Pool Boiling Heat Transfer to Pure Liquids S. A. ALAVI FAZEL, S. ROUMANA Chemical Engineering Department Islamic Azad University, Mahshahr branch Mahshahr, Khuzestan province IRAN alavifazel@gmail.com Abstract: - Nucleate pool boiling heat transfer coefficients for several pure liquids have been experimentally measured on a horizontal rod heater at atmospheric pressure. The measurements are based on more than two hundred data points on heat fluxes up to 400 kw.m -2. The major existing correlations are summarized and the individual performances of each correlation to the present experimental data are briefly discussed. A new empirical correlation is proposed based on dimensional analysis which presents a superior performance in compare to other existing correlations. Key-Words: - pool boiling, heat transfer, temperature, liquid, atmospheric pressure 1 Introduction Nucleate pool boiling of pure liquids is involved in many chemical and petrochemical applications such as distillation, air separation, refrigeration and power cycles. Design, operation and optimization of the involved equipments require an accurate prediction of the boiling heat transfer between surface and the boiling liquid. Despite of wide-ranging researches of pool boiling through the past over few decades, fundamental mechanisms of pool boiling are still not fully understood. This is because of the intense complexity of the boiling phenomena due to the nonlinear mutual interaction between a numbers of sub-processes. These sub-processes are including nucleation problems, capillary, buoyancy and viscous forces implicated in bubble dynamics, evaporation associated with mass transfer in mixtures boiling, conduction and convection heat transfer mechanisms and also the Marangoni effect. Also, mutual interactions including interaction between bubbles and heating surface and also between neighbouring nucleation site plays significant role in boiling heat transfer coefficient. At very high heat fluxes, radiation heat transfer has also a contribution in the total heat transfer which is not discussed here. The structure of heat transfer surface may be rigorously complicated and may contain nucleation cavities with various shapes and sizes. Practically, micro- surface information is not fully available for any given heating surface, which has significant role in determination of boiling heat transfer. There are many predictive correlations for boiling heat transfer coefficient for pure liquids. These correlations are generally empirical or semi-empirical. Comparisons between existing correlations as a function of heat flux presents somewhat conflicting value of boiling heat transfer coefficients. In this article, the major predictive correlations for pool boiling heat transfer have been briefly reviewed. The experimental results have been correlated to the predictive correlations. Finally, a new empirical correlation has been proposed, which provides better accuracy in compare to other existing correlations. 2 Literature review Vinayak-Balakrishnan [1] has a wide-ranging survey on some correlations including Gorenflo [2], Stephan- Abdelsalam [3] and McNelly [4] for pure boiling liquids. The applicability and constancy of some other correlations such as Boyko-Kruzhilin [5] and Mostinski [6] could be found in some other references [7]. The major existing correlations for pure boiling systems are summarized in Table 1. As a general rule, each correlation has some conflicting advantages and disadvantages. Among this complexity, ISSN: 1790-5095 211 ISBN: 978-960-474-158-8
Table1. Major existing correlation for prediction of the pool boiling heat transfer coefficient Author Correlation Ref. Mostinski 3.596 5.. 1.8. 4. 10 [6] McNelly Labantsov 0.225... [4] 1 0.075 110. 273.15.. [8] Boyko- Kruzhilin Kutateladze 0.082 273.15. 3.37 9.. 273.15 [5] [9] Stephan- Abdelsalam 0.23..... [3] Nishikawa 31.4... 8... 1 0.99. ; 0.125 [10] Gorenflo ;. ; 0.90.3 1.2. 2.5 1 ; [2] ISSN: 1790-5095 212 ISBN: 978-960-474-158-8
Gorenflo [2] has a major distinction in compare to other exiting correlations with two tuning parameters. These tuning parameters are already found for many different pure boiling systems. These tuning parameters could also be empirically determined. 