Heat-pump-assisted microwaves drying of white-leg shrimp: Parameter optimization and quality assessment

Abstract

The response surface methodology (RSM) is used to optimize the drying process of Vietnamese white-leg shrimp utilizing a heat pump (HP) combined with microwaves (MW). The study's main objective was to evaluate the dried white-leg shrimp quality in terms of final product moisture, rehydration rate, and shrinkage rate of dried shrimp as a function of drying parameters. The primary optimal factors influencing the upon goal are drying temperature (25 ÷ 35 °C), drying air velocity (1 ÷ 2 m/s), drying time (20 ÷ 40 minutes), and microwave power (1.4 ÷ 2.8 W/g). The results illustrated that the optimal parameters for the white-leg shrimp drying process with the HP-MW method for the best product quality were drying temperature T of 29.34 °C, microwave power MW of 2.08 W/g drying airspeed V of 1.50 m/s, drying time TM of 37.574 minutes. Drying air relative humidity ranges from 15% to 17%, characterized by a maximum desirability function of 0.979. Besides, the experimental study results also demonstrated the finished product value: shrimp shrinkage rate was 22.30%, the rehydration rate was 2.38, and the final moisture of white shrimp was 21.114%. Research results also demonstrate that increased microwave power affected shrimp's color and drying time. This work would promote the development of the technical extent of designing microwave-assisted heat pump dryers applicable for drying seafood with high economic value shortly.

Keywords:  Heat pump drying; Microwave; Response surface methodology; White-leg shrimp; Quality assessment; Parameter optimization

Highlights

Response surface methodology (RSM) was applied to simultaneously optimize objectives such as water recovery ratio (RR), final product moisture content (Mc), and shrinkage ratio (Sh) for dried shrimp by the HP-MW drying method

Microwave power had the most significant effect on reducing shrimp moisture content compared to air velocity, temperature, and drying time

The HP-MW drying method had the lowest impact on shrimp color, shrinkage, and recovery water absorption rate compared to the MW one

1 Introduction

White-leg shrimps are one of Vietnam's most important agricultural exports (Le & Tran, 2023). In addition, dried shrimp is one of Vietnam's most important seafood products. The dried shrimp value depends on the shrimp's quality of color, size, dryness, and taste. Traditionally, drying shrimp includes two steps: boiling it in salt water and then drying it under the sun for a week (Hoang et al., 2020; Le & Tran, 2023; Tirawanichakul et al., 2008). However, this method's products have many limitations, such as the small and manual production method significantly reducing the dried shrimp quality. Notably, many dried shrimp production bases still use homemade drying ovens, which use wood, firewood, coal, etc., to produce their products. These drying methods usually dry at high temperatures or extended drying times. Moreover, product quality (such as taste and color) is affected by dust, smoke, and charcoal (Hoang et al., 2020; Le & Tran, 2023). Thus, food safety and hygiene problems are uncontrolled, leading products to a reduction in economic, quality, and export values (Le & Tran, 2023; Tirawanichakul et al., 2008).

Recently, an infrared (IR) drying approach or heat pump-assisted infrared radiation (HP-IR) has given good dried shrimp quality but with high energy costs and a long drying time (Farhang et al., 2011; Le & Tran, 2023). Likewise, the infrared-assisted freeze-drying (IRFD) approach produces the best-quality dried shrimp, but its drying time takes so long (Chakraborty et al., 2011). While as the microwave drying method significantly reduces the drying time, especially when the microwave power increases (Wang et al., 2004). However, the microwave drying method also has limitations, such as uneven heating resulting in product rough drying and lack of dry product uniformity due to varying exposure to radiation. Furthermore, increasing the microwave power will reduce product quality due to the burned product surface and shrinkage quickly (Le & Tran, 2023). Therefore, combining hot air or heat pump drying processes with microwave drying can improve the final product quality and drying speed (Le & Tran, 2023; Macedo et al., 2022; Shahriar et al., 2022). Combining microwave drying with other drying approaches, like freeze-drying or heat pumps, could be better for receiving excellent uniformity and maintaining the dried product quality (Le & Tran, 2023; Wang & Chen, 2007). Hence, the microwave-assisted heat pump (HP-MW) method is the most effective way to reduce dry time (Le & Tran, 2023).

