.5 m/s for the air velocity DATA REDUCTION The measured frost mass was compared with the estimated one calculated by using Eq (1) to verify the validity of the methodology of the frost thickness and frost temperature measurements m f,e = ρ f,e · δ f,m · W d x (1) Figure Typical frost profiles at four different positions (wa = 3.67 g/kgDA , Tw = 263.15 K, Ta = 275.15 K, Va = 1.5 m/s, t = 120 min) heat transfer engineering (2) The measured average frost density might be determined by using Eq (3) m f,m (3) ρ f,m = Aal δ f,m The uncertainty was ±1.2% for the frost thickness and ±8.2% for the frost mass through the uncertainty analysis suggested by Moffat [16] RESULTS AND DISCUSSION The measured frost mass was compared with the estimated one to verify the methodology of the frost thickness and frost temperature measurements as shown in Figure The estimated and measured frost masses agreed within 8%, which is within the uncertainty range This means that the methodology utilized for the frost thickness measurement is appropriate The effect of the cooling surface temperature on the local frost thickness at a position of 75 mm from the entrance and the frost mass are shown in Figure Both the local frost thickness and frost mass were increased as the cooling surface temperature was decreased The local frost thicknesses for a cooling surface temperature of 258.2 K were larger by 33.5% than those for a cooling surface temperature of 263.2 K and by 63.3% than those for a cooling surface temperature of 268.2 K The frost masses for a cooling surface temperature of 258.2 K were larger by 5.3% than those for a cooling surface temperature of 263.2 K and by 13.6% than those for a cooling surface temperature of 268.2 K The cooling surface temperature affected more severely the local frost thickness than the frost mass The reason is as follows As vol 31 no 12 2010 968 S YOON ET AL Figure Effect of cooling surface temperature Figure Effect of air humidity the cooling surface temperature decreases, heat from the phase change process of a water molecule may be easily absorbed into the frost layer, and then the surface temperature of the frost layer is maintained at a low level This reduces the humidity of the boundary between the surface of the frost layer and the air, and thus maintains a large concentration driving force As a result, a larger amount of frost is produced However, it is supposed that the lower temperature of the frost surface causes the formation of small droplets or particles of water molecule, consequently resulting in a coarse frost later, and then the structure made during early crystal growth period affects the growth of the frost layer Figure shows the effect of the air humidity on the local frost thickness and frost mass The local frost thicknesses at a position of 75 mm from the entrance for a humidity of 4.16g/kgDA were larger by 21.4% than those for a humidity of 3.67g/kgDA and 52.3% than those for a humidity of 2.98g/kgDA The frost masses for a humidity of 4.16g/kgDA were larger by 16.4% than those for a humidity of 3.67g/kgDA and 115.3% than those for a humidity of 2.98g/kgDA The effect of humidity on the frost mass was almost the same order with the effect of cooling surface temperature This might be mainly because the high humidity causes a high concentration driving force that transports a greater amount of water vapor from the air to the frost layer Figure shows the effect of the air temperature on the local frost thickness and frost mass Even though air temperature was ascertained to have a small effect compared to air humidity and cooling surface temperature, an influence was nevertheless found The local frost thicknesses at the position of 75 mm from the entrance for an air temperature of 273.5 K were larger by 1.2% than those for an air temperature of 275.2 K and by 8.5% than those for an air temperature of 280.2 K However, the frost masses for an air temperature of 273.5 K were smaller by 5.2% than those for an air temperature of 275.2 K and by 12.6% than those for an air temperature of 280.2 K The structure of the frost layer constructed in the early crystal growth period might play a role resulting in a large frost mass During the early crystal growth period, higher air-side surface temperatures of the frost layer decrease the probability of small droplets or particles formation from water vapor, and then cause a thinner and dense frost layer Increase of the frost density, which means a decrease of the porosity, provides the larger specific surface area and then causes the water vapor on the frost surface to diffuse easily into the inner frost layer like a pumping effect Figure shows the effects of air velocity on local frost thickness and frost mass They are comparably smaller than the effects of the air humidity and the cooling surface temperature The local frost thicknesses at the position of 75 mm from the heat transfer engineering vol 31 no 12 2010 S YOON ET AL 969 Figure Effect of air temperature Figure Effect of air velocity entrance for an air velocity of 2.5 m/s were larger by 4.0% than those for an air velocity of 1.5 m/s and by 6.1% than those for an air velocity of 1.0 m/s This might be because higher air velocity results in a larger quantity of frost layer, slightly increased frost layer thickness, and accelerated densification of the layer Most literature reports related to frost for the freezer stated that the frost under the freezer condition is mainly due to the high temperature of outside air Based on the literatures for the freezer, the freezer condition was set to 15 ≤ Ta (◦ C) ≤ 25, 6.94 ≤ wa (g/kgDA ) ≤ 12.50, and −25 ≤ Tw (◦ C) ≤ −15 A few papers expanded the range to ≤ T a (◦ C) ≤ 25, 3.58 ≤ wa (g/kgDA ) ≤ 12.50, and −35 ≤ Tw (◦ C) ≤ −15 Frost for the heat pump is mainly caused by the cold air of outside in winter The air temperature and the absolute humidity of air for the heat pump are lower than those for the freezer, while the cooling surface temperature for the heat pump is higher than that for the freezer The heat pump condition was set to ≤ Ta (◦ C) ≤ 7, 2.98 ≤ wa (g/kgDA ) ≤ 4.16, and −15 ≤ Tw (◦ C) ≤ −5 Frost characteristics for the heat pump might be different from those for the freezer due to different operating conditions Figure shows the applicable range of the freezer condition as a dotted circle and the heat pump condition as a solid circle Most literature reports suggested average values for the frost thickness and frost mass instead of local values Correlation equations for the local frost thickness and frost density are proheat transfer engineering posed as shown in Eqs (4) and (5) by using measured local data (ρ f,m and δ f,m ) and modifying the empirical equations suggested by Yang and Lee [11]: δ f, p = 3.782(L ∗ )−1.352 (wa )1.704 (Fo)0.6803 (T ∗ )2.035 (Re L )0.251 (4) Figure Applicable ranges of the proposed correlations vol 31 no 12 2010 970 S YOON ET AL Figure 10 Local frost thickness and frost density Figure 11 Comparison of the measured average frost thickness and frost mass with the values predicted by some correlations under heat pump conditions ρ f, p = 1.852 × 10−4 (ρice )(L ∗ )−0.976 (wa )2.312 ×(Fo) 0.550 ∗ 3.035 (T ) (Re L ) 0.346 Figure 10 shows the local frost thicknesses and frost densities measured and predicted The local frost thickness and local frost density get smaller along the air flow direction Heat and mass transfer at the leading edge is relatively brisk because of the leading edge effect The average values predicted by Yang and Lee [11] were larger by 16 to 58% than the measured data, since they predicted the values under the freezer condition The correlation equations for local frost thickness and frost density under the heat pump condition in the present study might predict much more accurately than the other correlation equations The average frost thickness and frost density might be expressed as Eqs (6) and (7) by taking the average of local frost thickness and frost density shown in Eqs (4) and (5) δ¯ f, p = L ρ¯ f, p = (5) Tt p − Tw αa t x ρ Va L , L∗ = , Fo = , Re L = a T∗ = Ta − Tw L L µa δ f, p d x (6) L heat transfer engineering L ρ f, p d x L (7) The frost mass might be also estimated as shown in Eq (8) by using Eqs (4) and (5) for the local values L m¯ f, p = ρ f, p δ f, p W d x (8) Figure 11 shows a comparison of the measured average frost thicknesses and frost mass data with the values predicted by the correlation equations developed under freezer condition The predicted values by the correlation equations under the freezer condition suggested by Mao et al [10], Yang and Lee [11], and Lee and Ro [12], including data by Serker et al [17], were compared with the predicted values by the present correlation equations (6) and (8) The comparison was done for condition of Figure The values predicted by the correlation equations under the freezer condition were larger by a maximum of 30–50% than the values predicted by the present correlation equations under the heat pump condition This is mainly due to the differences in the conditions such as air humidity, air temperature, and surface temperature The freezer condition is vol 31 no 12 2010 S YOON ET AL 971 on the frost thickness and frost mass were experimentally investigated under the heat pump condition Correlation equations for the local and average frost thickness and frost mass under the heat pump condition were proposed The values predicted by the correlation equations under the freezer condition were larger by a maximum of 30–50% than the values predicted by the present correlation equations under the heat pump condition The proposed correlation equations might be applied to part of the freezer condition NOMENCLATURE area, m2 Fourier number ( = αa t/L2) length of the flat plate, m local frost mass, g average frost mass, g temperature, ◦ C time, velocity, m/s width of the flat plate, m absolute humidity, kg/kg DA position from the entrance of the flat plate, mm A Fo L m m¯ T t V W w x Figure 12 Comparison of the measured average frost thickness and frost mass with the values predicted by some correlations under freezer conditions usually expected to have more frost than the heat pump condition Existing correlation equations under the freezer condition including data overpredict by 30 to 50% the frost density and frost mass under the heat pump condition Correlation equations suggested in the present study might be extended to the freezer condition This was examined by comparing the predicted values by the same correlation equations utilized in Figure 11 and data by Serker et al [17] with the predicted values by the present correlation equations (6) and (8) at condition of Figure Figure 12 shows the comparison The predicted values by the present correlation equations agreed with the data by Serker et al [17] within a maximum of 10% This means that the proposed correlation Eqs (4) and (8) might be applied to the part of the freezer condition CONCLUSIONS Greek Symbols α δ δ¯ µ ρ ρ¯ thermal diffusivity, m2/s local frost thickness, mm average frost thickness, mm viscosity, N-s/m2 local frost density, kg/m3 average frost density, kg/m3 relative humidity,% Subscripts a al e f ice m p w air aluminum tape estimated value frost ice condition at Tf measured value predicted value triple point of water cooling surface The present study can be summarized as follows REFERENCES The estimated and measured frost masses agreed within an uncertainty range of 8% The sensitivity analysis of the parameters such as air temperature, air humidity, air velocity, and surface temperature heat transfer engineering [1] Trammel, G J., Little D C., and Lillgore, E M., A Study of Frost Formed on a Flat Plate Held at Sub-Freezing Temperature, ASHRAE Journal, vol 7, no 10, pp 42–47, 2004 vol 31 no 12 2010 1008 Y YANG ET AL liquid-phase mass fraction (β) and the number of liquid droplets per unit volume (η) To make the simulation availability and efficient, the condensing steam flow is assumed to be adiabatic and inviscid Since droplet sizes are quite small, it is assumed that the volume of the condensate is negligible and the velocity slip between the droplets and gaseous phase is zero Under the foregoing assumptions, the Euler equations may be written in integral form as follows: β (8) (1 − β) Vd (ρl /ρg ) Vd = π¯r (9) where ρl , Vd , and r¯ denote the liquid density, the average droplet volume and the average droplet radius η= (1) Nucleation Model and Droplet Growth Model for Nucleating Particles where x, y, and t are the space and time coordinates, respectively; U, F, and G are defined as: ⎡ ⎤ ⎡ ⎡ ⎤ ⎤ ρu ρ ρv ⎢ ρu + P ⎥ ⎢ ρu ⎥ ⎢ ⎥ ρuv ⎢ ⎥ ⎥ ⎥G = ⎢ U =⎢ ⎣ ρv ⎦ F = ⎣ ⎣ ⎦ ρv + P ⎦ ρuv ρE (ρE + P)v (ρE + P)u The present model considers only homogeneous nucleation in pure substance and relies on the classical theory corrected for nonisothermal effects by Young [9] In the model, the classical homogeneous nucleation theory describes the formation of a liquid phase in the form of droplets from a supersaturated phase in the absence of impurities or foreign particles, and the nucleation rate is given by: ∂F ∂G ∂U + + =0 ∂t ∂x ∂y and the internal energy and specific enthalpy are determined as follows: E = h0 − P ρ (2) 2 h0 = h + u + v h = (1 − β)h g + βh l (3) (4) Description of the Two-Phase Mixture In this article, the two-phase flow after the homogeneous condensation was described as a wet-steam mixture consisting of the continuous vapor phase at temperature T and pressure P, interspersed with a large number of spherical liquid droplets It is assumed that the liquid is monodispersed—that is, that all droplets are of the same size at one point in the flow, and the interactions between droplets are neglected The density of the mixture is approximated as the following equation by neglecting the volume occupied by the liquid droplets: ρ = ρg /(1 − β) (5) To model wet steam, two additional transport equations are needed [8] The first transport equation governs the mass fraction of the condensed liquid phase (β) and the second transport equation (η) determines the number of droplets per unit volume The two equations are combined to the model in the following expression: ∂ρ β + ∇(ρvβ) = ∂t (6) ∂ρ η + ∇(ρvη) = ρI ∂t (7) heat transfer engineering I = ρ2v qc + θ ρl 2πRT exp Mm3 π − 4πr∗2 σ 3K b T (10) where qc is condensation coefficient, Kb is the Boltzmann constant, Mm is the mass of one molecule, σ is the liquid surface tension, and θ is a nonisothermal correction factor that is given by the following relation: θ= 2(γ − 1) h lv (γ + 1) RT h lv − 0.5 RT (11) where h lv is the latent heat of evaporation at pressure P and γ is the ratio of specific heat capacities The nucleation model just describes the quantity of droplets at a location in the continuous gas phase, and the droplets growth rate can be derived on the basis of heat transfer conditions surrounding the droplet [10] The droplets growth equation can be written as: P γ+1 ∂ r¯ = C p (Tl − T ) (12) √ ∂t h lv ρl 2πRT 2γ The vapor state departure from thermal equilibrium is quantified by the supercooling (Tsubc ), Tsubc = Ts − T (13) where Ts is the saturation temperature at the local pressure P, and the droplet temperature Tl is assumed to maintain its quasisteady value [11]: Tl = Ts − 2σTs ρl h lvr (14) This assumption is equivalent to neglecting droplet temperature relaxation and is justified because the time constant associated with this process is extremely short The difference between the liquid and saturation temperatures given in Eq (14) is due to surface curvature effects and is significant only for very small droplets vol 31 no 12 2010 Y YANG ET AL Based on the preceding modeling, the mass generation rate is given by the sum of mass increase due to nucleation and also due to growth/demise of these droplets, and therefore is written as: ∂ r¯ πρl I r∗3 + 4πρl η¯r ∂t Position X YB YC where r∗ is the Kelvin–Helmholtz critical droplet radius The droplet will grow as long as its radius is larger than r∗ ; otherwise the droplet will evaporate The term r∗ is given as follows: P Psat (T ) 0.5 0.05 0.06 0.072 0.075 (17) Equation of