




































 Agricultural Science; Vol. 3, No. 3; 2021 
ISSN 2690-5396   E-ISSN 2690-4799 

https://doi.org/10.30560/as.v3n3p1 

1                             Published by IDEAS SPREAD 
 

The Solar-Heat Pump Combined Drying Characteristics and Dynamic 
Model of Kelp Knots 

Yang Li1, Zicheng Hu1, Yongguang Hu2, Fenghua Ge1 & Hongzhi Cai1 

1 School of Energy and Power Engineering, Jiangsu University, Zhenjiang, China 
2 School of Agricultural Engineering, Jiangsu University, Zhenjiang, Jiangsu, China  
Correspondence: Yang Li, School of Energy and Power Engineering, Jiangsu University, Zhenjiang, 212013, 
China. E-mail:  
 
Received: August 9, 2021   Accepted: August 15, 2021   Online Published: August 29, 2021 
 
The research is financed by National Natural Science Foundation of China (51806088) and Jiangsu University 
Scientific Research Foundation for the Senior Scholars (14JDG186).  
 
Abstract 
For controlling the entire drying process of a material, it is crucial to understand the moisture ratio of the material 
in the drying process. In order to ascertain the moisture change rules of kelp knots in the solar-heat pump combined 
drying process, an analysis was made on the impacts of different drying temperatures, wind speeds and loading 
capacities on the drying rate in this research; meanwhile, three common drying dynamic models were selected and 
compared to know their applicability to the solar-heat pump combined drying of kelp knots. Further, the model 
coefficient was determined and the optimal model was obtained. The results reveal as follows: drying temperature, 
wind speed and loading capacity have significant impact on and significant correlation (P<0.05) with the drying 
rate of kelp knots; under different drying conditions, the drying rate is always high in the early stage, lowered and 
gradually moderate in the later stage. After fitting the drying dynamic model, it is found that among the 
experimental data, regression coefficient (R2) is the largest in the Verma model, and the sum of squares for error 
(SSE) and root mean square error (RMSE) are low. This indicates that the Verma model can be used to accurately 
express and predict the change rules of moisture in kelp knots during the solar-heat pump combined drying. 
According to Fick's second diffusion law, the effective diffusion coefficient Deff increases with the increase in 
drying temperature and wind speed, and decreases with the increase in loading capacity.  
Keywords: kelp knots, solar-heat pump combined drying, drying characteristics, drying dynamic model 
1. Introduction 
The kelp production in China accounts for about 50% of the total kelp production in the world. Fresh kelp is an 
important marine resource due to its high moisture ratio, seawater growth environment, wide distribution, rich 
nutrients and low cost (Wang, et al., 2008), but usually needs to be dried and dehydrated because of its high 
moisture ratio and perishability. Due to the huge demand for kelp in Chinese market, it is necessary to apply 
industrial equipment and technology, such as drying equipment and technology, to the preservation and 
transportation of kelp (Song, et al., 2014). 
Drying process is widely used in various fields (2000), and drying is also a technological operation with high 
energy consumption. According to statistics, in developed countries such as Britain, the United States, and France, 
the energy consumption of drying process accounts for about 12% of the total energy consumption (Bhesh, et al., 
2015). Therefore, it is of important practical significance to research the energy saving and consumption reduction 
in the drying process, and research new drying process. 
Usually, fresh kelp knots are dried in the open air without any cost. However, this drying method is of low 
efficiency, easy to get the material mouldy under environmental influence, and has a narrow range of application, 
leading to insufficient drying of the material and loss of nutritional value. In contrast, solar drier as a new energy-
saving drying machine can convert light energy into heat energy (Ban, et al., 2011) to improve the drying efficiency 
of material greatly. However, it is not applicable to continuous operation for reason that it is susceptible to weather, 
day and night (Kapsalis, et al., 2016). Heat pump has high drying stability, low operating cost and short drying 
cycle. In actual application, solar collector is combined with heat pump to form a solar-heat pump combined drier 