Furthermore, the Taguchi approach applies orthogonal strings to experimental planning. It supports us in doing a minimum of crucial experiments to investigate the effect of drying conditions on a specifically chosen reaction of a product or process, leading to faster-optimized parameter adjustments (Alin, 2010; Heydari et al., 2017). In addition, an optimization method, Response surface methodology (RSM), allows for analyzing the studied parameters' impact and harmony, assessing their effect level, and determining the optimization reliability. The RSM optimal approach is usually applied to optimize food processes (Aghilinategh et al., 2015; Alavi et al., 2023; Haneef et al., 2023; Nwakuba et al., 2018). However, studies of microwave power, drying temperature, and drying airspeed influence on dried shrimp quality and estimating the optimal drying conditions for white-leg shrimp with an HP-MW approach are still lacking on these subjects (Le & Tran, 2023). Thus, this study used HP-MW's hybrid drying approach to take advantage of its advantages and limit disadvantages, thus optimizing the drying parameters to be the optimal drying factors for white-leg shrimp (Le & Tran, 2023; Wang & Chen, 2007). We aimed to evaluate the effects of drying parameters such as temperature from 25 °C to 35 °C, wind speed from 1 to 2 m/s, microwave energy density from 1.4 W/g to 2.8 W/g, and drying time from 20 to 40 minutes to obtain the final moisture, recovery water absorption rate, shrinkage and color change of dried white-leg shrimp dried by HP-MW drying method.

2 Materials and methods

2.1 Materials

The investigation subject was white-leg shrimp, which is 50 shrimps/kg in size. The fresh shrimp has a natural color and fishy smell. The shrimp was purchased in Cam Ranh Bay of Khanh Hoa province and maintained in insulated foam buckets. The shaved ice was placed on the box's bottom, middle, and top to cover the shrimp's surface. The shrimp buckets were transported to NTU's laboratory by car in less than an hour (Le & Tran, 2023). Firstly, the shrimp was cleaned with ice-cold water and boiled in 3% brine solution (NaCl) for about 7 minutes (Le & Tran, 2023; Tirawanichakul et al., 2008). The boiled shrimp was then dried by an HP-MW dryer, which designed drying parameters like Taguchi's experimental planning matrix, shown in Table 1a. Each experimental drying progress ended as the dried shrimp reached the final moisture of [(20 ÷ 40) ± 1] %, upon the experimental design.

Table 1
Input factors and levels.

(a) Input factors and levels
Input parameters	Low level	Low level	High level	Variation range
Drying temperature, T (°C)	25	30	35	5
Air velocity, V (m/s)	1	1.5	2	0.5
Microwave power density, MP (W/g)	1.4	2.1	2.8	0.7
Drying time, TM (minutes)	20	30	40	10
(b) Optimal goals and constraints

Parameters	Target	Lower limit	Target value	Upper limit	Weight	Import
T (°C)	In range	20		40
V (m/s)	In range	1		2
MP (W/g)	In range	1.4		2.8
TM (min)	In range	20		40
RR (g wet sample/g dried sample)	Maximum	1.51	2.38	2.44	1	2
Sh (%)	Minimum	20.10	22.00	34.40	1	1
Mc (%)	Target	18.17	20.00	40.22	1	1

2.2 Experimental equipment

2.2.1 Heat-pump-assisted microwave drying (HP-MW)

Figure 1 shows the HP-MW dryer and its measuring and controlling equipment. The HP-MW dryer was designed and created at the refrigeration laboratory of the Mechanical Engineering Faculty at Nha Trang University. It was created with the technical features: capacity of 1kg/batch, microwave power of 0.7 kW, heat pump power of 0.745 kW, and centrifugal fan of 0.1 kW. The HP-MW dryer can easily modify the drying data through technical requirements, such as drying temperature from 20 °C to 40 °C, microwave power from 100 to 500 W, and air velocity from 1 m/s to 2 m/s (Le & Tran, 2023).

Figure 1
Images of HP-MW dryer and equipment for measuring and controlling. (1) Compressor; (2) Air condenser I; (3) Stop valve; (4) Air condenser 2; (5) Evaporator; (6) Transformer; (7) Fan 1; (8) Drying rack; (9) Glass plate; (10) Electrical cabinet; (11) Microwave source; (12) Refrigerant distributor; (13) Air duct; (14) Drying cabinet; (15) Air supplied; (16) Exhaust air after drying; (17) Condensate drain tray; (18) Refrigerant Filter; (19) Capillary coil; (20) Air filter; (21) Fan 2.