State In the present work the equation of state reported in the study of Vukalovich is used [12], which was tested for extrapolation into supercooled states [13] This equation of state utilizes a Virial formulation, in which the Virial equation of state along with relations for vapor pressure, liquid density, and specific heat data provides the basis for calculating all properties required in the simulations, for both equilibrium and supercooled states [14] CFD Solution Methodology In the study, the nonequilibrium condensation model has been implemented within the commercial computational fluid dynamics (CFD) code FLUENT, which provides the framework for the solution of the hydrodynamic equations The liquid- and gas-phase conservation equations are discretized using a conservative finite-volume integration over a control volume Secondorder upwind schemes are selected, and in this approach, highorder accuracy is achieved at cell faces through a Taylor-series expansion of the cell-centered solution about the cell centroid In the simulation, turbulence is modeled via the standard κ–ε model The source terms in the κ–ε equations not consider the influence of the liquid droplets on turbulence conditions However, this effect is indirectly modeled via the velocity field introduced to the κ–ε equations in each iteration This is assumed adequate for droplets of submicrometer size The mesh and model were created in a two dimensional (2-D) domain The geometries of the expansion portion of these nozzles (Figure 1) were taken to be the same as the nozzles used in the experiment of Moore et al [4] To retain the calculation speed advantage coming with the use of the regular block-structure element, a multiple-block technique was applied to make the heat transfer engineering Position Throat (16) where S is the supersaturation ratio defined as the ratio of vapor pressure to the equilibrium saturation pressure: S= -0.2 0.05635 0.06635 -0.25-0.2 -0.1 -0 0.1 0.2 0.3 0.4 0.5 X/m Figure Geometries of the converging-diverging nozzles (nozzles (B) and (C) used by Moore et al [4]) concentration of grid density focused on the areas where significant phenomena were expected The boundary conditions and the assumptions made were as follows: At the nozzle inflow, subsonic flow was specified using total pressure (P0in ), total temperature (T0in ), and flow angle normal to the inlet plane In addition, a turbulent intensity of 0.05 and an eddy length scale of 0.075 of the nozzle inlet diameter were used At the wall a no-slip adiabatic wall condition was used and it was assumed that the liquid droplets, upon impact with the wall, were reflected back into the flow with a coefficient of restitution equal to 0.1 Assuming that the flow is symmetrical about the nozzle centerline, symmetry conditions were enforced for all flow variables along this plane At the exit plane, either supersonic outflow or subsonic outflow was applied For the supersonic outflow condition, all of the flow parameters were extrapolated from the interior of the domain to the exit plane For the subsonic outflow, a series of back-pressures (Pb ) was specified to examine the effect of the aerodynamic shock on the spontaneous condensation 0.9 The Proposed Model The Isentropic Model Experiment Moore et al [4] 0.8 Pressure Ratio/(P/Poin) 2σ r∗ = ρl RT L n S -0.25 0.05635 0.06635 (15) Y/m = 1009 0.7 0.6 0.5 0.4 0.3 0.2 0.1 -0.25-0.2 -0.1 0.1 0.2 0.3 0.4 0.5 Distance form Throat X/m Figure Pressure distribution along the nozzle centerline compared with the experiment for nozzle (B) vol 31 no 12 2010 1010 Y YANG ET AL 0.8 The Proposed Model The Isentropic Model Experiment Moore et al [4] Pressure Ratio/(P/Poin) 0.7 Level Pressure: 13 17 4000 8000 12000 16000 20000 0.6 17 0.5 -0.2 15 -0.1 13 12 0.1 0.2 0.3 0.4 0.5 0.4 Distance form Throat X/m 0.3 Figure The isogram of pressure (P, Pa) for nozzle B computed by isentropic model 0.2 0.1 -0.25-0.2 -0.1 0.1 0.2 0.3 0.4 0.5 Distance from Throat X/m Figure Pressure distribution along the nozzle centerline compared with the experiment for nozzle (C) NUMERICAL DESCRIPTION OF SUPERSONIC CONDENSING STEAM FLOW WITH CONDENSATION SHOCK Numerical Validation: Comparison With Experimental Values The present model has been validated against the experimental data of Moore et al [4], who obtained centerline pressure distributions and the exit droplet sizes for a series of converging–diverging nozzle configurations In Figure and Figure 3, the pressure distribution along the centerline for the nozzle is compared with the experimental values and the results are in excellent agreement with experiments for the converging–diverging nozzles As shown in these figures, in the Laval nozzle, the crosssectional flow area first decreases to the throat and then increases monotonically in the supersonic region As the steam flows through the nozzle, it expands and the temperature falls rapidly Because the saturation vapor pressure decreases exponentially with temperature, a high supersaturation can be achieved Eventually the steam acquires sufficient supercooling for the nucleation of droplets in the diverging section of the nozzle, where the flow is supersonic The subsequent release of latent heat thus results in a deceleration of the flow and a rise in pressure, known as the “condensation shock.” Based on the comparison with the isentropic expansion solution, the location of the condensation shock can be revealed clearly As is shown in Figure 4, different from the isentropic expansion (Figure 5), at the region near x = 0.1, the pressure rises abruptly in a narrow space, showing clearly that the homogeneous nucleation happens suddenly As a great amount of latent heat of condensated droplets has been released, the temperature of the steam increases dramatically (Figure 6), while in the isentropic expansion solution the temperature decreases monotonically (Figure 7) Also, condensation shock has a clear boundary effect emerging in the form of isograms of pressure and temperature, as shown in Figure and Figure Simulation for the Condensation Shock The numerical results by the proposed model have been compared with the isentropic expansion solution for nozzle B The two-dimensional simulation results for the condensation shock caused by the homogeneous nucleation are shown in Figures to Figure and Figure give the isogram of pressure for the Laval nozzle calculated by the proposed model and the isentropic model, while Figure and Figure demonstrate the temperature for the Laval nozzle computed by the two different models Level Pressure: 25 -0.2 24 22 21 -0.1 13 19 25 7000 9000 14000 20000 0.1 0.2 0.3 0.4 Effect of Shock on Spontaneous Condensation To qualitatively describe the physics of spontaneous condensing steam flow with or without shock, a sample of the calculated Level Temperature: 3000 12 19 17 1413 10 11 SHOCK EFFECT ON THE SPONTANEOUS CONDENSING FLOW WITH HOMOGENEOUS NUCLEATION 15 0.5 Distance form Throat X/m Figure The isogram of pressure (P, Pa) for nozzle B computed by proposed model heat transfer engineering -0.2 13 -0.1 12 0.1 11 13 19 270 307 330 365 0.2 Distance form Throat X/m 0.3 0.4 0.5 Figure The isogram of temperature (T, K) for nozzle B computed by proposed model vol 31 no 12 2010 Y YANG ET AL 1011 Level Temperature: 14 14 -0.2 13 -0.1 11 9 13 220 255 290 330 0.1 0.2 0.3 0.4 0.5 Distance form Throat X/m Figure The isogram of temperature (T, K) for nozzle B computed by isentropic model results for Laval nozzle C is shown in Figures to 13 The boundary conditions at the inflow were P0in = 25 kPa and T0in = 358.6 K, and at the exit plane a series of back-pressures (Pb = 7027.5 Pa, 12 kPa, 15 kPa, 16.5 kPa, 20 kPa, 22 kPa) was specified to examine the effect of the shock on the spontaneous condensation As is apparent in Figures to 13, at the location of the condensation shock, the temperature decreases rapidly to make the isentropic expansion vapor cross the saturation line quickly and stay in a supersaturated state until the spontaneous condensation occurs suddenly where supercooling is achieved