An experimental study on pool boiling of milk

Heat Transfer—Asian Research, 40 (2), 2011

An Experimental Study on Pool Boiling of Milk Mahesh Kumar,1 Om Prakash,2 and K.S. Kasana3 Mechanical Engineering Department, Guru Jambheshwar University of Science & Technology, Hisar, India 2 Mechanical Engineering Department, National Institute of Technology, Patna, India 3 Galaxy Global Group of Institutions, Dinarpur, Ambala, Haryana, India, and Ex-Professor, Mechanical Engineering Department, National Institute of Technology, Kurukshetra, India

1

This research paper reports the results for convective heat transfer coefficient and nucleate boiling heat flux for pool boiling of milk during khoa making. Various indoor experiments were conducted for different heat flux inputs varying from 9638.55 to 14457.83 W/m2. Experimental data obtained for pool boiling of milk were analyzed by using the Rohsenow correlation with the help of simple linear regression analysis. The convective heat transfer coefficients were estimated in the range of 334.48 to 837.78 W/m2 °C for the given heat inputs. The results for heat flux were found to be varying from 3344.8 to 8377.8 W/m2 at 10 °C excess temperature of the aluminum pot surface above the saturation temperature of the milk. The experimental errors in terms of percent uncertainty were also calculated. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res, 40(2), 159–170, 2011; Published online 21 January 2011 in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.20336 Key words: milk, khoa, khoa making, pool boiling, convective heat transfer coefficient

1. Introduction Today, India has emerged as the largest milk producing country in the world with an annual production of more than 91 million tonnes [1]. It has been estimated that nearly 7% of the total milk production is being utilized for making khoa due to its large scale consumption [2, 3]. Khoa is a rich source of energy containing fat, protein, lactose, and other minerals. Khoa making involves intensive heating during the desiccation process with an aim of evaporating the large quantity of water present in the milk. The natural and boiling convection heat transfer are the major heat transfer mechanisms which occur during heating process. Determination of the convective heat transfer coefficient is required for the proper design of an evaporator for a given shape [4, 5]. Pool boiling has been one of the most intensely investigated areas in heat transfer for more than seven decades. In general, nucleate boiling research has been focused on to the investigation of the physical mechanism and the development of theoretical and empirical correlations to estimate the heat transfer coefficients as well as critical heat fluxes, under different conditions [6]. A number of © 2011 Wiley Periodicals, Inc. 159

researchers have also studied the different aspects of nucleate pool boiling heat transfer with a variety of liquids. Rohsenow [7] proposed constant values of the exponents in dimensionless numbers and provided a list of values of Csf for some surface-fluid combinations that has been extended by Vachon et al. [8]. Rohsenow pool boiling correlation has also been evaluated experimentally by many researchers at sub-atmospheric, atmospheric, or higher pressure [8–13]. Many varieties of boiling surfaces like plates [9, 14, 15], single tubes [16], wires [17], and strips [18] have been used. Tiwari et al. [4] have evaluated the convective heat and mass transfer coefficient under pool boiling condition for sugarcane juice during preparation of jaggery. The heat transfer coefficients were found to vary from 50.65 to 345.20 W/m2 °C for heat flux inputs ranging from 6299.21 to 13385.83 W/m2. Analysis of these earlier works shows that the main parameters that affect the heat transfer coefficient under pool boiling are heat flux, thermophysical properties of working fluid, saturation pressure which ranged from atmospheric to critical, and some characteristics of the boiling surface materials like surface finishing, micro-structure, dimensions, thickness, etc. In the design of the heat exchanger, lack of thermal design data or correlation including that of the heat transfer coefficient as a function of heat flux, thickness of heater wall, and surface geometry poses a serious problem [4]. Thus, the development of a simple and easily adoptable procedure is required to determine the heat transfer coefficient under pool boiling conditions. To the best knowledge of the authors, review of the literature indicates that there is no analysis of experimental data for pool boiling of milk, which is the main objective of present study. Recently, Kumar et al. [19] have experimentally studied the natural convective heating behavior of milk for khoa making by the conventional heating method. The present study has been set forth to experimentally investigate nucleate pool boiling of milk in a circular aluminum pan during khoa making for the different heat inputs. Experimental data obtained for pool boiling of milk have been analyzed by using the Rohsenow correlation for the surface boiling of liquids to determine the constants and the convective heat transfer coefficient. Nomenclature A: Cpl: Csf: F: g: h: hfg: kl: mev: . mev: n: Pr: qnucleate: T: Ts: Tsat:

area of pan, m2 specific heat, J/kg °C experimental constant that depends on surface-fluid combination fat content, % gravitational acceleration, m/s2 convective heat transfer coefficient, W/m2 °C enthalpy of vaporization, J/kg thermal conductivity of milk, W/m °C mass evaporated, kg rate of mass evaporated, kg/s experimental constant that depends on fluid Prandtl number nucleate boiling heat flux, W/m2 temperature, °C average surface temperature, °C saturation temperature, °C 160

_w: _ Xw: µl: ρl: ρv: σ:

weight of milk, g average water content % in time interval viscosity of milk, kg/m⋅s density of milk, kg/m3 density of vapor, kg/m3 surface tension of milk, N/m 2. Materials and Methods

2.1 Theoretical consideration The heat transfer analysis of the experimental data obtained for pool boiling of milk has been performed by using the most widely acknowledged correlation proposed by Rohsenow [7]. The correlation is expressed as  Ts − Tsat   qnucleate Cpl n  = Csf Pr h  µlhfg  fg 

1/3

 σ  √  g(ρ − ρ ) l

v

(1)



Equation (1) can also be written as 1/2

 g(ρl − ρv)  qnucleate = µlhfg  σ  

3

 Cpl(Ts − Tsat)   n   CsfhfgPr 

(2)

The Prandtl number is calculated by using the following expression Pr =

µlCpl kl

(3)

The average convective heat transfer coefficient can be given by h=

qnucleate Ts − Tsat

(4)

The rate of water evaporated is determined by dividing Eq. (2) by the enthalpy of vaporization and multiplying the area of the pan mev =

Qboiling Aqnucleate = hfg hfg

(5)

Now with the help of Eq. (5), Eq. (2) can be rearranged as follows: 1/3

Cpl(Ts − Tsat)  Aµl  CsfPr = m  hfg  ev  n

161

1/6

 g(ρl − ρv)    σ  

(6)

After substituting 1/3

Cpl(Ts − Tsat)  Aµl  K= m  hfg  ev 

1/6

 g(ρl − ρv)    σ  

Equation (6) becomes K = CsfPrn

(7)

logK = nlogPr + logCsf

(8)

Taking logarithm on both sides of Eq. (7),

The above equation represents the straight line in the following form, y = mx + c

(9)

where y = logK, m + n, x = logPr = log(µlCpl / kl), and c = logCsf. K in the above expression is calculated for various excess temperatures, and (Ts − Tsat) is recorded during the pool boiling experiments by using the thermal-physical properties of milk. The corresponding values of x and y are also computed. Thus the values of m and c in Eq. (9) are obtained by using the following formulae obtained by the linear regression method: NΣxy − ΣxΣy NΣx2 − (Σx)2

(10)

Σx2Σy − ΣxΣxy NΣx2 − (Σx)2

(11)

m=

c=

2.2 Physical properties of milk The following expressions are used for calculating the different physical properties of milk such as specific heat Cpl [20], surface tension σ [21], density ρl [22], viscosity µl [23], thermal conductivity kl [24], and enthalpy of vaporization hfg [25]. Cpl = 2.976T + 3692

(12)

σ = 1.8 × 10−4T2 − 0.163T + 55.6

(13)

where σ is in N⋅m–1 × 10–3. 162

ρl = −0.2307 × 10−2T2 − 0.2655T + 1040.51 − F(−0.478 × 10−4T2 + 0.969 × 10−2T + 0.967)

(14)

lnµl = 4.03 × 10−5T2 − 2 × 10−2T + 0.827

(15)

where µl is in Pa⋅s × 10–3. __ kl = 0.356439Xw + 0.223544 __ hfg = (hfg of water) × Xw

(16) (17)

The thermal-physical properties of milk have been determined at an average temperature in the time interval. 2.3 Experimental error The experimental error has been evaluated in terms of percent uncertainty (internal + external). The following two equations have been used for internal uncertainty [26]: UI =

√  sd21 + sd22 + . . . sd2n No

(18)

where No is the number of sets and sd is the standard deviation, which is given as sd =

__ Σ(X − X)2 N

 √

(19)