2.2.2 Other measuring devices used in the study

The initial moisture of shrimp was determined using an OHAUS MB120 moisture determination scale of 120g, Readability: 0.01%/0.001 g, made in China. The weight of the white-leg shrimp during the drying process was obtained by the Switzerland electronic scale type XT2200C with an ± 0.01g error. A Taiwan digital tachometer LM81AT calculated the drying chamber airspeed with a ± 3% mistake. The room-air-relative humidity was established by a digital hygrometer Testo 605H1. The drying temperature was determined by a Taiwan digital-display-thermometer EXTECH with 12 probes, type TM500, with an ± (0.004 + 1) °C accuracy (Hoang et al., 2020; Le & Tran, 2023). The color of white-leg shrimp before and after drying was determined using a Chroma Meter CR-400 colorimetric device made in Japan. The white-leg shrimp's before and after drying color was determined using Japan's Chroma Meter CR-400 colorimetric device. The water activity of dried shrimp was measured by a laboratory water activity analyzer of the manufacturer Rotronic, HYGROLAB C1. Shrimp size was measured by a MITUTOYO 500-181-30 electronic caliper made in Japan.

2.3 Research Methods

2.3.1 Experimental design based on the Taguchi approach

First, Table 1a shows input optimization data that used the Taguchi approach to set up most of the experimental white-leg shrimp drying processes. The main parameters of the white-leg shrimp drying process were chosen from the results of previous studies (Alin, 2010; Hoang et al., 2020; Le & Tran, 2023; Mathews, 2004).

2.3.2 Response surface method optimization

The RSM mathematical-statistical approach is applied to predict the experimental model. This approach can display the relation of the input and output variables (Hoang et al., 2020; Le & Tran, 2023). Besides, regression inquiry was used to determine the experimental model to predict the significant aim functions (R_R, Sh, Mc). The input-output relationship was defined by using quadratic Equation 1 with the following k input variables (Aghilinategh et al., 2015; Hoang et al., 2020; Le & Tran, 2023; Nwakuba et al., 2018):

$Y=b_o+{\displaystyle \sum _{i=1}^k{b}_{ij}}{X}_i+{\displaystyle \sum _{i,j=1}^k{b}_{ij}}{X}_i{X}_j+{\displaystyle \sum _i^k{b}_{ii}}{X}_{ii}^2$ (1)

Where Table 1a shows the problem input parameters as independent variables. They include drying temperature T (X₁), air velocity V (X₂), microwave power density MP (X₃), and drying time TM (X₄). The b_o value is the sample constant, b_i is the linear coefficient, b_ij (j = 1,2,3) are coefficients of cross-product, and b_ii is the quadratic coefficient. In Table 1b, Y is considered as a dependent variable of an output response, including the shrinkage rate Sh (%), rehydration ratio R_R (g wet sample/g dried sample), and final moisture content Mc (%), Table 2 presents the experimental results of the Taguchi method.

Table 2
Matrix and experimental results.

Test	Encoding variable				Real variable				Experiment results
	X1	X2	X3	X4	T	V	MP	TM	RR [-]	Sh	Mc
					[°C]	[m/s]	[W]	[min]		[%]	[%]
1	1	1	1	1	25	1.00	1.40	20	2.42	21.50	40.22
2	1	1	1	1	25	1.00	1.40	20	2.43	21.40	39.71
3	1	1	1	1	25	1.00	1.40	20	2.44	21.30	39.85
4	1	2	2	2	25	1.50	2.10	30	2.39	25.30	22.34
5	1	2	2	2	25	1.50	2.10	30	2.40	25.50	22.23
6	1	2	2	2	25	1.50	2.10	30	2.39	25.20	22.50
7	1	3	3	3	25	2.00	2.80	40	1.80	29.50	19.27
8	1	3	3	3	25	2.00	2.80	40	1.71	29.70	19.34
9	1	3	3	3	25	2.00	2.80	40	1.71	29.90	19.50
10	2	1	2	3	30	1.00	2.10	40	2.29	23.60	23.20
11	2	1	2	3	30	1.00	2.10	40	2.29	23.50	24.16
12	2	1	2	3	30	1.00	2.10	40	2.28	23.60	24.50
13	2	2	3	1	30	1.50	2.80	20	1.99	27.20	18.77
14	2	2	3	1	30	1.50	2.80	20	1.99	27.50	18.50
15	2	2	3	1	30	1.50	2.80	20	2.00	27.70	18.17
16	2	3	1	2	30	2.00	1.40	30	2.22	20.10	32.12
17	2	3	1	2	30	2.00	1.40	30	2.21	20.30	31.10
18	2	3	1	2	30	2.00	1.40	30	2.21	20.50	32.50
19	3	1	3	2	35	1.00	2.80	30	1.87	34.50	20.67
20	3	1	3	2	35	1.00	2.80	30	1.86	34.10	21.00
21	3	1	3	2	35	1.00	2.80	30	1.88	34.40	20.50
22	3	2	1	3	35	1.50	1.40	40	2.38	21.10	36.00
23	3	2	1	3	35	1.50	1.40	40	2.31	21.50	36.50
24	3	2	1	3	35	1.50	1.40	40	2.31	21.70	36.00
25	3	3	2	1	35	2.00	2.10	20	1.61	28.20	20.98
26	3	3	2	1	35	2.00	2.10	20	1.51	28.40	21.11
27	3	3	2	1	35	2.00	2.10	20	1.51	28.60	20.56