near 40 K (Figure 10), with a resulting significant amount of liquid droplets generated, approximately 1022 droplets per second per unit volume (Figure 11) A sharp rise in wetness fraction is observed, reflecting the rapid growth of the droplets immediately following the peak nucleation (Figure 12) Referring again to Figure 10, it is shown that after peak nucleation, the supercooling level rapidly drops to near equilibrium conditions (Tsbuc ≈ 1–2 K) This near equilibrium condition prevails the remaining length of the nozzle for the supersonic outflow case (Pb = 7027.5 Pa) For the case of a normal aerodynamic shock (Pb = 12 kPa, 15 kPa, 16.5 kPa), the flow conditions upstream of the aerodynamic shock are the same as for the flow condition in the supersonic outflow case (Pb = 7027.5 Pa) But through the aerodynamic shock the supercooling level abruptly becomes negative (superheated conditions) and liquid droplets rapidly evaporate in response to the rapid pressure and temperature Pb=22KPa 22 20 20KPa 18 Normal Aerodynamic Shock 16 14 Condensation Shock 12 16.5KPa 15KPa 12KPa 7027.5Pa -0.1 T in=358.6 K P in=25 KPa 7027.5Pa 1.6 1.4 1.2 16.5KPa15KPa 12KPa 20KPa 0.8 0.6 Pb=22 KPa 0.2 -0.25 -0.2 -0.1 0.1 0.2 0.3 0.4 0.5 Distance From Throat X/m Figure Frozen Mach number distribution along the nozzle centerline for various back-pressure values rise across the shock In the region between the condensation shock and the normal aerodynamic shock, wetness fraction and droplet size increase slightly as shown in Figure 12 and Figure 13 Downstream of the aerodynamic shock, the temperature falls abruptly due to re-acceleration of the flow, and after another peak point of the Mach number, the flow will decelerate with a small negative value of supercooling level to support heat movement toward the liquid phase as evaporation continues on droplet surfaces and wetness fraction reduces As is shown in the figures, as the back-pressure increases the normal aerodynamic shock moves toward the nozzle throat, and the strength of the aerodynamic shock decreases If the normal aerodynamic shock passes through the location of the condensation shock (Pb = 20 kPa, 22 kPa), the spontaneous condensation will be weakened or even not occur at all, because the aerodynamic losses of the shock make the steam flow decelerate to subsonic or low supersonic flow and the supercooling achieves only a small level or even superheated conditions 50 T in=358.6 K P in=25 KPa -0.25 -0.2 1.8 0.4 Supercooling Level (Tsubc/K) Pressure Ratio (P/Poin) 24 Frozen Mach Number (Mf) -0 0.1 0.2 0.3 0.4 0.5 Distance Form Throat X/m Figure Pressure distribution along the nozzle centerline for various backpressure values heat transfer engineering T oin=358.6 K P oin=25 KPa T subc=39.20 40 30 20 Pb=7027.5Pa 10 Pb=20 KPa -10 Pb=22 KPa -20 Pb=16.5 KPa Pb=15 KPa Pb=12 KPa -30 -40 -0.25 -0.2 -0.1 0.1 0.2 0.3 0.4 0.5 Distance From Throat X/m Figure 10 Supercooling level distribution along the nozzle centerline for various back-pressure values vol 31 no 12 2010 Y YANG ET AL 0.06 12 Pb=7027.5Pa Pb=12 KPa Pb=15 KPa Pb=16.5 KPa Pb=20 KPa Pb=22 KPa 10 0.05 Wetness fraction β Nucleation Rate I ( 1.0 E21·m-3·s-1 ) 1012 Pb= 20 KPa Nucleation Rate I / 1.0 E11·m-3·s-3 Pb= 22KPa Nucleation Rate I=0 4E-17 0.03 0.02 Pb= 20 KPa Pb= 22 KPa 3E-17 2E-17 1E-17 0.01 -0.5E-17 -0.25 -0.1 0.1 0.2 0.3 0.4 0.5 Profile of Enlargement 0 -0.25 -0.2 -0.25 -0.2 -0.1 0.1 0.2 0.3 0.4 Distance From Throat X/m Figure shows the frozen Mach number (Mf ) distribution along the nozzle centerline As shown in this figure, upstream of the location of the condensation shock, dry flow smoothly accelerates within the converging portion of the nozzle, passes the sonic condition at the throat, and continues accelerating up to Mf ≈ 1.3, at which point condensation shock takes place in the form of spontaneous nucleation Following the nucleation process, rapid release of latent heat toward the dry phase suddenly reduces the frozen Mach number while increasing pressure and the gas-phase temperature This rapid response behaves similar to but unlike a normal aerodynamic shock wave, in which the post-shock condition is subsonic, while in a condensation shock the post-shock condition could be sonic at most Besides, as the condensation shock is caused by the release of latent heat of the nucleation process, which is in continuing alteration, the rise of pressure and temperature and the drop of the Mach number are not as sharp as for the normal aerodynamic shock 12 Pb=7027.5 Pa Pb=12 KPa Pb=15 KPa Pb=16.5 KPa Pb=20 KPa Pb=22 KPa 0.1 0.2 0.3 A two-dimensional compressible numerical model has been described and used to predict a nonequilibrium spontaneous condensation phenomenon in Laval nozzles The thermodynamic and aerodynamic properties of both condensation shock and normal aerodynamic shock were studied and the difference between the condensation shock and the aerodynamic shock was investigated Based on the numerical simulation for the supersonic steam flow, we have obtained the following conclusions: Different from the isentropic expansion, in supersonic steam flow nonequilibrium spontaneous condensation will occur in the form of “condensation shock” downstream of the nozzle throat, when the supercooling achieves a high level The rapid response behavior of condensation shock is similar to but unlike a normal aerodynamic shock wave The post-shock condition of the condensation shock is always supersonic, in which the rise of pressure and temperature and the drop of the Mach number are not as sharp as for the normal aerodynamic shock As the back-pressure increases the normal aerodynamic shock moves toward the nozzle throat, and the shock has a complex influence on the homogeneous nucleation condensation If the normal aerodynamic shock passes through the location of the condensation shock, the spontaneous condensation will be weakened or even not occur at all Pb=20 KPa Pb=22 KPa 2E-10 NOMENCLATURE 1E-10 -0.25 -0.1 0.1 0.2 0.3 0.4 0.5 Profile of Enlargement -0.25 -0.2 -0.1 0.1 0.2 0.3 0.4 0.5 Figure 13 Wetness fraction distribution along the nozzle centerline for various back-pressure values 3E-10 0.4 Distance From Throat X/m CONCLUSIONS Difference Between Condensation Shock and Normal Aerodynamic Shock 10 -0.1 0.5 Figure 11 Nucleation rate distribution along the nozzle centerline for various back-pressure values Droplet radius r (nm) 0.04 Pb= 7027.5 Pa Pb= 12 KPa Pb= 15 KPa Pb= 16.5 KPa Pb= 20 KPa Pb= 22 KPa 0.5 Distance From Throat X/m Figure 12 Droplet radius distribution along the nozzle centerline for various back-pressure values heat transfer engineering E h I Kb m P r total specific internal energy (J/kg) static enthalpy (J/kg) nucleation rate (number of droplets/m3-s) Boltzmann constant (1.3807 × 10−23 J/K) mass (kg) pressure (Pa) radius of droplets (m) vol 31 no 12 2010 Y YANG ET AL r¯ r∗ S T Tsubc u v mean droplet radius of droplets (m) droplet critical radius (m) supersaturation ratio temperature (K) supercooling level (K) X-axial velocity (m/s) Y-axial velocity (m/s) [6] [7] Greek Symbols β γ η θ ρ σ mass fraction of the condensed phase ratio of specific heat capacities mass generation rate (kg/m3-s) number density for droplets (number of droplets/m3) nonisothermal correction factor density (kg/m3) liquid surface tension (N/m) Subscripts g l s [8] [9] [10] stagnation state condition gas (vapor) liquid saturated state condition [11] [12] Superscripts − → () () [13] vector average of a variable [14] REFERENCES [1] Wyslouzil, B E., Wilemski, G., Beals, M G., and Frish, M B., Effect of Carrier Gas Pressure on Condensation in a Supersonic Nozzle, Physics of Fluids, vol 6, pp 2845–2854, 1994 [2] Gerber, A G., and Kermani, M J., A Pressure Based Eulerian–Eulerian Multi-Phase Model for NonEquilibrium Condensation in Transonic Steam Flow, International Journal of Heat and Mass Transfer, vol 47, pp 2217–2231, 2004 [3] Simpson, D A., and White, A J., Viscous and Unsteady Flow Calculations of Condensing Steam in Nozzles, International Journal of Heat and Fluid Flow, vol 26, pp 