3 Experimental Apparatus and Procedure The boiling vessel is a vertical hollow cylinder of stainless steel containing 38 L of test liquid connected to a vertical condenser to condense and recycle the evaporated liquid. The whole system is heavily isolated for better control and reduction of the heat loss. The temperature of the liquid inside the tank is constantly monitored and controlled to any set point by a thermal regulator which is involved with thermocouples and a band heater covering the outside of the tank. Before any experiment, the liquid inside the tank is preheated to the saturation temperature using the mentioned band heater. The pressure of the system is monitored and regulated continuously. A safety pressure relief valve is also installed. The test section is a horizontal rod heater with a diameter of 10.67 mm and a heating length of 99.1 mm which can be observed and photographed through observation glasses. This heater consists of an internally heated stainless steel sheathed rod and four stainless steel sheathed thermocouples with an exterior diameter of 0.25 mm are entrenched along the circumference of the heater close to the heating surface. One thermocouple inside the rod heater was used as a protection trigger to cut off the electric power if the temperature exceeds the maximum limit. The test heater is manufactured by Drew Industrial Chemicals Co. according to specifications by Heat Transfer Research Incorporated (HTRI). A PC-based data acquisition system was used to record all measuring parameters. The input power to the rod heater is precisely equal to the heat flux and could be calculated by the product of electrical voltage, current and cosine of the difference between electrical voltage and current. The average of five readings was used to determine the difference between heating surface and the bulk temperature of each thermocouple. Initially, the entire system including the rod heater and the inside of the tank were cleaned and the test solution was introduced. The vacuum pump is then turned on and the pressure of the system is kept low approximately to 10 kpa for 5 h to allow all the dissolved gases especially the dissolved air be stripped from the test solution. Following this, the tank band heater was switch on and the temperature of the system allowed rising to the saturation temperature. This procedure presents a homogeneous medium for boiling heat transfer experiment. Then the electric power was slowly supplied to the rod heater and increased gradually to a predetermined value. Data acquisition system, video equipments including a digital camera were simultaneously switched on to record the required parameters including the rod heater temperature, bulk temperature, heat flux and also all visual information. All experimental runs were carried out with decreasing heat flux to eliminate the hysteresis effect. Some runs were repeated twice and even thrice to ensure the reproducibility of the measurements. In this set of experiments, water, ethanol, methanol, acetone, isopropanol have been used as the test liquids. 4 Experimental Results Figure.1 presents the raw experimental values of the boiling heat transfer for tested liquids. Based on the graph, by increasing the heat flux, the boiling heat transfer coefficient is smoothly increased by any tested liquid. However, there are a few fluctuations which are principally related to the experimental error and also hysteresis effect. Note that the performance of A/D (Analogue to Digital converter) is sensitive to the ambient condition. ISSN: 1790-5095 213 ISBN: 978-960-474-158-8
Fig. 1. The raw experimental data of pure liquid pool boiling heat transfer coefficient Table 2. The performances of different correlations [%] [* = very off] Model 2 propanol Ethanol Methanol Water Acetone Mostinski 24 34 70 * * McNelly 38 61 88 71 36 Boyko kruzhiline 66 66 67 79 53 Stephan Abdelsalam 28 63 * 83 70 Gorenflo 21 21 12 15 15 Nishikawa 23 52 79 66 64 Fujita * * * * 53 Labantsov 93 93 92 94 * Jung 52 * * * 93 Cooper 39 77 * * 66 5 The performances of existing correlations Generally, because of the complexity of the boiling phenomena, a fully theoretical predictive model is still not developed. There are many influencing parameters on the pool boiling heat transfer which requires more intensive researches to be correlated to the boiling heat transfer coefficient without any empirical tuning parameter(s). Table 2 compares the performances of the major existing predictive correlations to the current experimental data. The absolute relative error indicated in the mentioned table is calculated by the following relation: % 1 100 1 Among these correlations, the Gorenflo [2] correlation shows the best performance. However, the two reference tuning parameter should be known for any specific boiling system. In fact, with adjusting the two tuning parameter α 0 and q 0, in this correlation, any experimental data can be fitted superbly to this ISSN: 1790-5095 214 ISBN: 978-960-474-158-8