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to overcome the unfavorable factors (Xu, et al., 2004). Currently, solar-heat pump combined drying technology 
has been applied to drying of lentinula edodes (Zhu, et al., 2020), tobacco (Li, et al., 2021) and Chinese chestnut 
(Liu, et al., 2020), etc. and obtained remarkable effects. 
Moisture ratio is an important indicator affecting the drying quality of a material, but difficult to be determined in 
the drying process. In order to better control the drying process, it is necessary to establish a mathematical model 
and analyze the drying process by mathematical means. Both in China and foreign countries, there have already 
been a large number of researches on the dehydration of fruits, medical materials and other materials. Reference 
(Zhang, et al., 2021) studied the characteristics and dynamic model of the hot-air drying of yellow peach fruits and 
found that temperature played a key role in the drying of yellow peach fruits; with the increase in drying 
temperature, the drying time was shortened and the drying rate was significantly improved. Reference (Liu, et al., 
2020) studied the characteristics and dynamic model of the hot-air drying of Chinese chestnuts and discovered that 
page model conformed to the drying characteristics of Chinese chestnuts. Reference (Wu, et al., 2020) researched 
the characteristics and dynamic model of the drying of seahorse in different drying methods and proved that page 
model and Midilli model were more suitable for characterizing the hot-air drying process of seahorse, while page 
model and weibull model can describe the vacuum drying model of seahorse accurately. However, there are few 
researches on the characteristics and dynamic model of the drying of kelp knots (Hu, et al., 2019), making it 
important to research the solar-heat pump combined drying of kelp knots. 
Taking fresh kelp knots as the research object, solar-heat pump combined drying technology is used in this paper 
to research the rules in which different drying temperatures, wind speeds and loadings affect the drying 
characteristics of kelp knots, and determine the drying dynamic model suitable for characterizing the change in 
moisture ratio of kelp knots in the drying process. The result can provide a technical support and theoretical basis 
for the application of solar-heat pump combined drying technology in the drying of kelp knots in the future. 
2. Materials and Methodology 
2.1 Materials and Instruments 
The experimental materials are fresh kelp knots purchased from the local market of Zhenjiang, China, with uniform 
size and without mechanical damage. 
A set of solar-heat pump combined drying equipment was designed and installed in order to research the drying 
characteristics of kelp knots. The flow chart of the equipment is as shown in Figure 1. 

 

Figure 1. Flow chart of the drying equipment 
 
Working principle: Water in the water tank is heated up by the solar radiation energy absorbed by the solar collector, 
then passes through the radiator below the drying box under the traction of the water pump, and exchanges heat 
with the air filled in the radiator by the fan; after that, the heated air passes through the pallet loaded with dried 
materials and flows through the wet materials at constant speed to finish the heat and mass transfer. In this 
equipment, the temperature and wind speed can be adjusted as required. 
The heat pump is used for auxiliary heating. When the temperature in the water tank is lower than the set 
temperature, the heat pump will start to compensate for the heat till reaching the set temperature. The intelligent 
control system is used to control (temperature and wind speed) and digitalize the drying process. 
 



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Figure 2. Picture of the real solar-heat pump combined drying equipment 
 

Other instruments and devices: FA1604N analytical balance (Jiangsu Jiangdong Precision Instrument Co., Ltd.); 
FLUKE-923 hot-wire anemometer (Changsha Tesai Measurement and Control Technology Co., Ltd.). 
2.2 Experimental Method 
In order to explore the impacts of different drying conditions on the drying characteristics of kelp knots, the 
experiments were respectively conducted at different drying temperatures (35, 40, 45 and 50℃, with an error of 
±1℃) but constant loading capacity (3.6 kg±6 g) and wind speed (1.5±0.1 m/s), at different wind speeds (0.5, 1.0, 
1.5 and 2.0 m/s, with an error of ±0.1 m/s) but constant loading capacity (3.6 kg±6 g) and drying temperature 
(45±1℃), and at different loading capacities (1.2, 3.6, 6.0 and 8.0 kg, with an error of ±6 g) but constant drying 
temperature (45±1℃) and wind speed (1.5±0.1 m/s). The initial mass of the kelp knots was measured, and then 
the mass of the kelp knots was measured at an interval of 10 min during the drying till the moisture ratio of the 
kelp knots dropped to 0.2 and the drying is stopped. Each group was conducted three parallel experiments. 
2.3 Method for Calculation of Drying Parameters 
2.3.1 Moisture Ratio of Dry Basis  
The moisture ratio of dry basis can be calculated as per the following equation: 

ddtt m/)mm(M −=                          (1) 
In the equation, Mt is the moisture ratio of dry basis of the material at time t, in g/g; mt is the mass of the material 
at time t, in g; md is the mass of the absolutely dried material, in g; 
2.3.2 Drying Rate 
The equation of drying rate can be expressed as: 

