Experimental Analysis of the Pool Boiling Phenomenon of Sugarcane Juice Daniel Marcelo Aldana1,a, Paul Villar Yacila1,b, Raúl La Madrid Olivares1,c 1 Universidad de Piura, Av. Ramón Mugica 131, Urb. San Eduardo – Universidad de Piura, Perú a [email protected], [email protected], [email protected] Keywords: Heat transfer, Correlation of Rohsenow, Pool boiling, Sugarcane juice, Jaggery. Abstract. In Peru, jaggery making process has low energy efficiency and it is due to low heat transfer coefficients for natural convection linked to the sugar cane movement generated by the heat exchange between the sugarcane juice and the combustion gases. This low heat transfer coefficients are caused by improper heat exchangers designs. In this work, is performed an experimental analysis that consist in supplie heat to a pot containing sugarcane juice using a hot plate of constant electrical power. This study consist in identify boiling regimes and estimate the heat transfer coefficients linked to natural convection boiling, measuring: (i) the temperature at the bottom of the pot (ii) the temperature at the bottom level of sugarcane juice (iii) the temperature at middle level of sugarcane juice (iv) the temperature at free surface of sugarcane juice (v) rate of water evaporated. The method of linear regression and the correlation of Rohsenow were used for obtaining the values of the heat transfer coefficients ranging from 4088.6 W/m2°C to 12592.8 W/m2°C with power input ranging from 700W to 1300W. Introduction The boiling phenomenon consists in the phase change form liquid state to vapor state which occurs when the wall temperature of the heated surface is above than the saturation temperature of the liquid [1]. This process is characterized by the rapid formation of vapor bubbles in the solid-liquid interface which are separated from the surface when they reach a certain size and have a tendency to rise to the top of the liquid [2]. In our study case, according to the classification suggested in the literature pool boiling is analyzed, because quiescent liquid is heated in a pot [3]. The first attempts to study the boiling of different liquids showed that the main parameters affecting the heat transfer coefficient in pool boiling are: heat flux, saturation pressure, thermophysical properties of the working fluids and some characteristics of the material contact surface (thermophysical properties, dimensions, surface finishing, microstructure, etc) [4]. Besides knowing the process of boiling sugarcane juice and its dynamics, was also studied the heat transfer rate associated with this process, mainly, to estimate heat transfer coefficients for each case. The production process to obtain jaggery begins when sugarcane pass through mills. The subproducts obtained are sugarcane juice and bagasse. The residual bagasse is burned in a combustion chamber and the combustion products pass through a flue gas duct giving its thermal energy to the open pan heat exchanger [5].The sugarcane juice contained in the pot is heated in order to evaporate the water contained on it. The equation of heat transfer is expressed by the Newton’s law of cooling [6]: q ho Tg Tl (1) Where q (W/m2) is the heat flux exchanged between the hot combustion gases and the sugarcane juice, ho (W/m2°C) is the global heat transfer coefficient, Tg (°C) is the temperature of hot gases produced by the bagasse combustion, Tl is the sugarcane juice temperature. The value of ho is calculated through the sum of the thermal resistances network acting on the process. These resistances are in series and are: resistance to heat transfer by the flow of the combustion