Accepted Manuscript Experimental studies on the liquid thermal conductivity of three saturated fatty acid methyl esters components of biodiesel Jing Fan, Zixuan Zhu, Xiaopo Wang, Fenhong Song, Lihui Zhang PII: DOI: Reference:
S0021-9614(18)30485-3 https://doi.org/10.1016/j.jct.2018.06.005 YJCHT 5436
To appear in:
J. Chem. Thermodynamics
Received Date: Revised Date: Accepted Date:
8 May 2018 30 May 2018 6 June 2018
Please cite this article as: J. Fan, Z. Zhu, X. Wang, F. Song, L. Zhang, Experimental studies on the liquid thermal conductivity of three saturated fatty acid methyl esters components of biodiesel, J. Chem. Thermodynamics (2018), doi: https://doi.org/10.1016/j.jct.2018.06.005
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Experimental studies on the liquid thermal conductivity of three saturated fatty acid methyl esters components of biodiesel Jing Fan a Zixuan Zhu a Xiaopo Wang b, * Fenhong Song a, c, * Lihui Zhang d ( a School of Energy and Power Engineering, Northeast Electric Power University, Jilin, Jilin 132012, People’s Republic of China) ( b Key laboratory of Thermo-Fluid Science and Engineering, Ministry of Education of China, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, People’s Republic of China) ( c Key Laboratory of Low-grade Energy Utilization Technologies and Systems, Ministry of Education of China, Chongqing University, Chongqing 400044, People’s Republic of China) ( d Key Laboratory of Special Purpose Equipment and Advanced Processing Technology, Ministry of Education of China, Zhejiang University of Technology, Hangzhou, Zhejiang 310014, People’s Republic of China) * Corresponding author Email:
[email protected] ;
[email protected]
Abstract: One of the attempts to reduce the consumption of fossil fuels is to replace them with renewable and clean fuels. Among these fuels, biodiesel has been considered as a promising alternative to petroleum diesel fuel. Thermal conductivity of biodiesel is a very important thermophysical property for its applications. In this work, the liquid thermal conductivity of three saturated fatty acid methyl esters(methyl myristate, methyl laurate and methyl caprate), usually the significant biodiesel components, was measured with the temperature ranging within (304 to 402) K, (283 to 402) K, (267 to 400) K, respectively. The total standard uncertainty of the experimental results was estimated to be less than 2 % and the repeatability was better than ± 0.5 %. The thermal conductivity data of each substance were fitted as a function of temperature, and the average absolute relative deviation and maximum absolute relative deviation between the experimental data and calculated results were 0.13 % and 0.44 % for methyl myristate, 0.21 % and 0.53 % for methyl laurate, 0.28 % and 0.80 % for methyl caprate, respectively. Keyword: Biodiesel; Fatty acid methyl esters; Thermal conductivity
1. Introduction
The traditional fossil fuels have been meeting most industrial and commercial demands in recent decades [1,2]. However, at present, unabated combustion of the remaining reserves of fossil fuels will cause severe climate change (e.g., global warming and air pollution) [3-5], which has caught much attention of scientists in worldwide. Therefore, it has been the new focus of plenty of researchers to develop dimethyl-ether, ethanol and biodiesel as renewable and alternative fuels [6-11]. Among these alternative fuels, biodiesel, which have many apparent benefits in the areas of being biodegradable, non-toxic, and derived from renewable energy resources [12-14], is considered as a clean and sustainable fuel because it may reduce the emission levels of pollutant gases and contribute less to the greenhouse gas emissions. The main components of the biodiesel are fatty acid ethyl esters (FAEEs) and fatty acid methyl esters (FAMEs) produced by the transesterification of triglycerides with ethanol and methanol. The biodiesel can be directly used in conventional diesel engine without significant modifications. Nevertheless the thermophysical properties of both bio- and petroleum-based diesels, such as thermal conductivity, density, viscosity and compressibility are different due to the differences in chemical structure [15-18]. In recent years, the investigations on the thermophysical properties of biodiesel has been the topic of many studies [1,3,12,15-30]. For example, Yang and Wang (2018) conducted the experimental studies on the density and viscosity of binary mixtures containing the component of the biodiesel, namely methyl myristate, with higher alcohols, including 1-propanol, 1-butanol and 1-pentanol at atmospheric pressure from (303.15 to 333.15) K [12]. Gülüm and Bilgin (2017) performed studies on the viscosity and density of biodiesel-diesel blends' from theoretical and experimental perspectives [1]. Nikitin and Popov (2015 and 2016) measured the
critical temperature and the critical pressures of some fatty acid methyl and ethyl esters [19-21]. Meng and Wang (2013) predicted the densities for three methyl ester biodiesels from room temperature to 523 K [22]. Shang et al (2016) studied the phase behaviour for three ternary systems (methanol+glycerol+methyllaurate/methyl myristate/methyl palmitate) at the temperature range within (493~523) K [25]. Zhang and He (2016) used the Brillouin light scattering methods to measure the speed of sound in three fatty acid methyl esters (methyl caprate, methyl laurate and methyl myristate) [26]. Nevertheless, the thermal conductivity of pure fatty acid (methyl and ethyl) esters, which is a very important thermophysical property and is necessary for the thermal design in an extensive range of areas [31-35], is scarce in the literature. In this work, the thermal conductivity of three components of biodiesel, including methyl myristate, methyl laurate and methyl caprate, was measured in liquid phase at atmospheric pressure.