2.3.3 Determining methods

2.3.3.1 White-leg shrimp moisture content determination (M_C)

The shrimp's initial moisture content was determined by drying the sample in an oven at 105 °C until a constant mass (Hoang et al., 2020; Le & Tran, 2023; Tirawanichakul et al., 2008). The weight of dried shrimp during the drying process was periodically measured every 5 minutes by a digital scale, and the current moisture content was calculated by following Formula 2 (Hoang et al., 2020; Le & Tran, 2023; Tran et al., 2023).

$M_{Ci}=100-\frac{(100-M_{C1})}{G_i}{G}_1$ (2)

Where M_Ci is the moisture content in the drying sample at the time i (% WB), M_C1 is the dry sample's initial moisture content (% WB), G_i is the drying sample mass at the time i (g), and G₁ is the drying material initial mass (g).

2.3.3.2 Drying rate (D_R)

Equation 3 below was used to estimate the white-leg shrimp drying rate dried by HP-MW (Aghilinategh et al., 2015; Shi et al., 2014; Şimşek et al., 2021):

$D_R=\frac{M_{ct}-M_{c(t+\Delta t)}}{\Delta t}$ (3)

Where Δt is the time interval (hour); M_ct and M_c(t+Δt) are sample moisture contents at t and (t+Δt) (% w.b);

2.3.3.3 Determine water activity a_w

Water activity specifies the relationship between the product water vapor pressure and the pure water saturation pressure at the same temperature. It is expressed as “aw” and in the range of (0 to 1), which is an important index to evaluate the storage safety level of dry products after drying (Clark et al., 2014; Wang & Chen, 2007). The water activity of dried shrimp was measured by a laboratory water activity analyzer, HYGROLAB C1.

2.3.3.4 Rehydration ratio determination (R_R)

The rehydration rate of dried shrimp was estimated by soaking the dried shrimp in distilled water at a temperature from about 25°C to 27°C. We took the soaked shrimp sample out to weigh every 30 minutes. The experiment was repeated until the soaked shrimp samples' weight between two consecutive weighings did not change. The white-leg shrimp rehydration ratio (R_R) was estimated by the Equation 4. (Chakraborty et al., 2011; Haneef et al., 2023; Le & Tran, 2023; Wang et al., 2014):

$R_R=\frac{m_w}{m_d}$ (4)

Where m_w and m_d (g wet sample) are the white-leg shrimp sample mass after soaking in water and after drying (g dried sample) processes.

2.3.3.5 Change in color (ΔE)

The color value of dried white-leg shrimp was measured using a Chroma Meter CR-400 colorimeter. The color of dried shrimp was measured at three positions: P1 (the head of the sample), P2 (the middle of the sample), and P3 (the tail of the sample), as shown in Figure 2. Additionally, positive color values L-a-b indicate brightness, red, and yellow, while the negative color values L-a-b represent darkness, greenness, and blueness, respectively. Besides, we used Equation 5 to determine the total color difference (ΔE) (Haneef et al., 2023; Tirawanichakul et al., 2008; Wang et al., 2014).

$\Delta E=\sqrt{\left[{(L_o-L_f)}^2+{(a_o-a_f)}^2+{(b_o-b_f)}^2\right]}$ (5)

where,

L₀ and L_f are the sample's initial and final brightness values.

a₀ and a_f are the initial and final sample redness values, respectively.

b₀ and b_f are the initial and final sample yellowness values, respectively.

Figure 2
Measuring drying shrimp color. (a) Image of shrimp after drying process; (b) Location for measuring color values of shrimp; (c) Experimental image measurement of the shrimp color.

2.3.3.6 Shrinkage rate (Sh)

The shrimp samples' shrinkage rate before and after drying was determined by the sample average value measured by an electronic caliper with an accuracy of ± 0.05 mm. This experiment was repeated three times, and the shrinkage rate was determined as follows in Equation 6 (Tirawanichakul et al., 2008; Wang et al., 2014):

$Sh=\frac{D_{initial}-D_{final}}{D_{initial}}\times 100$ (6)

where D_initial is the average geometric diameter of white-leg shrimp at the beginning of the drying process, and D_final is the average geometric diameter of white-leg shrimp at the end of the drying process.