__ where X − X is the deviation of observation from the mean and N is the number of observations in each set of heat input. The % internal uncertainty therefore has been determined using the following expression: % internal uncertainty = (UI/mean of the total observations) × 100

(20)

For external uncertainty, the least counts and the accuracies of all the instruments used in measuring the observation data have been taken. 2.4 Experimental details The schematic diagram of the experimental set-up is shown in Fig. 1. It consists of a hot plate (178 mm in diameter ) of 1000 W capacity connected through a variac to control the rate of heating of the milk in an aluminum pot of 3.2 liters capacity. The heat input was measured by a calibrated wattmeter (accuracy within ±0.5% of full scale value 1500 W), having a least count of 1 W. Four 163

Fig. 1. Schematics of experimental set-up for pool boiling of milk. calibrated copper-constantan thermocouples connected to a ten-channel digital temperature indicator (least count of 0.1 °C, accuracy ±0.1%, range of –50 to 200 °C) were used to measure the temperature of the milk (T1), the surface temperature of the aluminum pot at the bottom (T2) and outer side (T3), and room temperature (T4). A thermocouple for measuring the surface temperature of the pot at the bottom has been attached to the pan surface by sticking aluminum foil using an adhesive at a distance of R/3 from the center of the pot, where R is the radius of the pot. Milk surface temperature (T5) has also been measured by infrared thermometer (Raytek-MT4), having a least count of 0.2 °C with an accuracy of ±0.2% on a full scale range of –1 to 400 °C. The relative humidity (γ) and temperature above the milk surface (T6) have also been measured by a digital humidity/temperature meter (model Lutron-HT3006 HA). It had a least count of 0.1% relative humidity with an accuracy of ±3% on the full scale range of 10 to 95% of relative humidity and 0.1 °C temperature with an accuracy of ±0.8 °C on the full scale range of 0 to 50 °C. The mass of water evaporated during heating of milk has been measured by using an electronic weighing balance of 6 kg capacity (Scaletech, model TJ-6000) with a least count of 0.1 g with an accuracy ±2% on the full scale. 2.5 Experimental procedure

In order to determine the convective heat transfer coefficient of milk during khoa making under the pool boiling mode, the following procedure has been employed: 1. Locally available fresh milk (obtained from a herd of 15 cows) was heated in an aluminum cylindrical pot 200 mm in diameter, 102 mm deep, and 1.6 mm thick without any cover for different values of heat inputs ranging from 240 to 360 W. The experiments follow a path of increasing heat inputs. For each run of the test, a fresh sample of milk was taken from the same herd of cows. 2. In the traditional method of khoa making, milk is heated in an open pan and simultaneously stirred and scraped with a palta (iron scraper) to prevent the scorching of milk solids sticking to the pan. In the present research work, light manual stirring and scraping of milk has been carried out with the help of a Teflon scraper (width = 20 mm, length = 200 mm, having a wooden handle) to avoid 164

Table 1. Observations for Pool Boiling of Milk in Open Pan (Atmospheric Pressure) at Heat Input = 240 W

the scaling and burning of the product. Skin formed at the milk surface has been broken by stirring the milk gently at frequent intervals (4 to 5 times per minute). 3. The necessary data of temperature and other parameters during heating of milk have been started to record once the milk temperature becomes equal to 90 °C (i.e., pool boiling mode range) and were taken before the solidification of concentrated milk. Temperatures and relative humidity have been measured at various locations as shown in Fig. 1. 4. The mass of water evaporated during heating of the milk for each set of observations has been obtained by subtracting two consecutive readings in a given time interval. 5. All the experimental parameters have been recorded after every 10-minute time interval. 6. Different sets of heating of milk have been obtained by varying the input power supply from 240 to 360 W to the electric hot plate with the help of the variac. The experimental results for different sets of heating are reported in Tables 1 to 4.