2. Experimental 2.1 Principle of experiment The transient-hot-wire method is considered to be one of the most accurate and reliable methods to measure thermal conductivity in the liquid phase [31,32,36]. In this paper, methyl myristate, methyl laurate and methyl caprate in the liquid phase was measured using a transient hot-wire instrument with one bare platinum wire. The basic working equation is as follows [33]: Tid r0 , t
q 4
ln t
4a ln 2 4 r0 C q
(1)
where ΔTid refers to the ideal temperature rise of wire, r0 stands for the radius of hot wire, t represents the elapsed time, q refers to the power input per unit length of wire, λ stands for the thermal conductivity of fluid, a symbolizes the thermal diffusivity of
fluid, and C=1.781… stands for the exponential of Euler’s constant. Equation (1) demonstrates that there exists a linear relationship between the ideal temperature rise and the logarithm of the elapsed time t. The thermal conductivity λ is obtained by the following equation: T , P
q 4 k
(2)
where λ(T, P) refers to the thermal conductivity of fluid at reference temperature T and the working pressure P,
k stands for the slope of the line that fits the
temperature rise in the ideal condition as a function of the logarithm of the elapsed time t, as shown in Equation (3): k
d Tid d ln t
(3)
Detailed corrections for the thermal conductivity measurements using transient hot-wire instrument have been illustrated in many literatures [33-35] and were not shown here. 2.2 Experimental measurement system The experimental system for thermal conductivity measurement consists of a transient-hot-wire cell, data acquisition system, vacuum system, temperature measurement system and thermostatic bath. Figure 1 is a schematic drawing of transient -hot-wire cell. The experimental cell and connected pipes are made from stainless steel. The operation at temperature range of the experiment reaches up to 400 K, and the designed experimental temperature is 470 K due to the restriction of the lead wires. The volume of the experimental cell was minimized to reduce the filling quantity of measured liquids and the real volume is approximately 45 mL. A 20-μm-diameter and 85-mm-long bare platinum wire was adopted in this instrument to decrease the effects because of its limited length and physical properties while
remaining excellent uniformity and tensile strength. The wire was welded with the lower and upper platinum hooks along with an axial stress of pre-decided magnitude by hanging one copper weight at the bottom. Moreover, in order to effectively reduce the end effects and makes the instrument accord with ideal model well, two voltage potential leads of the same diameter platinum wire are spot-welded at positions about 10 mm away from the end of the wires.
1.effused pipeline 2.injected pipeline 3.PTFE framework 4.spring 5.voltage lead 6.vessel 7.platinum wire 8.Cu O-ring 9.flange 10.PTFE O-ring 11.seal 12.steel cover 13.extension line
Figure 1 thermal conductivity experimental cell
The experimental cell was put into thermostatic bath with temperature stability within ±5 mK over 20 min. The silicon oil was chosen to be the bath fluid to control temperature during the experiment. The total uncertainty of temperature measurement is better than 10 mK [36]. The vacuum system includes vacuum gauge as well as a mechanical pump. The data acquisition system as demonstrated in Figure 2, comprises an industrial computer, a Keithley 2400 SourceMeter, a standard resistor, two Keithley 2010 digital
multimeter(one for measuring the current though wire, the other for measuring the voltage applied to the wire), two ballast resistances, three electron switches. The industrial computer via IEEE-488 interface can implement all data acquisition and instrument control.
