Estimation of Heat and Mass Transfer Coefficients During Air-Freezing of Cucumber

Figures & data

Figure 1 Experimental duct [a]: (1) sample, (2) electronic scale, (3) airflow homogenization grid, (4) vanes, (5) fan, (6) dumper. Test chamber [b]: (1) homogenization grid, (2) electronic scale, (3) sample, (4) insulation, (5) cylinders holding the sample, (6) anemometer.

Table 1 Characteristics of the tested cucumber samples used in the fifteen examined experimental cases

T (°C)	V(m^.s^−1)	L(cm)	D(mm)	S(cm^2)	G o (g)
−10	0.5	10.0	39.5	124.09	128.50
	1.0	14.0	40.5	178.13	190.07
	1.5	15.0	39.0	183.78	183.78
	2.0	15.0	42.0	197.92	207.73
	5.0	10.0	39.5	124.09	128.50
−18	0.5	15.0	42.0	197.92	217.88
	1.0	15.0	41.5	195.56	211.04
	1.5	13.5	41.0	173.89	182.75
	2.0	12.0	43.0	162.11	180.95
	5.0	14.0	40.0	175.93	174.80
−25	0.5	15.0	40.5	190.85	194.52
	1.0	12.0	41.0	154.57	166.23
	1.5	15.0	42.0	197.92	214.71
	2.0	11.0	41.5	143.41	162.74
	5.0	15.0	40.0	188.50	192.40

Table 2 The values of a, b, and c of Eq. (2) with the related statistical parameters

T a (°C)	Re	a	b	c		SEE
−10	1460–15,700	0.725	0.030	−0.388	99.96	0.0066
−18	1609–16,800	0.805	0.024	−0.339	99.98	0.0036
−25	1607–17,819	0.845	0.020	−0.295	99.99	0.0029

Figure 3 Water vapour pressure deficit change with the surface temperature of the freezing produce (solid lines are estimated by Eq. 2).

Figure 2 The surface temperature during the freezing process for the tested air temperatures (−10, −18, −25°C) and velocities (0.5, 1.0, 1.5, 2.0, 5.0 m^.s⁻¹).

Table 3 The estimated , , and values for air-freezing of unpeeled cucumber (present experiment) compared to values from Dincer and Genceli^{[ 16 ]} and Dincer^[2] conducted experiments

			(W m^−2 K^−1)		(m s^−1)
V a (m s^−1)	Re	This study	Dincer & Genceli	Dincer	This study	This study
0.5	1460–1794	10.99 ± 0.16	—	—	8.98 ± 0.24	18.07 ± 0.38
1.0	2993–3474	15.14 ± 0.09	28.02 ± 1.20	18.22 ± 0.76	12.56 ± 0.25	24.71 ± 0.39
1.5	4323–5593	18.89 ± 0.17	37.21 ± 1.81	21.31 ± 0.97	15.42 ± 0.41	30.88 ± 1.18
2.0	6208–7382	22.23 ± 0.17	52.11 ± 3.02	26.56 ± 1.09	18.12 ± 0.31	37.86 ± 0.84
5.0	14,739–17,819	40.07 ± 0.15	—	—	32.40 ± 0.63	64.99 ± 1.64

Figure 4 Estimated values based on Hilpert correlation from the present experiment (points) compared to Dincer^[2] and Dincer and Genceli^{[ 16 ]} experiments for air-cooling of unpeeled cucumber.

Figure 5 Sherwood number variation with Re for air-freezing of unpeeled cucumber (present experiment).

Table 4 The estimated values of , δ_θ ± std, δ_d ± std, and the experimental measured values of i _m ± std for air-freezing of unpeeled cucumber

V a (m s^−1)	Re	(j H , j M )^.10^3	10^3(m)	10^3(m)	.10^6(kg m^−2 s^−1)
0.5	1460–1794	13.20 ± 0.32	2.14 ± 0.03	20.96 ± 7.65	4.87 ± 3.0
1.0	2993–3474	9.19 ± 0.16	1.57 ± 0.02	15.06 ± 5.06	6.44 ± 3.58
1.5	4323–5593	7.54 ± 0.18	1.24 ± 0.02	10.56 ± 3.27	7.88 ± 4.56
2.0	6208–7382	6.64 ± 0.09	1.05 ± 0.02	7.07 ± 2.44	11.38 ± 5.40
5.0	14,739–17,819	4.76 ± 0.07	0.58 ± 0.01	5.46 ± 2.61	13.82 ± 9.13

Figure 6 The reduced mass loss (%) during the freezing process for the tested air temperatures (−10, −18, −25°C) and velocities (0.5, 1.0, 1.5, 2.0, 5.0 m^.s⁻¹).

Table A1 The calculated , , , and values and the experimentally measured values for all the tested cases

T(°C)	V(m^.s^−1)		(W m^−2 K^−1)		(m s^−1)	(kg m^−2 s^−1)
−10	0.5	1526 ± 28	11.19 ± 0.007	17.54 ± 0.15	9.24 ± 0.005	5.29 ± 3.10
	1.0	3130 ± 57	15.25 ± 0.009	24.51 ± 0.21	12.60 ± 0.007	6.68 ± 3.94
	1.5	4541 ± 80	19.10 ± 0.04	29.63 ± 0.33	15.78 ± 0.03	8.67 ± 5.33
	2.0	6498 ± 109	22.17 ± 0.04	36.98 ± 0.38	18.32 ± 0.03	13.66 ± 5.33
	5.0	15,337 ± 249	40.00 ± 0.07	62.86 ± 0.63	33.05 ± 0.06	22.18 ± 10.62
−18	0.5	1674 ± 27	10.82 ± 0.005	18.31 ± 0.14	8.67 ± 0.004	4.91 ± 3.36
	1.0	3300 ± 60	15.04 ± 0.01	25.12 ± 0.21	12.05 ± 0.006	6.60 ± 3.64
	1.5	4917 ± 85	18.81 ± 0.04	31.12 ± 0.33	15.07 ± 0.03	7.64 ± 3.81
	2.0	6923 ± 118	22.08 ± 0.05	38.45 ± 0.40	17.69 ± 0.03	10.02 ± 4.91
	5.0	16,084 ± 301	39.98 ± 0.09	64.73 ± 0.75	32.03 ± 0.07	14.99 ± 6.95
−25	0.5	1665 ± 39	11.02 ± 0.01	18.27 ± 0.19	8.60 ± 0.004	4.38 ± 2.46
	1.0	3092 ± 46	15.16 ± 0.01	24.38 ± 0.17	11.83 ± 0.005	5.92 ± 3.10
	1.5	5236 ± 138	18.73 ± 0.06	32.35 ± 0.53	14.61 ± 0.05	7.04 ± 4.17
	2.0	6872 ± 204	22.46 ± 0.09	38.27 ± 0.70	17.52 ± 0.06	10.15 ± 5.27
	5.0	16,764 ± 401	40.19 ± 0.13	66.41 ± 0.98	31.35 ± 0.09	8.18 ± 4.96