2.3.3.7. Evaluating-error method of the prediction and experimental equation

Equation 7 is used to determine the mean percentage error E [%] (Hoang et al., 2020; Le & Tran, 2023):

$E\%=\frac{100}{N}{\displaystyle \sum \frac{\left|{\widehat{Y}}_{i,MP}-Y_{i,TN}\right|}{{\widehat{Y}}_{i,MP}}}$ (7)

Where n is the experiments' number; are the predicted and experimental values.

3 Results and discussion

Herein, the shrimp's initial weight (G₁) was about 100 grams, and the moisture content of the boiled white-leg shrimp before drying was determined using the OHAUS MB120 moisture determination scale, with an initial moisture Mc1 of 70%. Formula 2 was used to determine the shrimp moisture content (Mc) during drying time throughout the drying process. The Rehydration ratio of dried shrimp (R_R) was determined according to Formula 4; the Shrimp shrinkage rate (Sh) was determined according to Formula 6. Each experiment was repeated three times to ensure accuracy. Table 2 presents the study results according to Taguchi's experimental matrix.

3.1 Building regression equations and using the RSM method to evaluate the main factors influencing white-leg shrimp drying by HP-MW

Due to the experimental results shown in Table 2, all regression formulas were created to forecast Mc, R_R, and Sh values for white-leg shrimp dried by HP-MW. Besides, the variance analysis ANOVA results using the RSM approach for shrinkage rate Sh (%), moisture content final Mc (%), and rehydration ratio R_R (g wet model/g dried model) are shown in Table 3.

Table 3
ANOVA results for rehydration ratio (R_R), shrinkage rate (Sh), and moisture content final (Mc) of white-leg shrimp dried with HP-MW.

Source	RR	Sh (%)	Mc (%)
	(g wet sample/g dried sample)
	P-value	P-value	P-value
Regression	0.000	0.000	0.000
Linear	0.000	0.000	0.000
T	0.000	0.000	0.000
V	0.000	0.005	0.000
MP	0.000	0.000	0.000
TM	0.000	0.000	0.724
Square	0.000	0.000	0.000
T2	0.000	0.000	0.000
V2	0.000	0.000	0.011
MP2	0.006	0.946	0.000
TM2	0.000	0.000	0.000
R2	0.9934	0.9986	0.9982
R2 (Adj)	0.9904	0.9969	0.9973
R2 (Pred)	0.9834	0.9980	0.9958

3.1.1 The regression formula and influence of drying parameters on rehydration rate (R_R)

The rehydration ratio R_R is a vital norm that determines the quality of dried shrimp. Table 3 presents the analysis of variance (ANOVA) results for the quadratic formula forecasting R_R. It can be seen that all drying values (such as T, V, MP, TM, T², V², and TM²) were p < 0.05; only MP² was p = 0.006 (p < 0.05), which is a higher insignificant term in the model. It is clear that the parameters (T, V, MP, TM) significantly affected the rehydration ratio R of dried shrimp. Specifically, Figures 3a, b show that increasing the MP, T, and V will decrease R_R. On the contrary, when MP, T, and V are reduced, the recovery rate of water absorption increases. Furthermore, the determination coefficient R² was high, with 0.9934, nearly equal to 1.0. The determination coefficient of the predicted value R² (Pred) could be equalled to 0.9834, and the adjusted value R²(Adj) equalled to 0.9904; all determination coefficients were high, close to 1, as illustrated in Table 3. The above result demonstrates that the created regression formula is suitable for experimental and statistical significance, as shown in other studies (Chakraborty et al., 2011; Hoang et al., 2020; Le & Tran, 2023). Finally, the regression Formula 4) is reliable for forecasting the rehydration ratio (R_R) for white-leg shrimp dried with an HP-MW dryer. Equation 8 shows that the value of microwave power density MP had the most significant impact on water absorption recovery rate, and drying time has less effect on R_R.

Figure 3
The correlations between T, V, MP, and TM parameters on the rehydration rate (R_R) (a, b); the shrinkage rate (Sh) (c, d); and the final humidity content (Mc) (e, f) of white-leg shrimp dried with HP-MW.

$\begin{array}{l}{R}_R=-2.576+0.241\times T+2.360\times V-0.535\times MP+0.0696\times TM\\ -0.00447\times T^2-0.907\times V^2+0.0498\times M{P}^2-0.00105\times T{M}^2\end{array}$ (8)

Herein, R² is the determination coefficient, Seq SS is the squares sequential sum, F is Fisher's variance ratio, P is probability value, variables (p < 0.05; means significant at 95% confidence level), otherwise input variables (p > 0.05; means variables negligible impact on the output objective function, R² (Pred) is a predicted parameter, R² (Adj) is an adjusted parameter.