gases ( 1 / hc ), the resistance offered by the wall thickness of the pan with its related thermal conductivity ( e / k ), a factor representing the fouling layer (Rf) y and the resistance of the heat exchange fluid to evaporate ( 1 / hl ). With this it can be calculated the overall heat transfer coefficient as follows [7]: 1 1 e 1 (2) Rf ho hc k hl The term 1/hl of the equation 2 is the most relevant because the other three terms are negligible. So, equation 2 can be simplified to: (3) ho hl And equation 1 can be rewritten as: q hl Ts Tl (4) Where Ts (°C) is the contact temperature between the pot bottom and the sugarcane juice. Nukiyama´s experiments To predict the value of heat transfer coefficient of the liquid phase in this process is necessary to know the boiling process. In 1934, Nukiyama was the first researcher to identify the different regimes of boiling water [9], using a platinum resistance wire placed horizontally as heat source submerged in saturated water at atmospheric pressure. The heat flux Q (W) from the horizontal wire to the saturated water was determined by measuring electrical current I (Amperes) in the wire and voltage V (Volts). The temperature of the wire was determined by calculating the electrical resistance [10]. Boiling regimes identified in this experiment were defined in relation to the temperature difference (), as shown in the following figure: Fig. 1 shows that the heat transfer coefficient for nucleate boiling for saturated pure water will increase from point A to point C, reaching a maximum value that matches the critical heat flow. For pure water, the critical or maximum heat flow quantity exceeds 1 MW/m2 [11]. The nucleate boiling regime is the most appropriate in the case of jaggery making process because in this regimen it can achieve the higher heat transfer rates. It should be noted that although the boiling curve given in the Fig. 1 is for water, its general shape is the same for different fluids [6], including sugarcane juice. Procedure The experiment involves placing 3 kg of sugarcane juice in a circular stainless steel pot of 0.5 cm thick, 22 cm in diameter and a height of 25 cm, under constant heat inputs. Heat inputs to sugarcane juice will be provided by hot plate of 2000W capacity. A variac is used to ensure that the electrical power provided to the hot plate is constant, which is measured by watt meter. Four sensors PT-100 were used, which were place (see Fig. 2) to measure: temperature at the bottom of the pot (T1), temperature at the bottom level of sugarcane juice (T2), temperature at middle level of sugarcane juice (T3) temperature at free surface of sugarcane juice (T4). These sensors were connected to a data acquisition module that showed temperature values at real time and the data was taken for each 5 minutes. In order to measure the quantity of evaporated water (in kilograms) it was used a digital high precision balance. Fig. 3 shows a scheme of the system. It can be seen that the heating is carried out at atmospheric pressure, which is an important consideration for the calculation of thermophysical properties of sugarcane juice. The data was taken at four constants heat input rate: 700W, 900W, 1100W, 1300W. HEAT INPUT 900 W HEAT INPUT 700 W Mass evap. (g) Time difference (min) T1 (°C) T2 (°C) T3 (°C) T4 (°C) Weight (g) 3000 0 5 91.17 88.94 85.39 84.56 3118 0 2950 50 5 97.61 97.78 94.50 96.44 3100 18 92.88 2890 60 5 99.72 99.44 96.39 98.11 3032 68 94.14 2810 80 5 99.78 99.78 96.22 96.89 2950 82 95.50 94.36 2735 75 5 99.83 99.89 95.70 96.67 2871 79 95.67 95.45 2660 75 5 99.72 100.11 96.34 96.26 2787 84 99.56 95.72 95.99 2590 70 5 99.72 