                                   21

21
R tt

MMD
−
−=

                              
(2)

 
In the equation, DR is the drying rate, in g/(g·min); M1 is the moisture ratio of the dry basis when the material is 
dried to t1, in g/g; M2 is the moisture ratio of the dry basis when the material is dried to t2, in g/g; 
2.3.3 Moisture Ratio 
The equation of moisture ratio can be expressed as: 

                                 e0

et
R MM

MMM
−
−=

                              
(3) 

In the equation, MR is the moisture ratio; Me is the moisture ratio of dry basis of the material at drying equilibrium, 
in g/g; M0 is the initial moisture ratio of dry basis of the material, in g/g. 
2.4 Drying Dynamic Model and Evaluation Parameters 
The drying of kelp knots can be classified as a dehydration process of wet porous media, which is a typical heat-
mass coupling process. Through a large amount of experimental and data analysis, scholars both in China and 



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foreign countries (Shi, et al., 2010; Yang, et al., 2013; Li, et al., 2016;) have summarized multiple theories on the 
rules in which moisture ratio changes with time in the drying process and established semi-empirical and empirical 
models. As found by reading relevant documents, the most common drying dynamic models for drying agricultural 
products are as illustrated in Table 1 (Shi, et al., 2013). Hence, the dynamic model used in this experiment is as 
shown in Table 1. 
 
Table 1. Drying Dynamic Mathematical Models Selected 

 
By analyzing the R2, SSE and RMSE between the experimental data and the predicted data, it is concluded that the 
higher the R2 is, the lower the SSE and RMSE are and the better the fitting effect is. 
2.5 Effective Moisture Diffusion Coefficient 
Effective moisture diffusion coefficient represents the ability to remove moisture by diffusion and transfer. Since 
the width of kelp knot is much larger than its thickness, it is assumed that the mass transfer only occurs in axial 
one-way manner. Hence, Fick’s second law can be used to characterize the moisture diffusion in the drying process 
of kelp knots well. The volume shrinkage of kelp knot is ignored in the drying process (Simal, et al., 1997). 
Assuming that the samples have the same initial moisture distribution, the effective moisture diffusion coefficient 
can be calculated as per the following equation: 

 
t

L
Deff)8(lnMln 2

2

2R
π

π
−=

                    
(4)

 
In the equation, MR is the moisture ratio; t is the drying time (h); L is the thickness of the sample (m); Deff is the 
effective moisture diffusion coefficient (m2/h), which is estimated in slope method; the average Deff at different 
temperatures can be obtained as per the logarithmic drying curve. Letting the slope of equation (4) be k0, the 
effective moisture diffusion coefficient can be expressed as: 

 
2

2
0 LkeffD
π

−=
                            

(5)
 

2.6 Data Processing 
The software Origin2018 was used for drawing, and Matlab2020a was applied to linear/non-linear regression 
fitting of the experimental data; based on this, the degree of fitting was analyzed. 
3. Results and Analysis 
3.1 The Impact of Drying Temperature on the Drying Characteristics of Kelp Knots 
Figure 3a shows the drying characteristic curves of kelp knots at different drying temperatures. As shown in Figure 
3a, when the set drying temperature is within the range of 35 ~ 50℃, the moisture ratio of dried kelp knots shows 
a decreasing trend with time (fast in early stage but gradually gentle in the later stage). Within this drying 
temperature range, the higher the drying temperature is, the faster the drying is, which greatly reduces the drying 
time. This is because in this drying method, low-humidity hot air is used as the drying medium, the heat-humidity 
exchange with material is conducted in form of convection; when the air temperature rises, the moisture on the 
surface of the kelp knot will get more heat, leading to moisture diffusion inside the kelp knot, acceleration of water 
evaporation and shortening of the drying time. When the drying temperatures are 35℃ and 40℃, the drying times 
are 380 min and 280 min, respectively. However, long drying time is not conducive to saving cost. When the 
drying temperatures are 45℃ and 50℃, the drying times are 150 min and 200 min respectively and the drying 
trends are almost the same. Comprehensive analysis reveals that about 45℃ is the suitable temperature for solar-
heat pump combined drying of kelp knots. 