3.1.2 The regression equation and drying parameters influence shrinkage rate (Sh)

Shrinkage rate Sh is a vital norm that determines the quality of dried shrimp. Table 3 shows the ANOVA results for the quadratic formula predicting Sh, demonstrating that the drying conditions (such as T, V, MP, TM, T², V², and TM²) showed that the p-value was less than 0.05 (p < 0.05), only the p-value MP² was greater than 0.05, i.e., p = 0.946 (p > 0.05), then the result is insignificant. Equation 9 shows that among the four established variables (MP, T, V, TM), MP had the most significant impact on the shrinkage of shrimp (Sh), followed by T and V. Furthermore, when the parameters (MP, T, V) increase, the shrinkage increases and vice versa when the parameters MP, T, V decrease, the shrinkage decreases. As for the TM parameter, the opposite is true: when TM increases, the shrinkage decreases, and when TM decreases, the shrinkage increases. Thus, the parameters (T, V, MP, TM) significantly affect the shrinkage rate (Sh) of dried shrimp. Specifically, Figures 3c, d demonstrate that increasing MP will increase shrinkage; otherwise, decreasing MP decreases shrinkage, which is entirely consistent with the study of Nabeela Haneef et al. (2023). Furthermore, in Table 3, the determination coefficient R² was high, with a value of 0.9986, the determination coefficient of the predicted value R² (Pred) was equalled 0.9980, and the adjusted value R² (Adj) was equalled 0.9969. All these values were high, close to 1. This regression formula is statistically vital and suited experimentally (Chakraborty et al., 2011; Hoang et al., 2020; Le & Tran, 2023). Hence, the regression Formula 9 is suitable for predicting the shrinkage rate (Sh) for the white-leg shrimp dried by an HP-MW dryer.

$\begin{array}{l}Sh=113-6.916\times T-18.767\times V+6.706\times MP+0.754\times TM\\ +0.119\times T^2+6.155\times V^2+0.0113\times M{P}^2-0.0132\times T{M}^2\end{array}$ (9)

3.1.3 The regression formula and drying parameters influence moisture content final (Mc)

Table 3 presents the ANOVA results for the quadratic formula forecasting Mc. The T, V, MP, T², V², MP², and TM² coefficients showed that the p-value was less than 0.05 (p < 0.05). Only the TM parameter showed that the p-value was greater than 0.05, i.e., p > 0.05 (p = 0.946), then the result is insignificant. Therefore, the parameters (T, V, MP, TM) significantly affect the moisture content final (Mc) of dried shrimp. Specifically, Figures 3e-f indicate that increasing MP and V values will decrease MC final moisture. Contrarily, reducing the values of MP and V, the final moisture remaining in shrimp is high. This result is entirely consistent with our previous study (Haneef et al., 2023). Furthermore, the determination coefficient R² was high at 0.9982 (nearly equal to 1.0), the standard deviation was low at 0.3945, and the predicted residual sum of squares (PRESS) value was low at 6.306 compared to other models (Chakraborty et al., 2011). The coefficient of determination expected value R² (Pred) equalled 0.9958, and the adjusted value R² (Adj) equalled 0.9973; i.e., high p-values (nearly equal to 1), especially since the difference between R2 (Pred) and R2 (Adj) was the smallest, at about 0.0015 as shown in Table 3. This result showed the built regression formula as reliable experimentally and statistically reasonable (Chakraborty et al., 2011; Hoang et al., 2020; Le & Tran, 2023). All the input parameters (T, MP, V, TM) had a negative relationship with moisture content. This means that they all contributed to the drying capacity of the method. Among them, MP had the highest effect on moisture content, indicating that the drying capacity of the technique increased significantly with MP, followed by V, T, and TM. Thus, the regression Formula 10 is trustworthy enough to forecast the Mc of white-leg shrimp drying with the HP-MW dryer.

$\begin{array}{l}{M}_C=184.379-4.428\times T-9.661\times V-57.749\times MP-0.877\times TM\\ +0.0716\times T^2+1.837\times V^2+10.973\times M{P}^2+0.0147\times T{M}^2\end{array}$ (10)

3.2 Multi-objective optimization determination of the white-leg shrimp drying parameters by the HP-MW dryer

Determine the optimal drying parameters for the dried shrimp quality goals, such as the maximum rehydration rate of dried shrimp R_R, the smallest shrinkage rate Sh of dried shrimp, and the shrimp final moisture Mc reached about 20%. Table 1b presents the multi-objective optimization method's input factors, objectives, and constraints using the RSM approach. It shows that the value of the overall desirability function nearly equals 1.0 (D = 0,97956), as shown in Figure 4. Thus, multi-goal optimizations result in a suitable and statistically significant response such as R_R, Sh, and Mc (Chakraborty et al., 2011; Hoang et al., 2020; Le & Tran, 2023). Finally, the while-leg shrimp optimal drying parameters by the HP-MW dryer included the air temperature of 29.34 °C, microwave power MP of 2.08 W/g, drying time TM of 37.58 min, and airspeed V of 1.50 m/s. Associated with the product goals, such as the final moisture content of 21.11%, the lowest shrinkage rate of 22.31 (%), and the highest rehydration ratio reached 2.38 g wet sample/g dried sample.

