Thermal Conductivity of the Binary Mixtures of N-Heptane and Fatty Acid Esters: Measurement and Correlation

Abstract

As a renewable energy source and potential substitute for fossil fuels, biodiesel plays an increasingly important role in both energy security and environmental protection. Accurate thermal conductivity data of biodiesels and their mixture with diesel are critical to engine design to achieve high combustion efficiency. This study measured the thermal conductivity of binary mixtures of heptane and biodiesel components, specifically methyl myristate, methyl laurate, and methyl caprate, over a temperature range of 298.15–328.15 K, using the two-wire 3ω method. Based on the experimental data, the effect of mass fraction, temperature, and carbon chain length of the fatty acid ester on the thermal conductivity was analyzed. The second-order Scheffé polynomial model, Flippov equation, Jamieson equation, and Chen equation were used to correlate the experimental data and compare to find a better one. The Flippov equation shows the lowest absolute average relative deviation of 0.80% for the binary mixtures of heptane with methyl myristate, methyl laurate, and methyl caprate.

1. Introduction

The search for new, sustainable, and environmentally friendly alternative energy sources for fossil fuel is of great practical significance for ensuring energy security and advancing environmental protection. Biodiesel, which is a typical renewable energy source, demonstrates excellent combustion and emission performance [1,2,3,4]. Moreover, it can be mixed with diesel in any ratio making it possible to be directly used in existing engines.

The thermophysical properties of biodiesel including density, viscosity, heat capacity, and thermal conductivity are necessary for the engine design of heat transfer and flow process [5]. Therefore, substantial experimental and theoretical research has focused on providing reliable data on these properties for biodiesel components. For instance, Yang et al. [6] measured the density and viscosity of binary mixtures of methyl myristate with 1-propanol, 1-butanol, and 1-pentanol at atmospheric pressure between 303.15 and 333.15 K. Wang et al. [7] studied the density of fatty acid methyl esters and fatty acid ethyl esters containing ethanol in the temperature range from 283.15 K to 318.15 K. Bogatishcheva et al. [8] investigated the heat capacity and thermal diffusivity of methyl esters of n-alkanoic acids in the temperature range from 303.15 to 373.15 K. Nikitin [9] measured the vapor-liquid critical properties of methyl esters of n-alkanoic acids. Shang et al. [10] explored the phase behavior of three biodiesel + methanol + glycerol ternary systems in the temperature range from 493 K to 523 K. Zhang et al. [11] used the Brillouin light scattering method to measure the sound velocity of methyl caproate, methyl laurate and methyl myristate in the temperature range from 288 to 498 K and at pressures of 0.1, 4.0, 7.0, and 10.0 MPa.

Improving the thermal conductivity can enhance combustion efficiency and reduce pollutant emissions, making accurate thermal conductivity data indispensable for optimizing biodiesel. Yuan et al. [12] determined the liquid thermal diffusivity of six fatty acid methyl esters and four fatty acid ethyl esters over a wide temperature range from 303.15 to 473.15 K using the dynamic light scattering method. Perkins et al. [13] explored the thermal conductivity of methyl oleate and methyl linoleate in the liquid phase over a wide range of temperatures and pressures. Fan’s group [14,15,16,17,18,19] measured the thermal conductivities of eight pure ethyl esters of saturated fatty acids and ten pure methyl esters of fatty acids at atmospheric pressure and correlated all the experimental data as a function of temperature. They also measured the thermal conductivities of methyl myristate, methyl laurate, and methyl caprate at temperatures in the range of 292–372 K and pressures up to 15 MPa as well as the thermal conductivities of binary mixtures of methyl myristate and three pure alcohols were measured in the temperature range of 292–362 K at atmospheric pressure. Zheng et al. [20,21,22] used a transient hot-wire device to measure the thermal conductivities of methyl laurate and methyl myristate over an extensive range of temperatures from 293.15 to 523.15 K and pressures up to 15 MPa. Summaries of the published experimental data on the thermal conductivity of biodiesel components and their mixtures with other compounds are provided in

Table 1. Experimental data of thermal conductivity of pure fatty acid ester.