Model name Model equation 
Logarithmic c)ktexp(aM R +−=  

Page )kt(expM n
R −=  

Verma  )gtexp()a1()ktexp(aM R −−+−=  



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The impacts of different drying temperatures on the drying rate of kelp knots are presented in Figure 3b. As can 
be seen, the drying rate of the material depends on temperature. Drying temperature is directly proportional to the 
highest drying rate (Baher, et al., 2018). The drying rate is high initially till reaching the peak, then maintains low 
for a long time. The reason may be as follows: in the early stage of drying, there is much moisture on the surface 
and much free moisture inside the material; the internal temperature is also rising increasingly while moisture on 
the surface is evaporated fast under the action of hot air, so that the free moisture inside the material transfers 
quickly outward and the drying rate is increased. As the drying time goes, the moisture of the material reduces, 
and the drying rate begins to reduce. This may be for reason that kelp knot is a porous media so that the internal 
moisture is evaporated out through the holes and cracks; with the shrinking and hardening of the kelp surface, the 
heat and mass transfer encounters enhanced resistance in the process of conveying the internal moisture to the 
surface of the material, resulting in lowered decrease in drying rate. From the 120th min of drying to the time 
finishing the final drying goal, there is no large difference in the drying rate at different drying temperature. This 
reveals that after the 120th min of drying, temperature almost has no effect on the drying rate. 
Provided that the drying efficiency is improved and the energy consumption is reduced, about 45℃ is the most 
suitable temperature for solar-heat pump combined drying of kelp knots. 
 

Figure 3a.                                        Figure 3b.   
 
3.2 The Impact of Wind Speed on the Drying Characteristics of Kelp Knots 
Figure 4a presents the drying characteristic curves of kelp knots at different wind speeds. As shown in Figure 4a, 
wind speed has a certain impact on the drying characteristics of kelp knots. When the wind speed is at 0.5 m/s, 1.0 
m/s, 1.5 m/s and 2.0 m/s, it takes 280 min, 260 min, 190 min and 150 min respectively to have the kelp knots dried 
to the target moisture ratio. This reveals that the time taken to have the material dried to the target moisture ratio 
is shortened significantly with the increase in wind speed. The reason is that with the increasing of wind speed, 
the coefficient of convective heat transfer between hot air and kelp knot is increased, leading to acceleration of the 
moisture evaporation on the surface of the kelp knot and improvement in the drying efficiency. The increase in 
wind speed can help take away the water vapor on the surface of the kelp knot as soon as possible, increase the 
partial pressure difference of water vapor between the surface of the kelp knot and the air. In the early stage of 
drying, the pressure difference measured by air promotes less diffusion of moisture inside the kelp knot. In the 
middle and late stages of the drying, increasing heat transfer resistance is faced between air and the material. The 
results demonstrate that in the drying process by heat pump, internal diffusion is the physical mechanism most 
possible to control the internal moisture of kelp knots. By comprehensive analysis of experimental results, it is 
determined that the suitable wind speed for drying of kelp knot is 1.5 m/s approximately. 
Figure 4b shows the impact of wind speed on the drying rate of kelp knots. As displayed, there is no stage of 
constant speed in the solar-heat pump combined drying process of kelp knots, but the stages of adjustment and 
deceleration, which is similar to the drying characteristics of Clausena lansium (Yang, et al., 2021). When the 
moisture ratio is fixed, the drying rate increases with the increase in wind speed. In the initial stage of drying, the 
kelp knot has a relatively high moisture ratio and contains much bound water on the surface, and the moisture 
evaporation speed is accelerated with the increase in wind speed; after the drying rate reaches the peak, the drying 
rate will maintain at low level for a long time. When the wind speed is 1.5 m/s, the drying rate is little different 



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from that at wind speed of 2.0 m/s in terms of the downtrend. 
On the premise of improving efficiency, as well as energy saving and emission reduction, the optimal wind speed 
for solar-heat pump combined drying of kelp knots is 1.5 m/s. 
 

Figure 4a.                                    Figure 4b. 
 
