Simultaneous Estimation of the Thermophysical Properties of Selected Liquid Dairy Products by a Transient Heat Flow Probe Method

Figures & data

Table 1 Compositions (mass fraction) of each component for each sample

	Composition (%)
Sample	Moisture	Protein	Fat	Carbohydrate	Ash
Whole milk	90.0	2.6	2.7	4.1	0.6
	80.0	5.3	5.4	8.1	1.2
	70.0	7.9	8.1	12.1	1.9
	60.0	10.5	10.8	16.2	2.5
Skim milk	90.0	3.5	0.1	5.6	0.8
	80.0	7.1	0.2	11.1	1.6
	70.0	10.6	0.3	16.6	2.5
	60.0	14.1	0.1	22.2	3.3
Whey	90.0	1.2	0.5	7.4	0.9
	80.0	2.4	1.1	14.8	1.7
	70.0	3.6	1.6	22.3	2.5

Figure 1 Schematic of the heat probe used to measure thermophysical properties.

Figure 2 Schematic of the experimental apparatus used to measure thermophysical properties.

Figure 3 Comparison of the observed temperature changes of the probe with the results calculated from Eq. (6) for whole milk at a concentration of 10% and a temperature of 50°C.

Figure 4 Comparison of the measured thermal conductivity and the result calculated from Eq. (10) for whey.

Table 2 The parameters, coefficient of determination (R²) and root means square (RMSE) of Eqs. (10), (11), and (12) for each sample

		Sample
Eq.		Whole milk	Skim milk	Whey
(10)	a 1 (W m^−1°C^−1%^−1)	−4.171 × 10^−3	−3.265 × 10^−3	−3.686 × 10^−3
	b 1 (W m^−1°C^−2)	1.181 × 10^−3	1.241 × 10^−3	1.393 × 10^−3
	d 1 (W m^−1°C^−1)	5.860 × 10^−1	5.817 × 10^−1	5.867 × 10^−1
	R^2 (−)	0.9898	0.9759	0.9960
	RMSE (W m^−1°C^−1)	0.0050	0.0065	0.0023
(11)	a 2 (m^2 s^−1%^−1)	−8.194 × 10^−10	−6.437 × 10^−10	−5.242 × 10^−10
	b 2 (m^2 s^−1)	1.593 × 10^−7	1.529 × 10^−7	1.543 × 10^−7
	R^2 (−)	0.9990	0.9329	0.9982
	RMSE (m^2 s^−1)	2.955 × 10^−10	1.930 × 10^−9	1.797 × 10^−10
(12)	a 3 (kJ kg^−1°C^−1%^−1)	−1.650 × 10^−2	−1.842 × 10^−2	−2.446 × 10^−2
	b 3 (kJ kg^−1°C^−2)	8.766 × 10^−3	9.313 × 10^−3	9.882 × 10^−3
	d 3 (kJ kg^−1°C^−1)	3.680	3.801	3.802
	R^2 (−)	0.9793	0.9516	0.9959
	RMSE (kJ kg^−1°C^−1)	0.0335	0.0566	0.0156

Figure 5 Empirical relationships between the thermal diffusivity and the concentration for each sample.

Figure 6 Empirical relationships the between specific heat and the temperature at four different concentrations for whole milk.