Chemical	T/K	p/MPa	Relative Expanded Uncertainty	Ref.	Thermal Conductivity/W·m−1·K−1
Methyl oleate	302–508	0.1–42	1%	Perkins [13]	0.1125–0.1565
Methyl linoleate	302–505	0.1–42	1%	Perkins [13]	0.1125–0.1525
Methyl butyrate	283.34–358.18	0.1	2%	Fan [17]	0.1207–0.1459
Methyl pentanoate	285.55–362.16	0.1	2%	Fan [17]	0.1194–0.1430
Methyl caprylate	273.56–393.54	0.1	2%	Fan [17]	0.1160–0.1450
Methyl caprate	267.10–399.95	0.1	2%	Fan [18]	0.1190–0.1492
Methyl laurate	283.81–402.69	0.1	2%	Fan [18]	0.1214–0.1488
Methyl myristate	304.02–402.41	0.1	2%	Fan [18]	0.1265–0.1481
Ethyl hexanoate	254..29–383.37	0.1	2%	Song [16]	0.1323–0.1474
Ethyl acetate	249.13–348.46	0.1	2%	Song [16]	0.1396–0.1618
Ethyl propionate	263.55–356.28	0.1	2%	Song [16]	0.1365–0.1547
Ethyl butyrate	268.57–363.52	0.1	2%	Song [16]	0.1311–0.1471
Ethyl pentanoate	249.21–363.57	0.1	2%	Song [16]	0.1314–0.1501
Methyl laurate	293.15–523.15	0.1–15	2%	Zheng [20]	0.1072–0.1469
Methyl myristate	293.15–523.15	0.1–15	2%	Zheng [20]	0.1069–0.1502
Methyl octanoate	293.15–523.15	0.1–15	2%	Zheng [22]	0.1007–0.1428
Methyl decanoate	293.15–523.15	0.1–15	2%	Zheng [22]	0.1010–0.1440
Methyl caproate	253.15–523.15	0.1–15	2%	Zheng [21]	0.0921–0.1372

and

Table 2. Experimental data of thermal conductivity of mixtures containing fatty acid ester.

Chemical	T/K	p/MPa	Relative Expanded Uncertainty	Ref.	Thermal Conductivity/W·m−1·K−1
1-propanol + methyl myristate	292–362	0.1	2%	Fan [14]	0.1355–0.1540
1-butanol + methyl myristate	292–362	0.1	2%	Fan [14]	0.1355–0.1507
1-pentanol + methyl myristate	292–362	0.1	2%	Fan [14]	0.1355–0.1500
1-propanol +methyl laurate	287–358	0.1	2%	Fan [15]	0.1326–0.1595
1-butanol + methyl laurate	287–358	0.1	2%	Fan [15]	0.1326–0.1569
1-pentanol + methyl laurate	287–358	0.1	2%	Fan [15]	0.1326–0.1562

.

To provide a guide for the application of biodiesel as an additive for diesel, some work on the thermophysical properties of biodiesel/diesel blends was conducted. Gulum et al. [23] measured the density and kinematic viscosity of biodiesel and diesel mixtures. Wang et al. [24] examined the density and viscosity of binary mixtures of n-hexadecane with three fatty acid ethyl esters (ethyl caprylate, ethyl caprate, and ethyl laurate) from 298.15 to 323.15 K. Heptane is usually used as the surrogate of diesel to study the combustion performance of biodiesel/diesel blends [25]. However, to the best of our knowledge, there is no study on the thermal conductivity of binary blends of heptane and biodiesel.

In the present work, the thermal conductivity of binary mixtures of heptane with biodiesel components containing methyl myristate, methyl laurate, and methyl caprate in the temperature range of 298.15–328.15 K were measured and correlated using the second-order Scheffé polynomial model, Flippov equation, Jamieson equation, and Chen equation [26,27,28] to provide new data for biodiesel’s application. The effect of mass fraction, temperature, and the carbon chain length of fatty acid ester on the thermal conductivity of binary mixtures of heptane blending with methyl myristate, methyl laurate, and methyl caprate was investigated to provide a guide for biodiesel’s thermal conductivity design. The classical 3ω method for measuring thermal conductivity faces the problem of heat loss in the axial direction during the heating process. In this paper, a two-wire 3ω method is used to eliminate the end effect.

2. Materials

Heptane, methyl caprate, ethyl caprate, and methyl myristate were obtained from Aladdin Chemistry Co. Ltd. with a purity of 98% or greater. All samples were used without further purification, and the binary mixtures were prepared according to the experimentally arranged mass ratios using the weighting method.

Table 3. Information of the used substances.