3.3 The Impact of Loading Capacity on the Drying Characteristics of Kelp Knots 
Figure 5a illustrates the drying characteristic curves of kelp knots with different loading capacities. As observed, 
loading capacity has certain impact on the drying of kelp knots, and the lower the loading capacity is, the larger 
the downtrend of the moisture ratio is, and the shorter the time is taken to reach the required drying goal. When 
the loading capacity is 1.2 kg, 160 min is needed for drying; when the loading capacity is 8.0 kg, the time for 
drying is 320 min. This indicates that the loading capacity is directly proportional to the drying time required. As 
can be seen from the figure, with the increasing of loading capacity, the spreading density of kelp knots on a single 
pallet is increased, the relative surface area of heat and mass transfer with the air is decreased, and the resistance 
to heat and mass transfer is increased. The greater the loading capacity is, the higher the total moisture ratio of 
kelp knots is, the more the moisture is to be evaporated to reach the same moisture ratio, the longer the drying time 
is. As discovered in Figure 5a, when the loading capacities are 1.2 kg and 3.6 kg, the drying times and curves tend 
to be consistent basically. Based on an analysis of the economic effects and experimental results, it is known that 
the suitable loading capacity for drying kelp knots is about 3.6 kg. 
The impact of loading capacity on the drying rate of kelp knots is demonstrated in Figure 5b. To be specific, the 
drying rate varies with the change in loading capacity. Given the same moisture ratio, the lower the loading capacity 
is, the shorter the drying time is and the higher the drying rate is. The increase in loading capacity contributes to 
the increase in drying time and decrease in drying rate. This may be for the following reasons: namely, the contact 
between materials becomes closer with the increase in loading capacity, resulting in decreased contact between air 
and the material; meanwhile, the increase in the material may also cause increase in the required moisture 
evaporation capacity; however, at certain drying temperature and wind speed, the heat is fixed. Hence, the increase 
in the material may lead to reduction in the heat provided to unit mass of the material in the unit time.  
On the premise of improving efficiency, the optimal loading capacity for solar-heat pump combined drying of kelp 
knots is 3.6 kg. 



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Figure 5a.                                     Figure 5b. 

 
3.4 Establishment of Dynamic Model 
3.4.1 Fitting Results of the Drying Dynamic Model of Kelp Knots 
The statistical results obtained by experimental data based nonlinear fitting of three common drying dynamic 
models are shown in Table 1. In detail, the R2 of Logarithmic, Page, and Verma models are the highest, all above 
0.994; the RMSE varies within the range of 0.0029 ~ 0.0059, 0.0035 ~ 0.0192, and 0.0029 ~ 0.0079, respectively; 
and the SSE is within the range of 0.0001 ~ 0.0014, 0.0001 ~ 0.0092, and 0.0001 ~ 0.0011, respectively. This 
demonstrates that the three models can be used to characterize the change rules of moisture ratio in the solar-heat 
pump combined drying process of kelp knots. Among them, the Verma model has the highest R2 (0.9996) and the 
lowest SSE (0.0004) and RMSE (0.0042), indicating that the Verma model has the highest fitting degree. Thereby, 
it can be confirmed that the Verma model is the dynamic model most suitable for characterizing the moisture ratio 
of kelp knots in the process of solar-heat pump combined drying. 
 

Table 1. Statistical Result of Drying Mathematical Models for Dried Kelp Knots 
Model SSE R2 RMSE 

Logarithmic 0.0006 0.9994 0.0053 
Page 0.0017 0.9988 0.0071 

Verma  0.0004 0.9996 0.0042 
 
3.4.2 Solving of the Verma Model 
Table 2 lists the statistical results of the parameters of the three models. On the basis of the parameters (a, k and 
g) of the Verma model, software matlab2020a was used to fit the experimental data and finally obtain the parameter 
values, taking drying temperature, wind speed and loading capacity as variables. The equations of the optimal 
results are expressed as follows: 

M060.0V6871.0T044.0124.3a +−−=  (R2=0.91) 
   M0221.0V0786.0T035.0457.1k −++−=  (R2=0.93) 

    M0589.0V0589.0T0053.0457.0g +++−=  (R2=0.90) 

In the equations, T is the drying temperature, in℃; V is the wind speed, in m/s; M is the loading capacity, in kg. 
 
 
 



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Table 2. Parameters Statistical Results of Three Models for Drying Process of Kelp Knots 

 
3.4.3 Verification of the Verma Model  
In order to verify the accuracy of the model, an experiment was made on the kelp knots under different drying 
conditions such as drying temperature of 45℃, wind speed of 1.5 m/s, and loading capacity of 3.6 kg respectively. 
The fitting verification result of the drying dynamic model for kelp knots is as shown in Figure 6. To be specific, 
the fitting degrees of the experimental result and the result predicted by the model are basically consistent and 
significantly correlated (P<0.05). This implies that the Verma model can well characterize the moisture ratio of 
kelp knots in the process of solar-heat pump combined drying. 