Figure 2 System of data acquisition.1,7: Keythley 2010; 2: Standard resistor(1 Ω); 3,4: ballast resistances(10 kΩ); 5:Keythley 2400; 6: Cell; 8:IEEE 488; 9: industrial computer
The estimation of the relative expanded uncertainty of the thermal conductivity measurement was mentioned as below [33]. A cathetometer was used to measure the length of the platinum wire between the potential leads with an uncertainty of 0.02 %. The temperature coefficient uncertainty of platinum wire was estimated within the range of 0.2 %, the uncertainty of heat generation of hot wire was less than 0.2 %, the uncertainty of temperature rise slope dΔT/ dlnt of hot wire was less than 0.8 %. Moreover, the uncertainty of deviations from mathematical ideal model and that of the other modes of heat transfer was calculated, which was decreased to one small magnitude in properly designed instrument under selected operating conditions. Consequently the total standard uncertainties of the present thermal conductivity measurements for liquid were estimated to be better than 2 %.
2.3 Sample Aladdin Chemistry Co. Ltd, China provided the sample of methyl myristate,
methyl laurate and methyl caprate. Table 1 shows the details of these three liquids. Table 1. Chemical specifications sample
CAS Number
source
mass fraction purity
purification method
methyl myristate
124-10-7
Aladdin
0.98
none
methyl laurate
111-82-0
Aladdin
0.99
none
methyl caprate
110-42-9
Aladdin
0.99
none
3. Results and discussion 3.1 Thermal conductivity of water and ethanol In order to check the performance of the present transient-hot-wire instruments, the liquid thermal conductivity of pure water and ethanol (with purity of mass fraction greater than 99.97 %) was measured, and more details were listed in our previous work [37]. The maximum absolute relative deviation between the experimental results and reference data [38,39] were 1.27 % and 1.34 %.
3.2 Thermal conductivity of three fatty acid methyl esters Thermal conductivity of methyl myristate, methyl laurate and methyl caprate in the liquid phase was measured in temperature range from (304 to 402) K, (283 to 402) K, (267 to 400) K, respectively. The experimental results are listed in Table 2. The experimental values were the average of two to three runs, whose repeatability was better than ± 0.5 % at the same temperature. In all measurements, the temperature rise of the platinum wire was about 3.0–4.0 K and the measurement time was 1s after the initiation of heating by adjusting the current through the wire.
Table 2 Liquid thermal conductivity of three methyl esters at pressure p= 0.1 MPa a T/K methyl myristate
λ/W·m-1·K-1
T/K
λ/W·m-1·K-1
304.02 304.33 320.10 320.81 327.18 327.53 338.31 338.55 342.21 342.28 354.31 354.58
0.1481 0.1479 0.1447 0.1443 0.1435 0.1428 0.1407 0.1408 0.1402 0.1398 0.1375 0.1366
359.14 359.27 369.45 369.47 377.12 377.13 386.13 386.27 394.31 394.48 402.41 402.41
0.1366 0.1361 0.1338 0.1337 0.1324 0.1322 0.1300 0.1300 0.1284 0.1283 0.1261 0.1265
0.1488 0.1484 0.1465 0.1464 0.1440 0.1440 0.1434 0.1443 0.1414 0.1410 0.1394 0.1388 0.1373
337.57 349.53 349.67 359.29 359.31 369.45 369.47 379.17 379.47 390.25 390.33 402.63 402.69
0.1370 0.1346 0.1339 0.1323 0.1325 0.1291 0.1296 0.1280 0.1274 0.1254 0.1250 0.1222 0.1214
0.1492 0.1494 0.1461 0.1471 0.1444 0.1445 0.1426 0.1423 0.1393 0.1392 0.1370 0.1368 0.1342 0.1340
348.66 348.81 354.58 354.59 360.11 360.61 368.98 369.47 379.50 379.65 389.35 389.39 399.87 399.95
0.1313 0.1312 0.1297 0.1299 0.1297 0.1285 0.1274 0.1262 0.1247 0.1236 0.1206 0.1205 0.1183 0.1190
methyl laurate 283.81 284.03 295.89 295.90 306.72 306.79 307.82 307.84 317.62 317.69 327.44 327.69 337.37 methyl caprate 267.10 267.11 277.00 277.07 288.82 288.84 300.83 300.86 311.66 311.87 324.72 324.92 336.71 336.71 a
Standard uncertainties u are u(T)= 10 mK, u(p)= 1 kPa, combined relative standard uncertainties urc are
0.02.