Chemical Name	Chemical Formula	CAS	Mass Fraction Purity	Source
Heptane	C7H16	142-82-5	≥0.99	Aladdin, Shanghai, China
Methyl caprate	C11H22O2	110-42-9	≥0.99	Aladdin, Shanghai, China
Ethyl caprate	C12H24O2	110-38-3	0.99	Aladdin, Shanghai, China
Methyl myristate	C15H30O2	124-10-7	≥0.98	Aladdin, Shanghai, China

shows the basic information of the four samples.

3. Experimental Setup

The two-wire 3ω method is described in detail in our previous work [29,30] and the experimental setup is illustrated in Figure 1 and Figure 2. The experimental equipment mainly includes a lock-in amplifier (SR830, 0.1 mHz~102.4 kHz, American SRS Corporation, New York, NY, USA), signal generator (Agilent 33220A, 20 MHz, Shanghai Pingxuan Scientific Instrument Co., Ltd., Shanghai, China), digital multimeter (Keithely 2700, Shanghai Zhengyang instrument factory, Shanghai, China), precision resistance box, differential amplifier, subtractor and computer, etc. Before starting the experiment, it is essential to construct a bridge circuit using a resistance box. This circuit is connected to a modest output voltage (4 mV) via a lock-in amplifier. By adjusting the resistance of the resistance box to be equal to the resistance difference between the two platinum wires, a balance is achieved. As the output voltage of the lock-in amplifier increases, the platinum wire undergoes heating. This process, conducted through the differential input of the lock-in amplifier, aims to eliminate the impact of the fundamental wave voltage in the circuit on the measurement of the triple-frequency voltage. Subsequently, by locking the frequency, the triple-frequency voltage can be accurately measured.

The thermal conductivity of the liquid can be calculated using Equation (1).

$$k=-{\displaystyle \frac{U^2\Delta U_{\omega }{\alpha }_R}{8\pi lR}}{\displaystyle \frac{d\ln \omega }{d{U}_{3\omega }}}$$

(1)

where l is the length of the platinum wire; R is the resistance of the platinum wire; α_R is the temperature coefficient; U_3ω is in a linear function relationship with the logarithm of the frequency lnω; and the slope of the linear function contains the information of the thermal conductivity k of the test liquid. Therefore, the thermal conductivity of the test liquid can be calculated by measuring U_3ω at different frequencies. The thermal conductivity of standard substances such as ethanol was used to calculate the length of the platinum wire.

We used a PT 005,808 platinum wire from GoodFellow (Goodfellow Cambridge Limited, Cambridge, UK) as the heater and temperature sensor for the experimental system. The purity of the platinum wire is 99.99%, with a radius of 9 μm. The uncertainty of the voltage U_3ω is 0.08%, the uncertainty of the platinum wire resistance R is 0.001 Ω, the uncertainty of the platinum wire length l is 7.18 × 10⁻⁵ m, the uncertainty of the temperature coefficient α_R is 7.68 × 10⁻⁷/K, and the uncertainty of ${\displaystyle \frac{d\ln \omega }{d{U}_{3\omega }}}$ is 2.39 × 10⁻⁷ V·s/rad. Thus, the estimated uncertainty of thermal conductivity measurements does not exceed 2%. Taking the confidence factor of 2, the extended uncertainty of the thermal conductivity measurement is less than 4%.

The effect of natural convection on thermal conductivity should be taken into account when measuring in the experimental body. Natural convection can be characterized by a dimensionless Rayleigh number Ra, which is expressed as:

$$Ra={\displaystyle \frac{(g\alpha \Delta T{L}^3)}{a\mu }}$$

where g is gravitational acceleration constant/m∙s⁻²; $\alpha$ is coefficient of thermal expansion/K⁻¹; L is feature length/m;$a$ is thermal diffusion coefficient/m²∙s⁻¹; $\mu$ is kinematic viscosity/m²∙s⁻¹. The larger Ra, the more obvious convection, when Ra is less than a critical value Ra_c, it is considered that the influence of the natural convection can be ignored. The critical value is about 10⁵. In the measurement in this paper, the temperature difference does not exceed 0.25 K, and the characteristic size is taken as the cavity radius 3 mm. The calculation result proves that natural convection can be ignored.