71–79, 2005 [4] Moore, M J., Walters P T., Crane R I., and Davidson B J., Predicting the Fog Drop Size in Wet Steam Turbines, Proc Wet Steam Conference, University of Warwick, paper no C37/73, University of Warwick, Warwick, UK, pp 101–109, 1973 [5] Bakhtar, F., and Zidi, K., Nucleation Phenomena in Flowing High-Pressure Steam, Part 2: Theoretical Analysis, heat transfer engineering 1013 Proc Institution of Mechanical Engineers, vol 204, pp 233–242, 1990 White, A J., and Young, J B., Time-Marching Method for the Prediction of Two-Dimensional Unsteady Flows of Condensing Steam, Journal of Propulsive Power, vol 9, pp 579–587, 1993 Bakhtar, F., Mahpeykar, M R., and Abbas, K K., An Investigation of Nucleating Flows of Steam in a Cascade of Turbine Blading—Theoretical Treatment, ASME Journal of Fluids Engineering, vol 117, pp 138–144, 1995 Ishazaki K., Ikohagi, T., and Daiguji, H., A HighResolution Numerical Method for Transonic NonEquilibrium Condensation Flows Through a Steam Turbine Cascade, Proc 6th International Symposium on Computational Fluid Dynamics, USA, vol 1, pp 479–484, 1995 Young, J B., Two-Dimensional, Nonequilibrium, WetSteam Calculations for Nozzles and Turbine Cascades, Journal of Turbomachinery, vol 114, pp 569–579, 1992 Young, J B., The Spontaneous Condensation of Steam in Supersonic Nozzles, Physico Chemical Hydrodynamics, vol 3, pp 57–82, 1982 Gyarmathy, G., On the Growth Rate of Droplets in a Supersaturated Atmosphere, Z Angew Math Phys vol 14, pp 280–293, 1963 Vukalovich, M P., Thermodynamic Properties of Water and Steam, 6th ed., Mashgis, Moscow, Russia, 1958 Bakhtar, F., and Piran, M., Thermodynamic Properties of Supercooled Steam, International Journal of Heat and Fluid Flow, vol 1, pp 53–62, 1979 Gerber, A G., Modeling the Steady and Transient Dynamics of Nucleating Two-Phase Steam Flow, Proc 2000 National Heat Transfer Conference, Pittsburgh, PA, 20–22 August 2000 Yong Yang is a Ph.D student at the School of Energy and Power Engineering, Dalian University of Technology (DUT), Dalian, China He received his bachelor’s degree in thermal energy engineering from the DUT in 2004 and was recommended to continue his study for the doctoral degree directly He is currently working on spontaneous condensation of vapor in transonic steam flow and the shock effect Shengqiang Shen is a professor of thermal sciences at Dalian University of Technology (DUT), Dalian, China He received his Ph.D degree from the DUT, China He is the head of the Institute of Energy Science and Technology in DUT His main research interests are in the field of heat and mass transfer with phase change, solar-powered refrigeration systems, seawater desalination, and energy conservation technologies He has published more than 200 articles in well-recognized journals and proceedings He is also the vice-chairperson of the Chinese University Research Association for Engineering Thermo-Physics and the executive associate editor-in-chief of the Journal of Thermal Science and Technology vol 31 no 12 2010 1014 Y YANG ET AL Taewoo Kong was a postdoctoral researcher at the School of Energy and Power Engineering, Dalian University of Technology, Dalian, China, from March 2006 to April 2008 He received his Ph.D degree from Gyoengsang National University, Korea He is now working in the Korea Institute of Machinery & Materials, Daejeon, Korea His main research interests are in the field of solar energy systems, steam ejector performance analysis and application, and seawater desalination heat transfer engineering Kun Zhang is a Ph.D candidate at the School of Energy and Power Engineering, Dalian University of Technology (DUT), Dalian, China He received his master’s degree in thermal engineering from the DUT, China, in 2005 Currently, he is working on the improvement of steam ejector performance vol 31 no 12 2010 Heat Transfer Engineering, 31(12):1015–1022, 2010 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457631003639026 Subcooled Boiling Heat Transfer of CO in A Horizontal Tube at Low Temperatures XIUMIN ZHAO and PRADEEP BANSAL Department of Mechanical Engineering, University of Auckland, Auckland, New Zealand This article presents an experimental investigation on the subcooled flow boiling heat transfer characteristics of CO2 in a horizontal tube with inner diameter of 6.16 mm below −30◦ C The effects of mass and heat fluxes and saturation temperature on the heat transfer coefficient are discussed Large deviations are noted between the predictions from previous empirical correlations and the current CO2 experimental data Hence a new empirical correlation is developed, which agrees within ±30% with the current CO2 experimental data It is expected that the data presented in this study would be beneficial to industry and designers of compact heat exchangers for CO2 at low temperatures INTRODUCTION Due to the high heat transfer coefficient, the subcooled flow boiling process is widely used in many applications Subcooled flow boiling exists when the liquid bulk temperature is below its corresponding saturation temperature, where the vapor quality is below zero, but the wall temperature is high enough to generate bubbles An open literature search on the available experimental data revealed some correlations that can be applied in partially subcooled or fully developed regions These correlations can be divided into three categories: (1) Chen [1] type correlation, which combines the convective and nucleate boiling heat transfer together, for example, Gungor and Winterton [2] and Haynes and Fletcher [3] correlations; (2) empirical curve fit correlation, which gives an explicit relation between heat flux and temperature difference, such as q = f ( T), for example, Shah [4] and Kandlikar [5] correlations; and (3) Nusselt number expressed as a function of several dimensionless numbers, such as Ja, Bo, and Pr, for example, Papell [6] and Moles and Shaw [7] correlations CO2 is emerging as one of the most promising environmentally friendly and energy efficient refrigerants It has already been investigated extensively as a near-critical or trans-critical refrigerant for mobile air conditioners, water heating, and heat Address correspondence to Professor Pradeep Bansal, Department of Mechanical Engineering, The University of Auckland, Private Bag–92019, Auckland, New Zealand E-mail: p.bansal@auckland.ac.nz pump applications Cascade refrigeration systems using CO2 as a working fluid at low temperatures are becoming popular in the food and refrigeration industry [8, 9] Thome and Ribatski [10] and Zhao and Bansal [11, 12] reviewed the experimental studies on flow boiling heat transfer of CO2 Most previous research focused on the flow boiling heat transfer of CO2 at relatively high saturation temperatures Recently, Bansal and Zhao [13] and Zhao and Bansal [14, 15] experimentally investigated the flow boiling heat transfer of CO2 at low saturation temperatures below −30◦ C There was, however, no practical relevant study in the open literature on the subcooled flow boiling heat transfer of CO2 at such low temperatures In order to fill in this vacuum, current study is extended to experimentally evaluate the subcooled flow boiling heat transfer performance of CO2 in a smooth tube with outer and inner diameters of 7.94 and 6.16 mm, respectively The study investigates the effects of heat and mass fluxes and saturation temperature on the subcooled flow boiling heat transfer coefficient, along with a comparison of several empirical correlations As a result, a new empirical correlation has been developed EXPERIMENTAL APPARATUS AND DATA REDUCTION A schematic diagram of the experimental rig is shown in Figure that mainly consists of a high-pressure source of liquid CO2 , needle valve, mass flow meter, subcooler, test tube, and a transformer High-pressure liquid CO2 is passed through the 1015 1016 X ZHAO AND P BANSAL Figure Schematic diagram of the experimental rig needle valve to reduce its pressure and hence the temperature CO2 then passes through a subcooler to achieve the desired temperature before