 

Figure 6. Verification of the Verma Model 
 
3.5 Effective Moisture Diffusion Coefficient in the Drying Process of Kelp Knots 
Drying is a process of mass, momentum and energy transfer. When the heat absorbed by the material is transferred 
from the outside to the inside, the moisture in the material will absorb the heat and be evaporated to the outside. 
Till reaching the critical moisture ratio, the drying process is finished. In order to simplify the calculation results, 
liquid diffusion theory was used in the drying process of the material regardless of the driving force of diffusion; 
the influence of all dynamics was counted in the diffusion coefficient; the effective diffusion coefficient Deff was 
used to characterize the average speed of moisture transfer in the drying process (He, et al., 2016); then nonlinear 
fitting was conducted on the lnMR and drying time t of kelp knots in different drying manners. 
Table 3 shows the moisture diffusion coefficient in the drying process of kelp knots under different conditions. As 
revealed in Table 3, provided that the drying temperature is 35 ~ 50℃ and other drying conditions are fixed, the 

Model Parameters 

35℃ 
1.5m/s 
3.6kg 

40℃ 
1.5m/s 
3.6kg 

45℃ 
1.5m/s
3.6kg

50℃ 
1.5m/s
3.6kg

45℃ 
0.5m/s
3.6kg

45℃ 
1.0m/s
3.6kg

45℃ 
2.0m/s
3.6kg 

45℃ 
1.5m/s 
1.2kg 

45℃ 
1.5m/s 
6.0kg 

45℃ 
1.5m/s
8.0kg

Logarithmic 
a 
k 
c 

0.9301 
0.0052 
0.0598 

0.9301 
0.0052 
0.0598 

0.8949
0.0114
0.1014

0.9849
0.0123
0.0169

0.9098
0.0074
0.0937

0.8798
0.0086
0.1017

0.9580
0.0127
0.0459

0.9319 
0.0117 
0.0591 

0.9007 
0.0097 
0.1224 

0.9335
0.0061
0.0613

Page 
k 
n 

0.0067 
0.9320 

0.1631 
0.0284 

0.0148
0.8993

0.0125
0.9904

0.0091
0.9215

0.0124
0.8854

0.0131
0.9721

0.0147 
0.9256 

0.0109 
0.9163 

0.0075
0.9392

Verma 
a 
k 
g 

0.0059 
-

0.0053 
0.0049 

0.0037 
0.03810.0057

0.6816
0.0136
0.0039

0.0006
0.7847
0.0119

0.9535
0.0070

-
0.0017

0.8356
0.0095
0.0009

0.0007
-0.0237
0.0118

0.0782 
0.0508 
0.0096 

0.9799 
0.0070 
0.9075 

0.2683
0.0104
0.0044



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effective moisture diffusion coefficient Deff is 3.9251×10-9 ~ 1.0012×10-8 m2/s; provided that the wind speed is 
0.5 ~ 2.0 m/s and other drying conditions are fixed, the Deff is 5.1118×10-9 ~ 1.0028×10-9 m2/s; when the loading 
capacity of the material is 1.2 ~ 8.0 kg and other drying conditions are fixed, the Deff is 2.1908×10-9 ~ 9.1282×10-

9 m2/s. The analysis demonstrates that the effective moisture diffusion coefficient in the drying process of kelp 
knots is directly proportional to the drying temperature and wind speed, and inversely proportional to the loading 
capacity. Moreover, the coefficient of determination R2 varies within the range of 0.9421 ~ 0.9994, indicating a 
good linear regression result. According to Pearson correlation analysis, drying temperature, wind speed, and 
loading capacity are of extremely significant correlation with Deff (P<0.01), which is consistent with the results 
of researches on potato (Yin, et al., 2016), Daqu (Xia, et al., 2018), tomato slices (Salih, et al., 2017) and seahorse 
(Wu, et al., 2020). 
 