In order to better quantify the experimental error and the deviation of the correlation, relative deviation (RD), average absolute relative deviation (AARD) and maximum absolute relative deviation (MARD) are defined as shown in Equations (2)–(4).

$$RD=100 (k_{\exp }-k_{\mathrm{ref}})/k_{\exp })$$

(2)

$$AARD={\displaystyle \frac{1}{N}}{\displaystyle {\sum }_{\mathrm{i}=1}^N}{\displaystyle \frac{|k_{\exp }-k_{\mathrm{cal}}|}{k_{\exp }}}\times 100\%$$

(3)

$$MARD= \max [{\displaystyle \frac{|k_{\exp }-k_{\mathrm{cal}}|}{k_{\exp }}}\times 100\%]$$

(4)

4. Results and Discussions

The liquid thermal conductivity of pure heptane, methyl caprate, ethyl caprate, and methyl myristate in the temperature range of 298.15–328.15 K was first measured using the two-wire 3ω method, and compared with the data in the literature [15]. The experimental results are shown in

Table 4. Liquid thermal conductivity of heptane at 0.1 MPa.

T/K	kexp/W·m−1·K−1	kref/W·m−1·K−1	RD/%
298.15	0.1186	0.1174	1.05
308.15	0.1157	0.1144	1.16
318.15	0.1123	0.1114	0.84
328.15	0.1091	0.1084	0.67

k_exp, experimental data; k_ref, reference data [31]; expanded uncertainty is less than 4%.

,

Table 5. Liquid thermal conductivity of methyl caprate at 0.1 MPa.

T/K	kexp/W·m−1·K−1	kref/W·m−1·K−1	RD/%
298.15	0.1440	0.1426	0.96
308.15	0.1412	0.1405	0.50
318.15	0.1392	0.1384	0.61
328.15	0.1353	0.1361	−0.62

k_exp, experimental data; k_ref, reference data [15]; expanded uncertainty is less than 4%.

,

Table 6. Liquid thermal conductivity of ethyl caprate at 0.1 MPa.

T/K	kexp/W·m−1·K−1	kref/W·m−1·K−1	RD/%
298.15	0.1434	0.1423	0.76
308.15	0.1405	0.1401	0.31
318.15	0.1377	0.1379	−0.13
328.15	0.1349	0.1356	−0.55

k_exp, experimental data; k_ref, reference data [15]; expanded uncertainty is less than 4%.

and

Table 7. Liquid thermal conductivity of methyl myristate at 0.1 MPa.

T/K	kexp/W·m−1·K−1	kref/W·m−1·K−1	RD/%
298.15	0.1506	0.1492	0.89
308.15	0.1481	0.1472	0.64
318.15	0.1444	0.1451	−0.46
328.15	0.1418	0.1429	−0.84

k_exp, experimental data; k_ref, reference data [15]; expanded uncertainty is less than 4%.

and Figure 3 and Figure 4. As shown in Figure 4, the relative deviation (RD) of the measured thermal conductivity between this study and the literature is basically within 1% and the absolute average relative deviation (AARD) is 0.60%. All RDs are within the measurement uncertainty, indicating that our device is accurate.

Then, the thermal conductivity of the mixture of heptane (20%, 40%, 60%, and 80%) with methyl caprate, ethyl caprate, and methyl myristate at different mass fractions was measured in the temperature range of 298.15–328.15 K. All the measurements were performed two times, and the average value was taken. The experimental results are shown in

Table 8. The measured liquid thermal conductivity of methyl caprate + heptane at 0.1 MPa.

w/wt%	T/K	kexp/W·m−1·K−1	kcal/W·m−1·K−1	RD/%
0.2	298.15	0.1240	0.1243	−0.24
	308.15	0.1211	0.1214	−0.25
	318.15	0.1177	0.1183	−0.51
	328.15	0.1146	0.1149	−0.26
0.4	298.15	0.1296	0.1296	0.00
	308.15	0.1263	0.1268	−0.40
	318.15	0.1239	0.1239	0.00
	328.15	0.1211	0.1204	0.58
0.6	298.15	0.1342	0.1347	−0.37
	308.15	0.1304	0.1319	−1.15
	318.15	0.1271	0.1293	−1.73
	328.15	0.1243	0.1257	−1.13
0.8	298.15	0.1389	0.1395	−0.43
	308.15	0.1352	0.1367	−1.11
	318.15	0.1325	0.1344	−1.43
	328.15	0.1285	0.1306	−1.63

k_exp, experimental data; k_cal, calculated values by the Flippov equation [27]; w is the mass fraction of methyl myristate. Expanded uncertainty is less than 4%.