99.78 96.52 96.01 2698 89 101.06 99.39 96.30 96.10 2515 75 5 99.78 100.00 96.72 96.7 2593 105 100.00 99.28 97.13 96.26 2455 60 5 99.67 99.78 97.63 96.88 2501 92 5 100.61 99.61 97.44 96.71 2380 75 5 100.11 100.17 97.40 96.99 2409 92 5 100.56 99.61 97.54 96.64 2300 80 5 99.78 100.00 97.78 97.10 2325 84 5 100.89 99.67 97.60 97.68 2230 70 5 99.67 99.78 98.10 97.48 2232 93 5 101.28 99.78 97.45 97.66 2170 60 5 99.89 99.56 98.46 97.62 2146 86 5 102.00 99.83 95.38 97.92 2090 80 5 100.11 99.41 98.61 97.68 2055 91 5 100.28 99.31 98.74 97.94 1973 82 5 100.06 99.73 99.00 98.00 1882 91 5 100.06 100.13 98.77 98.12 1784 98 5 101.06 100.48 99.25 98.24 1649 135 5 101.06 100.30 99.48 98.47 1629 20 5 101.11 100.95 99.50 99.13 1540 89 5 101.56 101.18 99.82 99.51 1450 90 5 102.10 101.25 100.02 99.78 1357 93 Time difference (min) T1 (°C) T2 (°C) T3 (°C) T4 (°C) Weight (g) 5 99.17 96.50 92.89 92.78 5 99.50 98.11 92.32 92.11 5 100.11 99.44 92.86 5 100.83 99.94 95.31 5 100.17 99.56 5 100.33 99.44 5 100.61 5 5 Table 1 Data obtained from boiling the sugarcane juice at 700 W. Mass evap. (g) Table 2 Data obtained from boiling the sugarcane juice at 900 W. HEAT INPUT 1100 W Time difference (min) HEAT INPUT 1300 W Mass evap. (g) Time (min) T1 (°C) T2 (°C) T3 (°C) T4 (°C) 3000 0 5 93.44 92.06 83.39 84.11 3002 0 2984 16 5 100.56 99.89 96.63 95.50 2962 40 96.33 2900 84 5 100.89 100.00 97.67 96.17 2922 42 97.50 96.32 2810 90 5 100.84 100.00 97.98 97.41 2880 93 100.20 100.06 97.95 97.31 2727 83 5 101.64 101.38 99.15 98.89 2787 130 5 100.44 100.06 97.58 97.45 2629 98 5 100.61 100.39 98.20 97.52 2510 119 5 101.95 101.73 99.85 99.45 2657 119 5 102.18 101.76 100.38 99.51 2538 105 T1 (°C) T2 (°C) T3 (°C) T4 (°C) Weight (g) 5 95.00 94.56 88.67 86.72 5 100.28 99.94 92.73 97.56 5 100.17 100.28 95.23 5 100.06 100.11 5 Weight Mass evap. (g) (g) 5 100.72 100.11 98.45 98.28 2364 146 5 101.00 100.47 98.73 98.62 2249 115 5 102.65 102.33 101.38 100.16 2433 102 5 101.06 100.84 99.03 99.41 2162 127 5 102.88 102.46 102.52 100.32 2331 116 5 101.28 100.88 99.73 98.96 2075 87 5 103.21 102.64 102.77 100.67 2215 89 5 102.41 101.05 100.00 99.40 1977 98 5 103.26 103.08 102.96 101.01 2126 95 5 102.65 101.20 100.31 100.05 1883 94 5 103.43 103.32 103.21 101.05 2031 116.3 5 102.86 101.37 100.15 100.21 1795 98 5 105.52 104.02 103.81 102.25 1915 113.5 5 103.12 101.61 100.77 100.76 1696 99 5 105.92 104.15 103.65 102.43 1802 110 5 103.59 101.87 101.28 100.49 1605 101 5 104.16 102.53 101.64 100.96 1520 95 5 106.47 104.61 104.18 103.16 1692 126 5 104.61 102.95 101.96 101.49 1432 108 5 107.40 105.00 104.29 102.71 1566 103.4 Table 3 Data obtained from boiling the sugarcane juice at 1100 W. Table 4 Data obtained from boiling the sugarcane juice at 1300 W. Figure 2 Arrangement PT-100 sensors. Figure 1 Pool boiling curve for pure water saturated at atmospheric pressure. [5] Figure 3 Photography system. Sugarcane juice was heated before it reaches the honey state, reaching concentrations no greater than 38 °Bx. Tables 1 to 4 shows the data obtained: Analytical Given the complexity presented by the dynamics of the process to be studied analytically, Rohsenow proposed the following correlation [12]: Csf Prl n 1 3 l h fg 1 g l v 6 c pl Ts qnucleate Tsat h fg (5) The rate of mass evaporated ( mev ) is: Qboiling Aqnucleate h fg h fg Taken into consideration the Eq. (6), Eq. (5) can be rearranged as follows: mev 1 Csf Prl n lA mev 3 1 g l v 6 c pl Ts Tsat h fg (6) (7) Using the following: 1 R lA mev 3 g 1 l v 6 c pl Ts Tsat h fg Where: R Csf Prl n Using the theory of logarithms to the above relation: ln R n ln Prl ln Csf (8) For the Prandtl number ( Prl ), the following expression