correlation. Stephan-Abdelsalam [3] correlation is one of the most used correlations in the literature. However, in this equation, the d b, the bubble diameter is sometimes very difficult to predict. These authors recommend using the Fritz [11] correlation for prediction of the bubble diameter as the following: 2 0.0146 2 In which the contact angle β is specified equal to 45 o for water and 35 o for other liquids by the author. It is noticeable that in the mentioned correlation, the impact of heat flux is not implicated, consequently, the bubble diameter as a key parameter can be considered as a substantial source of error in Stephan-Abdelsalam [3] correlation. The rest of the predictive correlations are not reliable and have an unacceptable performance. The tuning parameters are found equal to 3.2529579 and 0.87549808. Substituting Eqs.(3) and (4) into (5) and after some simplification, the following correlation is obtained for the pool boiling heat transfer prediction: 3.253.. /.. 6 Note that in Eq. (6), all parameters are in S.I. units. Fig.2 presents the experimental correlation of Π versus Π : 6 A New Empirical Model In this investigation, from all of the available influencing parameters, all possible dimensionless groups have been generated. The influencing parameters includes: fluid critical and saturation temperature, critical and atmospheric pressure, liquid and vapor thermal conductivities, viscosities, heat capacities, densities also boiling heat fluxes, surface tensions and heat of evaporations. Some parameters including thermal conductivity, heat capacity and density are combined to thermal diffusivity. This means eleven influencing parameter with five dimensions including: Q, L, T, θ and M which are related to heat, length, temperature, time and mass respectively. Based on the Buckingham theory and more than three hundred possible dimensionless groups, the following dimensionless numbers can be correlated with least error: Π... Π /.. 3 4 In the following equations,,,,, and / are boiling heat transfer coefficient, liquid thermal diffusivity, saturation temperature, surface tension, heat of evaporation and heat flux respectively. Π and Π can be simply correlated by the following form: Π Π 5 Fig.2. The correlation of Π versus Π Comparison between Eq. (6) and the experimental data presents an absolute average error of 25% which can be considered accurate enough for practical applications. Eq. (6) is considered as a general correlation and doesn t require any specific parameter for an individual boiling liquid. The impact of some other parameters on pool boiling heat transfer coefficient such as the surface roughness, pressure, surface physical properties and geometrical configuration of the heating surface is not considered. 7 Conclusion Pool boiling heat transfer coefficients for various pure liquids including water, acetone, isopropanol, methanol and ethanol have been experimentally measured at atmospheric pressure. The major predicting correlations for boiling heat transfer in pure liquids have been briefly reviewed. Comparisons between experimental data and the major existing correlations presents a significant error. In this article, based on the dimensional analysis, two new dimensionless groups have been generated which can relate the pool boiling heat transfer coefficient to the physical properties of boiling liquids. The new correlation presents better accuracy in compare to other existing correlations. ISSN: 1790-5095 215 ISBN: 978-960-474-158-8
References: [1] Vinayak Rao, G., Balakrishnan, A. R., Heat transfer in nucleate pool boiling of multicomponent mixtures, Experimental Thermal and Fluid Science, Vol.29, 2004, pp. 87 103. [2] Gorenflo, D., Pool boiling, VDI Heat Atlas, (chapter Ha), 1993 [3] Stephan, K., Abdelsalam, K., Heat transfer correlation for natural convection boiling, International Journal of Heat and Mass Transfer, Vol.23, 1980, pp. 73-87. [4] McNelly, M.J., A Correlation of rates of heat transfer to nucleate boiling of liquids, J. Imperial College Chem. Eng. Soc, Vol.7, 1953, pp. 18 34. [5] Boyko-Kruzhilin, Int. J. Heat Mass Transfer, Vol.10, 1967, pp. 361. [6] Mostinski, I.L., Application of the rule of corresponding states for calculation of heat transfer and critical heat flux, Teploenergetika, Vol.4, 1963, pp. 66. [7] Taboas, F., Valle`s, M., Bourouis, M., Coronas, A., Pool boiling of mmonia/water and its pure components: Comparison of experimental data in the literature with the predictions of standard correlations, Int. J. of Refrigeration, Vol.30, 2007, pp. 778-788. [8] Labuntsov, D.A., Heat transfer problems with nucleate boiling of liquids, Thermal Engrg., Vol.19, 1972, pp. 21-28. [9] Kutateladze, S.S., Heat Transfer and Hydrodynamic Resistance:Handbook, Energoatomizdat Publishing House, 1990 [10] Nishikawa, K., Fujita, Y., Ohta, H., Hidaka, S., Effect of the surfaceroughness on the nucleate boiling heat transfer over a wide range of pressure, Proceedings of the 7th International Heat Transfer Conference Mu nchen (Germany), Vol.4, 1982, pp. 1 66. [11] Fritz, W., Berechunung des maximal volumens von Dampfblasen, Phys. Z., Vol.36, 1935, pp. 379-384. ISSN: 1790-5095 216 ISBN: 978-960-474-158-8