it flows through the test tube The liquid CO2 flow rate is measured by a Coriolis-effect flow meter The test tube is a 4.5-m-long stainless-steel tube with inner and outer diameters of 6.16 mm and 7.94 mm, respectively Uniform direct heating is supplied by a transformer that has high AC current (and low voltage) output Pressure transducers are installed at the beginning and the end of the test tube Thermocouples are installed at several locations along the tube to measure the local refrigerant and tube surface temperatures The refrigerant temperatures are measured by K-type thermocouple probes having 0.5 mm diameter, which are inserted to the middle of the tube The tube surface temperatures are measured by T-type thermocouples They are placed at the top, the bottom, and the side at each location, and are electrically insulated from the tube using Teflon tape The details are shown in Figure All thermocouples were fully calibrated before assembling the test tube (see Table for their uncertainty values) flow boiling heat transfer coefficient, hth , is defined as h th = q Tw − Tmean where Tmean is the local mean liquid refrigerant temperature The inner wall temperature, Tw , is calculated from the measured outside wall temperature, Tw,o , using the equation of steady-state radial heat conduction through the tube and heat generation within the tube wall as [17] Tw = Tw,o − Qi 4πkw L i ξ(1 − ln ξ) − 1−ξ ξ= di Table Parameters and estimated uncertainties Fluid temperature Tube surface temperature Pressure Mass flow rate of CO2 Heat flux Thermodynamic quality Heat transfer coefficient 0.07–0.27K ±0.1 K ±2.5 kPa ±0.4% of the reading ±3–5% ±4–13% ±4–13% Figure Cross-section position of the thermocouples heat transfer engineering (3) The enthalpy of CO2 at the inlet of the test tube, ii , is determined from the measured inlet refrigerant pressure and temperature For any of the other test sections, the enthalpy of CO2 (ie ) at the other measurement points can be calculated from the total heat The thermophysical properties of CO2 were obtained from EES (Engineering Equation Solver) [16] The local subcooled Uncertainty (2) where Data Reduction Parameters (1) vol 31 no 12 2010 X ZHAO AND P BANSAL 10 10 10 x NVG x NVG x NVG Tsat 6 Tsat -5 Tsat h -5 h Wall superheat (K) -2 -1 Heat transfer coefficient (kW m K ) 1017 -5 h -2 q=9.8kW m -0.1 -0.05 -2 -1 -2 G=300 kg m s 0.05 -10 0.1 x th q=19.7kW m -2 -2 -1 q=29.9kW m G=300 kgm s -10 -0.1 -0.05 0.05 0.1 -0.1 x th (b) q = 19.7 kW m-2 -2 (a) q = 9.8 kW m -2 -1 G=300 kgm s -10 -0.05 0.05 0.1 x th (c) q = 29.9 kW m-2 Figure Variation of heat transfer coefficients of CO2 and wall superheat in the subcooled and early saturated conditions at Tsat = −30◦ C and G = 300 kg m−2 s−1: (a) q = 9.8 kW m−2, (b) q = 19.7 kW m−2 and (c) q = 29.9 kW m−2 supply, as EXPERIMENTAL RESULTS AND DISCUSSION ie = ii + ˙i Q m˙ r (4) Subcooled Flow Boiling Heat Transfer Coefficient of CO2 at −30◦ C The refrigerant thermodynamic quality, xth , is calculated as xth = The wall superheat, i e − il,sat i fg (5) Tsat , is defined as Tsat = Tw − Tsat The subcooled temperature, (6) Tsub is calculated as Tsub = Tsat − Tr (7) The test tube is insulated using tube insulation material (k = 0.036 W m−1 K−1) to minimize the heat gain from the ambient The heat gain from the ambient was estimated by comparing the electric heat input with the total heat transfer to the refrigerant, and was found to be within 4% of the electric heat input at the average refrigerant temperatures of −45◦ C This heat gain by the refrigerant was then duly accounted for in the analysis of experimental results Experimental Uncertainty The uncertainties of the measured and calculated parameters, associated with measurement devices and sensors, were determined by the RRS method following the procedures described by Moffat [18] and Holman and Gajda [19] The results are shown in Table heat transfer engineering Figure shows the subcooled flow boiling heat transfer coefficient of CO2 at corresponding saturation temperature of −30◦ C and mass flux of G = 300 kg m−2 s−1 with heat fluxes varying from 10 to 30 kW m−2 The corresponding wall superheat is also shown in the same figure using the right-hand Y axis In these tests, the inlet CO2 is highly subcooled with Tsub ≈ 14◦ C, and the liquid CO2 Reynolds number in the subcooled region is about 10,900 At heat fluxes of 10 and 20 kW m−2, the classical onset of nucleate boiling (ONB) behavior can be identified as shown in Figure 3, (a) and (b), where the wall superheat increases with thermodynamic quality, xth , and shows a distinct maximum value, after which nucleate boiling is initiated The subcooled boiling heat transfer coefficient of CO2 begins to rise as the liquid CO2 temperature approaches its corresponding saturation temperature For example, at heat flux of 10 kW m−2 (Figure 3a), in the highly subcooled region of xth = −0.1, the wall surface temperature is lower than the corresponding liquid saturation temperature, and the heat transfer is due to singlephase forced convection The heat transfer coefficient in this region is about 1–1.2 kW m−2 K−1 Subsequently, the temperatures of wall surface and liquid CO2 all increase along the test tube with increasing thermodynamic quality When xth > −0.05, the wall surface temperature starts to increase compared to the liquid CO2 saturation temperature As xth approaches zero (xth = −0.01), the wall surface temperature reaches its vol 31 no 12 2010 X ZHAO AND P BANSAL maximum value, and this location is called the onset of nucleate boiling (ONB) After ONB, the heat transfer coefficient increases substantially to 2.2 kW m−2 K−1 due to the additional heat transfer through the boiling process and the boiling effect starts to dominate The wall superheat temperature decreases as boiling process develops At heat flux of 19.7 kW m−2 as shown in Figure 3(b), the wall surface temperature is higher than the corresponding liquid CO2 saturation temperature even in the highly subcooled region xth −0.05, and the maximum wall surface temperature occurs at xth = −0.06; then ONB is initiated After that, the wall surface temperature starts to decrease, and the heat transfer coefficient increases from 1.3 kW m−2 K−1 (at xth = −0.06) to 3.1 kW m−2 K−1 (at xth = −0.03), and increases sharply with the increasing thermodynamic quality When heat flux increases to 29.7 kW m−2 (Figure 3c), even in the highly subcooled region xth ≈ −0.09, the wall surface temperature is about 10◦ C higher than the corresponding liquid CO2 saturation temperature The heat transfer coefficient is about 1.2 kW m−2 K−1 Then the wall temperature starts to decrease, at xth ≈ −0.05, and the heat transfer coefficient increases to 3.8 kW m−2 K−1, which is much higher than that of the other two test series as shown in Figures 3a and b, at the same thermodynamic quality The maximum wall surface temperature is not shown in Figure 3c, which indicates that ONB has been submerged inside the inlet test section due to the higher heat flux The experimental data shows that ONB occurs earlier with increasing heat flux The Net Vapor Generation The point of net vapor generation (xNVG ) represents the location where the net void fraction begins to be significant in the subcooled region, and the effect of convective and nucleate boiling components will be similar to that in the saturated boiling region Here, xNVG is calculated using the Saha and Zuber [20] correlation as xNVG = −0.0022Bo · Prl for Relo · Prl > 70, 000 −154Bo for Relo · Prl > 70, 000 The corresponding xNVG is also shown in Figure As the heat flux increases, xNVG occurs earlier, which coincides with the earlier ONB, resulting in higher heat transfer coefficients at low thermodynamic quality Effect of Heat and Mass Fluxes on Subcooled Boiling Heat Transfer Coefficient of CO2 Figure compares the subcooled boiling heat transfer coefficient of CO2 at −30◦ C with different heat and mass fluxes In the highly subcooled region (xth ≈ −0.1), the heat transfer is due to single-phase forced convection and the heat