is used: l c pl (9) Prl Kl This equation has the form of a straight line. The linear regression method to obtain the values of the constants n y Csf. The form of the equation for a straight line is as follows: y mx c (10) Linear regression method allows obtaining the constants of Rohsenow equation using the following relations: m N xy x2 N c So: n Csf x y x2 y N x2 (11) 2 x x x xy (12) 2 m ec Also, the average heat transfer coefficient by convection can be obtained as follows: qnucleate h Ts Tsat (13) Results and discussions With the experimental test, it was possible to appreciate the dynamics of this process, allowing identify regimes of natural convection and nucleate boiling. The data in tables 1 to 4 were used to calculate the values of the heat transfer coefficients and constants for Rohsenow pool boiling correlation, corresponding to each heat input, as shown Tab. 5. The expressions for finding the thermophysical properties present in this correlation are listed in Appendix-I [13-15]. To obtain the results shown in Tab. 5, it was considered that the surface temperature of the pot (Ts) is the temperature corresponding to the T1 and the temperature at which the thermophysical properties of sugarcane juice were found is the average of T2, T3 y T4. Heat input (W) Csf n h (W/m2°C) 700 900 1100 1300 0.0090 0.0039 0.0393 0.0027 -0.0475 -0.0300 -0.0164 -0.0100 4088.6 10556.8 10901.2 12592.8 Table 5 Values of constants for Rohsenow pool boiling correlation and heat transfer coefficients associated with the nucleate boiling of sugarcane juice for each heat input. Heat transfer coefficient (W/m2°C) The heat transfer coefficient due to natural convection movement on nucleate boiling of sugarcane juice range from 4088.6 to 12592.8 W/m2°C for heat inputs ranging from 700 to 1300W. Fig. 4 shows the variation of heat transfer coefficient as a function of the heat input. 14000 12000 10000 8000 6000 4000 2000 0 700 900 1100 1300 Heat input(W) Figure 2 Variation of heat transfer coefficient as a function of the heat input. Conclusions The value of the heat transfer coefficient increase proportionally with thermal power to sugarcane juice. In the same way with the increment of the thermal power, the difference temperature increases (Ts – Tsat) and that causes the acceleration in the rate of formation of vapor bubbles at the bottom of the pot. This factor also influences the mentioned heat transfer coefficient. While more nucleation places are generated, more vapor bubbles nucleate emerged increasing the heat (qnucleate) and the heat transfer coefficient. In the experimental test was observed that transmitted to the juice. The vertical movement of the vapor bubbles boiling. Apendix I 1043 4.854 Bx 1.07T l 1.718 10 5 4.620 10 8 T l Kl 0.3815 0.0051 Bx 0.001866T c pl 4187 (1 0.006 Bx) T T 0.001016 sat s 2 h fg 2499e Acknowlegdements the bubble size depends on the thermal power is the driving force for heat transfer by nucleate [kg/m3] [kg/ms] [W/m°C] [J/kg°C] [kJ/kg] This paper have been supported by the Fondo para la Tecnología (FINCyT), Perú, under the contract 174-FINCyT-IA-2013. Innovación, Ciencia y References [1] Md. Saimon Islam, Khadija Taslima Haque. Shuman Chandra Saha, “An experimental investigation of pool boiling at atmospheric pressure” Journal of Science and Technology vol 6, pp. 80-85, 2011. Daffodil International University – Bangladesh. [2] I. L. Pioro, “Experimental evaluation of constants for the Rohsenow pool boiling correlation” International Journal of Heat and Mass Transfer 42, pp. 2003-2013. [3] M. Kumar, K. S. Kasana, S. Kumar, O. 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