,

Table 9. The measured liquid thermal conductivity of ethyl caprate + heptane at 0.1 MPa.

w/wt%	T/K	kexp/W·m−1·K−1	kcal/W·m−1·K−1	RD/%
0.2	298.15	0.1219	0.1214	0.41
	308.15	0.1200	0.1212	−1.00
	318.15	0.1154	0.1179	−2.17
	328.15	0.1126	0.1148	−1.95
0.4	298.15	0.1284	0.1294	−0.78
	308.15	0.1259	0.1265	−0.48
	318.15	0.1228	0.1233	−0.41
	328.15	0.1202	0.1203	−0.08
0.6	298.15	0.1350	0.1343	0.52
	308.15	0.1318	0.1314	0.30
	318.15	0.1302	0.1284	1.38
	328.15	0.1277	0.1254	1.80
0.8	298.15	0.1415	0.139	1.77
	308.15	0.1377	0.1361	1.16
	318.15	0.1342	0.1332	0.75
	328.15	0.1308	0.1303	0.38

k_exp, experimental data; k_cal, calculated values by the Flippov equation [27]; w is the mass fraction of methyl myristate. Expanded uncertainty is less than 4%.

and

Table 10. The measured liquid thermal conductivity of methyl myristate + heptane at 0.1 MPa.

w/wt%	T/K	kexp/W·m−1·K−1	kcal/W·m−1·K−1	RD/%
0.2	298.15	0.1276	0.1257	1.49
	308.15	0.1249	0.1229	1.60
	318.15	0.1214	0.1194	1.65
	328.15	0.1183	0.1163	1.69
0.4	298.15	0.1321	0.1325	−0.30
	308.15	0.1297	0.1297	0.00
	318.15	0.1262	0.1262	0.00
	328.15	0.1214	0.1232	−1.48
0.6	298.15	0.1384	0.1389	−0.36
	308.15	0.1351	0.1362	−0.81
	318.15	0.132	0.1326	−0.45
	328.15	0.1300	0.1298	0.15
0.8	298.15	0.1455	0.1449	0.41
	308.15	0.1415	0.1423	−0.57
	318.15	0.1394	0.1387	0.50
	328.15	0.1355	0.136	−0.37

k_exp, experimental data; k_cal, calculated values by the Flippov equation [27]; w is the mass fraction of methyl myristate. Expanded uncertainty is less than 4%.

and Figure 5, Figure 6 and Figure 7.

From the measured results, it can be observed that for heptane, methyl caprate, ethyl caprate, methyl myristate, and their binary mixture, the thermal conductivity decreases almost linearly with increasing temperature. This phenomenon can be explained by the Bridgman theory [32]. For liquids, the molecular distance increases with increasing temperature, and the greater the average molecular kinetic energy of the liquid, the more violent the random motion of the molecules. Among the four pure compounds, the thermal conductivity of n-heptane is the most temperature-sensitive, which decreases by 2.4–2.6% with a 10 K increase in temperature. The thermal conductivity of the three fatty acid esters changes with temperature in a similar manner, which decreases by 1.6–1.8% with a 10 K increase in temperature. The thermal conductivity of the binary mixtures of n-heptane and methyl caprate, ethyl caprate, and methyl myristate also decreases as the temperature increases, and the mass ratio of n-heptane has no significant impact on the drop caused by a temperature increase considering the measurement uncertainty. The thermal conductivity of the binary mixtures of n-heptane and methyl caprate decreases by 2.3–2.6% with a 10 K increase in temperature when the mass ratio of methyl caprate is 20% and decreases by 2.7–3.0% when the mass ratio is 80%. For thermal conductivity of the binary mixture of ethyl caprate and n-heptane, the thermal conductivity decreases by 2.6–3.0% with a 10 K increase in temperature when the mass ratio of ethyl caprate is 20% and decreases by 2.5–2.7% when the mass ratio is 80%. The thermal conductivity of the binary mixture of methyl myristate and n-heptane varies with temperature at 2.4–2.7% under a different mass ratio of methyl myristate.