transfer coefficient at mass flux of 300 kg m−2 s−1 is a little higher than that at mass flux of 200 kg m−2 s−1 In this region, heat flux has heat transfer engineering Heat transfer coefficient (kW m-2K-1) 1018 -2 -2 -1 G=300(kg m s ) q (kW m ) 29.9 19.7 9.8 -2 -1 G=200(kg m s ) 29.3 19.7 9.8 Tsat = -30o C -0.15 -0.1 -0.05 0.05 0.1 Thermodynamic quality, x th Figure Heat transfer coefficients of CO2 in subcooled and early saturated conditions at Tsat = −30◦ C and mass fluxes of 200 and 300 kg m−2 s−1 almost no influence on the heat transfer coefficient, which indicates that forced convection is dominant As thermodynamic quality increases, the heat transfer coefficient increases sharply, while the heat flux effect becomes more pronounced For example, at xth ≈ −0.03, when heat flux increases from to 9.8, 19.7, and 29.9 kW m−2, the heat transfer coefficient increases respectively by about 74%, 185%, and 250% (compared with the heat transfer coefficient at q = kW m−2) In addition, at a given mass flux, ONB occurs earlier with increasing heat flux As heat flux increases, the number of active nucleation sites and amount of bubbles increase, and the nucleate boiling contribution increases At the same time, after ONB, the effect of mass flux is negligible, indicating that nucleate boiling starts to dominate Effect of Saturation Temperature on Subcooled Boiling Heat Transfer Coefficient of CO2 Figures 5a and b show the effect of saturation temperature on the heat transfer coefficient of CO2 at mass fluxes of 200 and 300 kg m−2 s−1 with heat fluxes ranging from 10 to 20 kW m−2, respectively In general, the subcooled boiling heat transfer coefficient of CO2 increases with saturation temperature The effect of saturation temperature increases with thermodynamic quality Onset of nucleate boiling occurs earlier at high saturation temperature due to the low surface tension The surface tension relates to the bubble generation and bubble diameter Bubbles generate easily for low surface tension, and hence the wall superheat temperature for the ONB is lower At the same time, the effect of saturation temperature on the subcooled boiling heat transfer is more pronounced at high saturation temperature This is due to the high wall superheat temperature at high heat flux leading to more bubble generation vol 31 no 12 2010 X ZHAO AND P BANSAL Table Comparisons between empirical correlations and current CO2 experimental data Deviation Haynes and Fletcher[3] Gungor and Winterton [2] Kandlikar [5] Shah [4] Papell [6] Moles and Shaw [7] 133 133 132.8 132.8 61.2 58.5 74.8 −17.4 106.8 184.2 184.2 Average deviationa Mean deviationb aAverage bMean deviation = deviation = N N h th, pr edicted −h th,ex periment h th,ex periment N × 100% i=1 N |h th, pr edicted −h th,ex periment | h th,ex periment i=1 × 100% COMPARISON OF PREVIOUS EMPIRICAL CORRELATIONS WITH THE CURRENT CO2 EXPERIMENTAL DATA One subcooled boiling heat transfer experimental database of CO2 is set up based on our current experimental data series It consists of 106 data points, covering saturation temperatures from −30◦ C to −45◦ C, mass fluxes from 150 to 300 Heat transfer coefficient (kW m-2K-1) -2 q (kW m ) Tsat o -30.1 C 19.7 -39.7 C o 20 -45 C o 20 o -30.2 C 9.8 -40.1 C o 10 -45 C o 10 -2 -1 G=200 kgm s -0.1 -0.05 0.05 0.1 Thermodynamic quality, x th (a) G = 200 kg m-2s-1 Heat transfer coefficient (kW m-2K-1) 1019 -2 q (kW m ) Tsat o -30.1 C 19.7 -39.7 C o 20 -45 C o 20 o 9.8 -40.1 C o 10 -45 C o 10 -30.2 C -2 -1 G=300 kgm s kg m−2 s−1 and heat fluxes from to 30 kW m−2 The thermodynamic qualities are within −0.1 to The comparison of the predictions from six empirical correlations and current CO2 experimental database is shown in Table For the first group, Gungor and Winterton [2] and Haynes and Fletcher [3] correlations always overpredict the current experimental database by more than 130% These two correlations were based on the Chen [1] correlation, and assumed the convective enhancement factor to be unity The Gungor and Winterton [2] correlation suggested the same nucleate boiling suppression factor as saturated boiling The Haynes and Fletcher [3] correlation set the nucleate boiling suppression factor as However, these correlations were not suitable for the current CO2 experimental database For the second group, the average and mean deviations of the Shah [4] correlation with current experimental database are 58.5% and 74.8%, respectively The Shah[4] correlation always underpredicts the CO2 experimental data in the early subcooled region, but overpredicts in the low subcooled region near the saturation point The prediction from the Kandlikar [5] correlation is better, with average and mean deviations of 4% and 61.2%, respectively Although the average deviation of Kandlikar [5] correlation is small, most of the predictions are located within ±50% (Figure 6) For the third group, the Moles and Shaw [7] correlation always overpredicts the current experimental database with average deviations of 184.2% Papell [6] underpredicts the current experimental database in highly subcooled region, but ovepredicts near the saturated point The simulation results show that predictions from none of the empirical correlations agree well with the current CO2 subcooled boiling heat transfer experimental data Therefore, there is a need to develop a new empirical correlation to predict the subcooled boiling heat transfer of CO2 at low temperatures DEVELOPMENT OF A NEW EMPIRICAL CORRELATION FOR SUBCOOLED FLOW BOILING HEAT TRANSFER OF CO2 -0.1 -0.05 0.05 0.1 Thermodynamic quality, x th (b) G = 300 kg m-2s-1 Figure Effect of saturation temperature on subcooled boiling heat transfer coefficient of CO2 with different mass fluxes of (a) G = 200 kg m−2 s−1 and (b) G = 300 kg m−2 s−1 heat transfer engineering A new correlation is developed based on the Chen [1] method and current CO2 subcooled flow boiling heat transfer experimental data, by dividing the heat flux into two parts, convective and nucleate boiling, as q = qcon + qnb = h (Tw − Tmean ) + Sh pb (Tw − Tsat ) (8) vol 31 no 12 2010 1020 X ZHAO AND P BANSAL -50% Kandlikar [5] correlation 0 h exp -2 -1 Tsat=-30 C Nucleate G=300.2 kg m s -2 q=24.8 kW m Heat transfer coefficient (kW m K ) hpre (kW m-2K-1) +50% -2 -1 Convective Experimental data x NVG -1 (kW m K ) -0.1 -0.05 (a) Tsat = -30 oC By combining Eqs (1) and (8), the subcooled boiling heat transfer coefficient can be expressed as where, the calculation procedure for hpb and S is described in the following Calculation of hpb In the highly subcooled region, if (Tw —Tsat )/(Tw —Tmean ) → 0, only convective heat transfer is accounted for When the liquid temperature rises to the corresponding saturation temperature, i.e., (Tw —Tsat )/(Tw —Tmean ) → 1, the subcooled boiling heat transfer changes to saturated boiling heat trans- -1 o Tsat=-40 C Total -2 (9) Heat transfer coefficient (kW m K ) (Tw − Tsat ) + Sh pb (Tw − Tmean ) x th Figure Comparison of Kandlikar [5] correlation with current experimental data h th = h o Total -2 -2 -1 G=300.1 kg m s Nucleate -2 q=10 kW m Convective Experimental data x NVG -0.1 -0.05 0.05 x th +30% Figure Comparison of predicted h from the new empirical correlation with two experimental data series: (a) T sat = −30◦ C and (b) T sat = −40◦ C hpre -2 -1 (kW m K ) (b) Tsat = -40 oC -30% 0 h exp -2 -1 (kW m K ) Figure Comparison of new empirical correlation with the current CO2 experimental data heat transfer engineering fer If (Tw —Tsat )/(Tw —Tmean ) is within (0, 1), the contribution of nucleate boiling increases with increasing bulk liquid mean temperature, whether or not it is fully developed Here, the Dittus–Boelter equation is used to calculate the liquid convective heat transfer coefficient The convective enhancement factor F in the subcooled boiling region is assumed to be The nucleate pool boiling heat transfer is calculated by the modified Cooper [21] correlation as h pb = 65 pr0.25 q 0.63 − log10 pr vol 31 no 12 2010 −0.55 M −0.5 (10) X ZHAO AND P BANSAL Calculation of S For the nucleate suppression