Figure 4
Multi-target optimization graph. Input parameters: Experimental range of drying temperature: T = (25-35 °C), Optimum temperature: T = 29.343 °C; Experimental range of air speed: V = (1-2 m/s), Optimum airspeed: V = 1.50 m/s; Experimental range of microwave power density: MP = (1.4-2.8 W/g), Optimum MP: MP = 2.08 W/g; Experimental range of Drying time: (20-40 min), Optimum TM result: TM = 37.57 min. Output target: Rehydration ratio R (g wet sample/ g dried sample), R: Maximum; Shrinkage rate Sh (%), Sh: reach minimum value; Final moisture content of shrimp after drying Mc (%), Mc: Target 20% achieved. Desirability function: D is the overall desirability function. D reflects the desired range of each function, di; di ranges from 0 to 1, di = 0 (respectively least desirable), and di ≈ 1 indicates a satisfactory optimum value.

3.3 The predictive model reliability evaluation compared to the optimal parameters for experimental shrimp drying

This section compares the error evaluation results of R_R, Sh, and Mc values predicted from Equations 8, 9, and 10 with the experimental results obtained from the optimal drying mode. Specifically, the error between the predicted and experimental values ​​of R_R is 3.36%; between the predicted and experimental values ​​of Sh is 4.79%; between the predicted and experimental values ​​of Mc is 4.54%. Thus, we can see that the mistakes are not significant, less than 5% (about 3.36% to 4.79%). The predicted results are in remarkable agreement with the experimental results. Therefore, the above equations predict the parameters R_R, Sh, and Mc in the theoretical study of heat calculation, heat transfer, mass transfer, and HP-MW whiteleg shrimp dryer design.

3.4 The white-leg shrimp quality comparison dried by HP-MW- and MW-dryer

Figure 5 shows the dried white-leg shrimp by HP-MW at optimal drying parameters had the boiled shrimp natural color, with a bit of color changing with ΔE = 11.93 compared to the MD drying method with ΔE = 14.512. The total color change ΔE of shrimp dried by MW was more significant than that of the HP-MW drying method by about 2.222. The reason may be that shrimp dried by HP-MW dryer had low shrimp surface temperature (the air has been cooled and dehumidified before entering the drying room). In contrast, shrimp dried by MW had a higher surface temperature, increasing the release of astaxanthin caused by the decomposition of carotenoproteins during protein denaturation. Besides, the interaction between amines and aldehydes leading to the Maillard reaction may be another reason causing the color change ΔE of shrimp (Verma et al., 2024). The research showed that the MW-dried shrimp had a water absorption ratio R_R of 2.12 g web sample/g dried sample, a shrinkage Sh of 30.25%, and a water activity a_w of 0.741. In addition, the HP-MW-dried shrimp had a water absorption capacity of 2.38, a shrinkage of 22.30%, and a water activity of 0.749. Compared to the MW method, the dried shrimp product of the HP-MW dryer had a higher water absorption capacity of about 0.26 g wet model/g dried model, the shrinkage was reduced by 7.95%, and the water activity remained almost unchanged. This result is consistent with the previous studies (Nguyen et al., 2022; Kaveh et al., 2023a), which show that the structure with lower shrinkage has a higher water R_R. This is explained by the MW drying method, which uses a high shrimp surface temperature, causing high moisture diffusion on the shrimp surface. When the water in the cell wall of the product evaporates, the air will replace it; therefore, the tissue cannot maintain the structural network, and the external structure of the cell collapses, leading to shrinkage (An et al., 2022). Moreover, the rehydration rate decreases with increasing microwave power and temperature (Kaveh et al., 2023b; Kumar et al., 2024). The shrimp dried using the HP-MW method in optimal drying conditions have a reasonable heat and mass transfer process. Thus, a film does not cover the dried shrimp's outer surface, and its inner structure is more porous. This finding is consistent with the study (Çetin, 2022), which showed that at lower drying temperatures, the sample's internal structure was less damaged, the pores increased, and the water absorption capacity was highly restored. It has better water absorption and reduces shrinkage, as illustrated in Figure 3c. Therefore, it can be concluded that the dried white-leg shrimp have the best quality when drying in optimal mode.