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3. Results and Discussion The values of m and c have been evaluated from Eqs. (10) and (11) by using the experimental data from Tables 1 to 4. After evaluating the m and c, the values of Csf and n can be obtained as Csf = ec and n = m. The values of the constants Csf and n were found to vary from 0.909 to 0.965 and –1.339 to –1.585, respectively, for the given heat inputs. All these results have been given in Table 5. The average values of the constants Csf and n have been observed as 0.941 and –1.472, respectively. The convective heat transfer coefficients have been computed from Eq. (4) by using the values of Csf and n for different values of heat inputs, which are also given in Table 5. Figure 2 illustrates the variation of convective heat transfer coefficient for the different values of heat input. It varies from 334.48 to 837.78 W/m2 °C for the given heat inputs ranging from 240 to 360 W. The increase in values of the convective heat transfer coefficient with the increase in the heat input may be due to the higher surface temperature of the pan and activation of more nucleation sites which causes rapid formation of the vapor bubbles at the pan-liquid surface. The experimental results obtained for convective heat transfer coefficients have also been compared with the Rohsenow correlation which are plotted in Fig. 2. It has been observed that the convective heat transfer coefficients are lower than that of Rohsenow correlation and vary in a range of 18.27 to 26.03%. Table 4. Observations for Pool Boiling of Milk in Open Pan (Atmospheric Pressure) at Heat Input = 360 W

166

Table 5. Values of Csf, n, and h for Pool Boiling of Milk at Different Heat Inputs

Figure 3 illustrates the prediction for variation of average values of heat flux with excess temperature. It was found to vary from 272.711 to 34089.27 W/m2 for the given excess temperatures ranging from 4 to 20 °C. The general trend is that heat flux rises exponentially with an increase in excess temperature. These results are in accordance with those reported in the literature [4, 27–29]. For comparison purpose, the heat flux values for water have also been determined from the Rohsenow correlation by taking the properties of water at the saturation temperature [25] and by keeping Csf = 0.011 and n = 1.26 [6]. The heat flux variation with excess temperature has been plotted in Fig. 4. It is observed from Figs. 3 and 4 that the values of heat flux for khoa are about 35 times lower than that of water. This may be due to the presence of fat and milk solids particulates. An analysis of the inaccuracies involved in the measurement of temperatures, mass evaporated, and power input was carried out to obtain the experimental errors in terms of percent uncertainty (internal + external). It was estimated in the range of 15.83 to 18.92% and the different values of convective heat transfer coefficients were found to be within this range. The experimental percent uncertainties are reported in Table 6. Error bars for convective heat transfer coefficients are given in Fig. 4.

Fig. 2. Convective heat transfer coefficient variation with heat inputs. 167

Fig. 3. Heat flux variation with excess temperature for different heat inputs.

Fig. 4. Heat flux variation with excess temperature for water.

Table 6. Experimental Percent Uncertainties for Pool Boiling of Milk at Different Heat Inputs

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Fig. 5. Error bars for convective heat transfer coefficients. 4. Conclusions The research reported herein has been set forth in order to evaluate the convective heat transfer coefficients for pool boiling of milk during khoa making in an aluminum pan. Experimental data obtained for pool boiling of milk have been analyzed by using Rohsenow correlation with the help of simple linear regression analysis. The values of convective heat transfer coefficients were found to increase from 334.48 to 837.78 W/m2 °C for the heat flux inputs ranging from 9638.55 to 14457.83 W/m2. This could be due to higher heating surface temperature which results in the formation of more active nucleation sites and rapid formation of the vapor bubbles at the pan-liquid surface. The variation of heat flux with excess temperature of milk have also been predicted which were found to vary exponentially with increasing excess temperature. The experimental errors in terms of percent uncertainty were found in the range of 15.83 to 18.92%. Literature Cited 1. Kurien V. The dairy scenario in ‘Dairy India’ (6th ed.). Dairy India Yearbook, Priyadarshini Vihar, New Delhi; 2007. p 7–8. 2. Rajarajan G, Kumar CN, Elango A. Distribution pattern of moulds in air and khoa samples collected from different sections of khoa plants. Indian J Dairy Sci 2007;60(2):133–135. 3. Kumar M, Prakash O, Kasana KS, Dabur RS. Technological advancement in khoa making. Indian Dairyman 2010;62(1):64–70. 4. Tiwari GN, Prakash O, Kumar S. Evaluation of convective heat and mass transfer for pool boiling of sugarcane juice. Energy Conversion and Management 2004;45:171–179. 5. Das SK. Process heat transfer. Narosa Publishing House; 2006. 6. Pioro IL. Experimental evaluation of constants for the Rohsenow pool boiling correlation. Int J Heat Mass Transf 1999;42:2003–2013. 169

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