factor, Haynes and Fletcher [3] and Gungor and Winterton [2] used the similar method with saturated boiling region, but their correlations showed larger deviations with current CO2 experimental data Here, we are trying to use some dimensionless parameters to represent the nucleate boiling heat transfer in the subcooled region as Bo, Wel , and Ja Based on current subcooled boiling heat transfer data of CO2 at low saturation temperatures, nucleate boiling suppression factor in the subcooled region is calculated as S = × 103 · Bo1.18 · J a −0.4 W el0.1 (11) The new empirical correlation is then compared with current CO2 experimental data in the subcooled region, where the average and mean deviations are respectively 0.1% and 19.8% The details are shown in Figure It is shown that most predictions from the new empirical correlation agreed to within ±30% The predictions from new empirical correlation are compared with two experimental data series at −30◦ C and −40◦ C as shown in Figures 8a and 8b, respectively The experimental data show that the nucleate boiling contribution is very low at low thermodynamic quality and convective boiling is dominant It then rises sharply after ONB and starts to dominate The predictions show similar trends for both the experimental data series F G h i ifg Ja k L M m˙ r pr Pr ˙ Q q Re S T We x xth 1021 convective enhancement factor mass flux, kg m−2 s−1 heat transfer coefficient, W m−2 K−1 enthalpy, kJ kg−1 latent heat of vaporization, kJ kg−1 Jacob number thermal conductivity, W m−1 K−1 length molecular mass, kg kmol−1 refrigerant mass flow rate, kg s−1 reduced pressure Prandtl number heat transfer rate, W heat flux, kW m−2 Reynolds number suppression factor temperature, ◦ C or K Weber number vapor quality thermodynamic quality Greek Symbols ξ dimensionless number Subscripts CONCLUSIONS This article presents an experimental investigation on subcooled flow boiling heat transfer of CO2 in a smooth tube at low saturation temperatures from −30◦ C to −45◦ C The experimental data show that in highly subcooled region, the wall surface temperature is lower than the corresponding liquid saturation temperature, resulting in the dominance of single-phase liquid convective heat transfer The heat transfer coefficient is around 1–1.3 kW m−2 K−1 As the wall temperature becomes higher than the corresponding saturation temperature, the heat transfer coefficient of CO2 starts to increase sharply with heat flux, indicating ONB and the dominance of nucleate boiling As heat flux increases from to 9.8, 19.7, and 29.9 kW m−2, the heat transfer coefficient at xth ≈ −0.03 increases by about 74%, 185%, and 250% (compared with the heat transfer coefficient at kW m−2) Furthermore, the subcooled boiling heat transfer increases with saturation temperature due to the low surface tension A new empirical correlation is developed that agrees with the current CO2 experimental data to within ±30%, with average and mean deviations of 0.1% and 19.8%, respectively c cb e exp i l lo mean nb NVG ONB pb pre r s sat sub v w w, o critical convective boiling convective boiling exit experimental inlet, inner liquid state liquid only mean nucleate boiling net vapor generation onset of nucleate boiling pool boiling predicted refrigerant steel saturation subcooled two-phase vapor state wall outer wall NOMENCLATURE REFERENCES Bo di boiling number inner diameter, m outer diameter, m [1] Chen, J C., Correlations for Boiling Heat Transfer to Saturated Fluids in Convective Flow, Industrial & Engineering heat transfer engineering vol 31 no 12 2010 1022 [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] X ZHAO AND P BANSAL Chemistry Process Design and Development, vol 5, pp 322–329, 1966 Gungor, K E., and Winterton, R H S., A general correlation for flow boiling in tubes and annuli, International Journal of Heat and Mass Transfer, vol 29, no 3, pp 351–358, 1986 Haynes, B S., and Fletcher, D F., Subcooled Flow Boiling Heat Transfer in Narrow Passages, International Journal of Heat Mass Transfer, vol 46, no 19, pp 3673–3682, 2003 Shah, M M., A General Correlation for Heat Transfer During Subcooled Boiling in Pipes and Annuli, ASHRAE Trans., vol 83, pp 202–217, 1977 Kandlikar, S G., Heat Transfer Characteristics in Partial Boiling, Fully Developed Boiling, and Significant Void Flow Regions of Subcooled Flow Boiling, ASME Journal of Heat Transfer, vol 120, no 5, pp 395–401, 1998 Papell, S S., Subcooled Boiling Heat Transfer Under Forced Convection in a Heated Tube, NASA Technical Note D-1583, Lewis Research Center, Cleveland, OH, 1963 Moles, F D., and Shaw, J F G., Boiling Heat Transfer to Subcooled Liquids Under Condition of Forced Convection, Trans Institute of Chemical Engineers, vol 50, pp 76–84, 1972 Bansal, P K., and Jain, S., Cascade Systems: Past, Present and Future, ASHRAE Trans., vol 113, no 1, pp 245–252, 2007 Getu, H M., and Bansal, P K., Thermodynamic Analysis of an R717-R744 Cascade Refrigeration System, International Journal of Refrigeration, vol 31, no 1, pp 45–54, 2008 Thome, J R., and Ribatski, G., State-of-the-Art of TwoPhase Flow and flow Boiling Heat Transfer and Pressure Drop of CO2 in Macro- and Micro-Channels, International Journal of Refrigeration, vol 28, no 8, pp 1149–1168, 2005 Zhao, X., and Bansal, K P., Critical Review of Flow Boiling Heat Transfer of CO2 –Lubricant Mixtures, International Journal of Heat and Mass Transfer, vol 52, no 3–4, pp 870–879, 2009 Zhao, X., and Bansal, P K., An Overview of Heat Transfer Characteristics of Carbon Dioxide (CO2 ) Refrigerant, IIRIRHACE International Conference on Innovative Equipment and Systems for Comfort and Food Preservation, Auckland, New Zealand, pp 297–304, 2006 Bansal, P K., and Zhao, X., Flow Boiling Heat Transfer of CO2 at Low Temperatures—Challenges and Op- heat transfer engineering [14] [15] [16] [17] [18] [19] [20] [21] portunities, 5th International Conference on Nanochannels, Microchannels and Minichannels, Puebla, Mexico, pp 979–988, 2007 Zhao, X., and Bansal, P., Experimental Investigation of Flow Boiling Heat Transfer of CO2 at Low Temperatures, Heat Transfer Engineering, vol 30, no 1–2, pp 2–11, 2009 Zhao, X., and Bansal, P K P., Flow Boiling Heat Transfer Characteristics of CO2 at Low Temperatures, International Journal of Refrigeration, vol 30, no 6, pp 937–945, 2007 EES Engineering Equation Solver, Madison, WI, 2008 Wambsganss, M W., Jendrzejczyk, J A., France, D M., and Tran, T N., Boiling Heat Transfer in a Horizontal Small Diameter Tube, Journal of Heat Transfer, vol 115, pp 963–972, 1993 Moffat, R J., Describing the Uncertainties in Experimental Results, Experimental Thermal and Fluid Science, vol 1, pp 3–17, 1998 Holman, J P., and Gajda, W J., Experimental Methods for Engineers, 5th ed., McGraw-Hill Book Company, Singapore, 1989 Saha, P., and Zuber, N., Points of Net Vapor Generation and Vapor Void Fraction in Subcooled Boiling, 5th International Heat Transfer Conference, Tokyo, 1974 Cooper, M G., Heat Flow Rate in Saturated Nucleate Pool Boiling—A Wide Ranging Examination Using Reduced Properties, Advances in Heat Transfer, vol 16, pp 157–239, 1984 Xiumin Zhao completed her Ph.D in the Department of Mechanical Engineering at the University of Auckland (New Zealand) She received her bachelor’s and master’s degrees from Harbin Institute of Technology (China) in 1996 and 1998, respectively Before coming to Auckland, she had been lecturing in Beijing University of Civil Engineering and Architecture Pradeep Bansal is a professor in the Department of Mechanical Engineering, and director of Energy & Fuels Research Unit at the University of Auckland (New Zealand) He is leading a research group on fundamental heat transfer studies on natural refrigerants, development of simulation models, and design and development of energy-efficient thermal systems, and has recently established an innovative Cascade Refrigeration Research Facility at the University of Auckland using CO2 as the low = stage refrigerant for achieving low temperatures (down to −50◦ C) for the food industry vol 31 no 12 2010