Figure3 displays the temperature dependence of the liquid thermal conductivity
for methyl myristate, methyl laurate and methyl caprate. We can apparently see that the current results decrease smoothly with the increase of temperature.
Figure 3 Temperature dependence of the thermal conductivity of three liquid at atmospheric pressure
Then, in order to satisfy the requirement of engineering application, the experimental data is required as the basis for the reliable and accurate predicted methods to calculate the thermal conductivity of fluid within liquid phase in different temperatures. Thus, the measured thermal conductivity data of methyl myristate, methyl laurate and methyl caprate were correlated with temperature by a polynomial function. The correlation equation is as follows:
a bT cT 2
(4)
In Equation (4), the unit of thermal conductivity λ and temperature T is W·m-1·K-1 and K, respectively. Table 4 is the coefficient of polynomial function for the three liquids. Table 4 Coefficients of correlations for different substance substance
-1 -1 a/W·m ·K
-1 -2 b/W·m ·K
-1 -3 c/W·m ·K
methyl myristate
0.19869
-1.26267×10-4
-1.32872×10-7
methyl laurate
0.20064
-1.52181×10-4
-1.07132×10-7
methyl caprate
0.17869
-3.46966×10-5
-2.89463×10-7
Figure 4 to Figure 6 illustrates the deviation between experimental data with the calculated results by Equation (4). For most of the points, the deviations are between -0.40 % to 0.40 %, and the average absolute relative deviation and maximum relative deviation are 0.13 % and 0.44 % for methyl myristate, 0.12 % and 0.53 % for methyl laurate, and 0.28 % and 0.80 % for methyl caprate, respectively.
Figure 4 Deviations of the liquid methyl myristate experimental thermal conductivity from the calculated results by Eq. (4).
Figure 5 Deviations of the liquid methyl laurate experimental thermal conductivity from the calculated results by Eq. (4).
Figure 6 Deviations of the liquid methyl caprate experimental thermal conductivity from the calculated results by Eq. (4).
Mukhamedzyanov and Usmanov [40] measured the liquid thermal conductivity of methyl myristate, methyl laurate and methyl caprate with a declared uncertainty of 1.5 % in 1971, and the results are listed in the book Thermal Conductivity of Liquids
[in Russian]. Comparison of the data published by Mukhamedzyanov and Usmanov and those presented in this work, which are depicted in Figure 7, shows that our values correlate well with their data at low temperatures. However, the value of (-dλ/dT) is greater in this work than that in the previous experiments. It leads to the fact that, the maximum relative deviations (at 393.15 K) of three esters are -5.15 % for methyl myristate, -4.58 % for methyl laurate and -.5.52 for methyl caprate. It is difficult to find the exact reasons which may cause the larger deviations, because the experimental details and the sample purity were not clear about the work of Mukhamedzyanov.
Figure 7 Deviations between our values and literature data
4. Conclusion The thermal conductivities of methyl myristate, methyl laurate and methyl caprate in liquid phase was measured at atmospheric pressure over the temperature range from (304 to 402) K, (283 to 402) K and (267 to 400) K, respectively. Results indicate that thermal conductivity decreases smoothly with negative slope as
temperature increases. Additionally, a polynomial correlation between thermal conductivity and temperature was fitted using experimental data. The average absolute relative deviation between the experimental and calculating results for these three fluids is 0.13 %, 0.12 % and 0.28 %, and the maximum deviation is 0.44 %, 0.53 % and 0.80 %, respectively.
Acknowledgments The authors acknowledge the financial support provided by National Natural Science Foundation of China (Grant No. 51606032), Key Laboratory of Low-grade Energy Utilization Technologies & Systems Foundation of Ministry of Education (No. LLEUTS-201818).
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Highlights 1. Measurement of thermal conductivity of three saturated fatty acid methyl esters components of biodiesel was carried out. 2. Thermal conductivitvalues of methyl myristate, methyl laurate and methyl caprate in liquid phase are reported for the first time. 3. Based on the experimental data, a fitting correlation of temperature by using a quadratic polynomial function was proposed.