Figure 5
Images of dried white-leg shrimp according to the drying method: a) Image of dried shrimp using the HP-MW method; b) Image of dried shrimp using the MW method.

3.5 Effect of microwave power density on color change of white-leg shrimp dried with HP-MW dryer

The color of dried shrimp products is a crucial factor that affects consumer tastes. Table 4 shows the microwave power density MP significantly affects the color of dried shrimp, precisely the comparison color values of L, a, and b. The results indicated that increasing MP from 1.4 W/g to 3.5 W/g will reduce the brightness, increase the red color, and increase the yellow level of dried shrimp, affecting the overall color change ΔE. That may be due to reduced moisture in the shrimp over time. The reason may be that as MW increases due to the penetration ability of microwaves, the internal temperature of shrimp increases, which will increase the release of astaxanthin due to the degradation of carotenoid protein during protein denaturation. As a result, the redness of dried shrimp products increases. In addition, as MW increases, the interaction between amine and aldehyde leading to the Maillard reaction may be another reason for the discoloration of shrimp ΔE. Thus, it can be said that as the temperature and microwave power increase, the total color changes ΔE and it increases (Farhang et al., 2011; Haneef et al., 2023; Tirawanichakul et al., 2008).

Table 4
Effect of microwave power density on color change of dried white-leg shrimp.

		Change in color
	ΔE	Lo	ao	bo
Microwave power density MP (W/g)		58.19	16.41	20.88
		Lf	af	bf
1.40	10.97	47.82	19.35	22.92
2.10	11.33	48.08	21.06	23.00
2.8	16.16	43.72	23.24	23.13
3.5	17.58	42.47	23.72	23.81

3.6 Effect of microwave power density on final moisture (Mc) and drying rate (D_R) of white-leg shrimp using HP-MW

Figures 6a, b show how microwave power density impacts the final moisture, drying speed, and drying time of white-leg shrimp under the HP-MW drying method. Specifically, as the MP value rises from 1.4 W/g to 3.5 W/g, the microwave power density increases, the DR drying speed increases, and the drying time shortens. It is remarkably similar to the study of Musielak & Kieca (2014), where the more the MP increases, the more the drying time decreases. An appropriate increase in microwave energy density will heat the dried product from its center inside, increasing the effective diffusion coefficient and the drying rate and reducing the drying time (Sakre et al., 2022). That is also the advantage of drying shrimp using the HP-MW method. However, Figure 6b shows that when drying at the MP 1.4W/g, due to the small microwave power, the drying speed is the lowest, and the drying time is the longest at over 40 minutes, but the final product moisture is still so high at 40% while the required humidity is 20%. The drying stage has not yet reached the deceleration drying stage, so its drying rate curve at the end differs from the other cases.

Figure 6
The relationships between moisture content/drying rate and drying time at various microwave power densities.

4 Conclusions

In summary, it could be concluded that increasing the microwave power density and drying temperature will increase the drying rate and reduce drying time. Besides, the increasing microwave power density affects the color and shrinkage of dried shrimp. The HP-MW drying approach notably can make product improvements in quality than the MW one. We found out the optimal drying mode for the white-leg shrimp by HP-MW method, including the drying temperature T = 29.34 °C, airspeed V = 1.50 m/s, microwave power density MP = 2.081 W/g, drying time TM = 37.57 minutes, drying air relative humidity φ = (15 - 17)%, white-leg shrimp initial humidity M_c1 = 70% with the highest rehydration ratio of 2.38, and the lowest shrinkage rate of 22.30% and the dried white-leg shrimp final moisture content Mc2 = 21.11%. This work would promote the development of the technical extent of designing microwave-assisted heat pump dryers applicable for drying seafood with high economic value shortly.

Acknowledgments

The authors acknowledge the support from the grassroots scientific research project of Nha Trang University, Vietnam, under grant number TR2022-13-09.

• Cite as:
  Le, N.-C., Tran, T.-B.-T., & Le, V.-H. (2024). Heat-pump-assisted microwaves drying of white-leg shrimp: parameter optimization and quality assessment. Brazilian Journal of Food Technology, 27, e2024039. https://doi.org/10.1590/1981-6723.03924
• Funding:
  Nha Trang University, Vietnam (TR2022-13-09).

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Edited by

• Associate Editor:
  Rosinelson da Silva Pena.

Publication Dates

• Publication in this collection
  06 Dec 2024
• Date of issue
  2024

History

• Received
  12 Apr 2024
• Accepted
  04 Oct 2024