Table 3. Effective Moisture Diffusion Coefficient of Kelp Knots under Different Drying Conditions 

Experimental 
number 

Drying 
temperature/℃ 

Wind 
speed/(m·s-1) 

Loading 
capacity/kg k0 R2 Deff/(m2·s-1)

1 35 1.5 3.6 -0.0043 0.9425 3.9251×10-9 

2 40 1.5 3.6 -0.0057 0.9862 5.2031×10-9 

3 45 1.5 3.6 -0.0084 0.9991 7.6677×10-9 

4 50 1.5 3.6 -0.0118 0.9994 1.0012×10-8 

5 45 0.5 1.5 -0.0056 0.9951 5.1118×10-9 

6 45 1.0 1.5 -0.0062 0.9915 5.6595×10-9 

7 45 2.0 1.5 -0.0112 0.9981 1.0028×10-8 

8 45 1.5 1.2 -0.0100 0.9984 9.1282×10-9 

9 45 1.5 6.0 -0.0064 0.9807 5.8420×10-9 

10 45 1.5 8.0 -0.0024 0.9421 2.1908×10-9 
 
4. Conclusion 
In this paper, a discussion is made on the impact of solar-heat pump combined drying equipment on the drying 
characteristics and dynamics of kelp knots at different drying temperatures, wind speeds and loading capacities, 
obtaining the following conclusions: 
First, as revealed in the analysis on the drying characteristics of kelp knots under three different drying conditions, 
the drying curves of the material under different drying conditions tend to be the same basically; there is a short 
period of adjustment in the initial stage of drying, but decelerated drying predominates in the whole drying process; 
with the increase in drying time, the moisture ratio of the material shows an exponential downtrend. 
Second, three common drying dynamic models was used to fit the experimental curves of different drying 
processes. By comparing R2, RMSE and other relevant evaluation parameters, it is found that the Verma model is 
the fittest model for characterizing the moisture ratio change in the solar-heat pump combined drying process of 
kelp knots. The equation of this model was obtained by linear regression analysis on the experimental data. As 
discovered by verification of the equation, the experimental value fits the value predicted by the model well. This 
further verifies that the Verma model is most suitable for characterizing the solar-heat pump combined drying 
process of kelp knots. 
Third, as calculated as per Fick's second diffusion law, the effective moisture diffusion coefficient Deff under 
different drying condition is within the range of 2.1908×10-9 ~ 1.0012×10-9 m2/s; it is directly proportional to the 
drying temperature and wind speed, and inversely proportional to the loading capacity. By comparing the impacts 
of the three drying conditions on the Deff, it is discovered that drying temperature has extremely significant impact 
on the Deff. 



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Acknowledgments 
The authors are grateful for financial support from the National Natural Science Foundation of China (51806088) 
and Jiangsu University Scientific Research Foundation for the Senior Scholars (14JDG186).  
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This is an open-access article distributed under the terms and conditions of the Creative Commons Attribution 
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    /NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit. De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 5.0 en hoger.)
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    /ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing.  Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
  >>
  /Namespace [
    (Adobe)
    (Common)
    (1.0)
  ]
  /OtherNamespaces [
    <<
      /AsReaderSpreads false
      /CropImagesToFrames true
      /ErrorControl /WarnAndContinue
      /FlattenerIgnoreSpreadOverrides false
      /IncludeGuidesGrids false
      /IncludeNonPrinting false
      /IncludeSlug false
      /Namespace [
        (Adobe)
        (InDesign)
        (4.0)
      ]
      /OmitPlacedBitmaps false
      /OmitPlacedEPS false
      /OmitPlacedPDF false
      /SimulateOverprint /Legacy
    >>
    <<
      /AddBleedMarks false
      /AddColorBars false
      /AddCropMarks false
      /AddPageInfo false
      /AddRegMarks false
      /ConvertColors /ConvertToCMYK
      /DestinationProfileName ()
      /DestinationProfileSelector /DocumentCMYK
      /Downsample16BitImages true
      /FlattenerPreset <<
        /PresetSelector /MediumResolution
      >>
      /FormElements false
      /GenerateStructure false
      /IncludeBookmarks false
      /IncludeHyperlinks false
      /IncludeInteractive false
      /IncludeLayers false
      /IncludeProfiles false
      /MultimediaHandling /UseObjectSettings
      /Namespace [
        (Adobe)
        (CreativeSuite)
        (2.0)
      ]
      /PDFXOutputIntentProfileSelector /DocumentCMYK
      /PreserveEditing true
      /UntaggedCMYKHandling /LeaveUntagged
      /UntaggedRGBHandling /UseDocumentProfile
      /UseDocumentBleed false
    >>
  ]
>> setdistillerparams
<<
  /HWResolution [2400 2400]
  /PageSize [612.000 792.000]
>> setpagedevice