Similarly, it can be found that the increase in the number of carbon atoms in a fatty acid ester will cause the thermal conductivity to increase. Longer carbon chains lead to larger molecules with stronger intermolecular interaction and more ordered molecular arrangement, facilitating better heat transfer [16]. Methyl myristate has 15 carbon atoms, while methyl caprate and ethyl caprate have 11 and 12 carbon atoms. At the same temperature, the thermal conductivity of methyl myristate as well as its mixture with heptane is obviously higher than methyl caprate and ethyl caprate. For binary mixtures of heptane with methyl caprate, ethyl caprate, and methyl myristate, the thermal conductivity increases with the proportion of fatty acid esters indicating that biodiesel can enhance the heat transfer of diesel. Adding 20%, 40%, 60%, or 80% of methyl caprate can promote an increase of up to 5.0%, 10.9%, 13.9%, and 18.0% to the thermal conductivity of heptane, respectively. Adding 20%, 40%, 60%, or 80% of ethyl caprate can promote an increase of up to 3.7%, 10.2%, 17.0%, and 19.9%, respectively. Adding 20%, 40%, 60%, or 80% of methyl myristate can promote an increase of up to 8.4%, 12.3%, 19.1%, and 24.1%, respectively.

The second-order Scheffé polynomial model [26] is often used to fit the thermal conductivity of the binary system, fitting the experimental data into a function of temperature and mass fraction. It can be written as:

$$k_{12}=k_1{w}_1^2+k_2{w}_2^2+2(A+BT)w_1{w}_2$$

(5)

where k₁₂ is the thermal conductivity of binary system; k_i and w_i are the thermal conductivity and mass ratio of compound I; and A and B are fitting parameters.

Three relationships related to mass fraction [27,28] were also used to fit the liquid thermal conductivity of the studied blends. For binary mixtures, they are expressed as follows:

Flippov equation [27]:

$$k_{12}=w_1{k}_1+w_2{k}_2-a{w}_1{w}_2(k_2-k_1)$$

(6)

Jamieson equation [27]:

$$k_{12}=w_1{k}_1+w_2{k}_2-a(k_2-k_1)(1-{(w_2)}^{{\displaystyle \frac{1}{2}}})w_2$$

(7)

Chen equation [28]:

$$k_{12}=w_1{k}_1+w_2{k}_2-(a+\left|{\displaystyle \frac{k_1}{k_2}}-0.5\right|)(k_2-k_1)w_1{w}_2$$

(8)

$$a=C+Dw+E{w}^2$$

(9)

where C, D, and E are the fitting parameters.

The calculated results of the four fitting equations are presented and compared in Figure 8, Figure 9, Figure 10, Figure 11 and Figure 12 and

Table 11. Parameters and AARDs of the second-order Scheff polynomial model.

Equation	A	B	AARD%
Second-order Scheff polynomial	0.2282	−3.1434 × 10−4	1.04

and

Table 12. Parameters and AARDs of fitting equations.

Equation	C	D	E	AARD%
Flippov	−0.1451	0.2492	−0.2359	0.80
Jamieson	−0.0539	0.1850	−0.2420	0.81
Chen	−0.4490	0.2492	−0.2359	0.82

. It can be concluded that all four fitting equations effectively correlate the thermal conductivity of the biodiesel + n-heptane binary mixture. The MARDs of these four equations are within 2.7%. The Flippov equation demonstrates the best overall performance, and its AARD is 0.80%, which is the lowest among the four equations. The RD of Flippov equation for these three binary mixtures is the most stable, which is basically around ±1%. Therefore, the Flippov equation is recommended for future applications involving the calculation of the thermal conductivity of these binary mixtures.

5. Conclusions

In this paper, the liquid thermal conductivity data for the binary system of heptane + biodiesel components were obtained using the two-wire 3ω method at 298.15 K, 308.15 K, 318.15 K, and 328.15 K and at mass ratios of 1:4, 2:3, 3:2, and 4:1. The measured thermal conductivity data of methyl caprate, ethyl caprate, and methyl myristate agree well with the literature. The thermal conductivity of the studied mixtures decreases with increasing temperature, and the mass ratio has no significant effect on this trend. The thermal conductivity of methyl myristate as well as its mixture with heptane is obviously higher than methyl caprate and ethyl caprate. Adding methyl caprate, ethyl caprate, and methyl myristate to heptane can increase its thermal conductivity, which is helpful to enhance heat transfer efficiency. Among the second-order Scheffé polynomial model, Flippov equation, Jamieson equation, and Chen equation, the Flippov equation demonstrated the best correlation for the binary mixtures of heptane with methyl myristate, methyl laurate, and methyl caprate the with AARD of 0.80% and MARD of 2.17%. Future work should focus on further improvement on the thermal conductivity of biodiesel by selecting the appropriate additives and expanding the measurement range to include a broader range of temperatures.