Compression and Fungal Heat Production in Maize Bulk Considering Kernel Breakage

: Breakage in maize kernels and vertical pressure in grains lead to the uneven distribution of grain bulk density, which easily causes undesired problems in terms of grain storage. The objective of this study was, therefore, to determine the compression and heat production of the whole kernel (WK) and half kernel (HK) under two different loadings, i.e., 50 and 150 kPa, in maize bulk. An easy-to-use element testing system was developed by modiﬁcation of an oedometer, and an empirical–analytical– numerical method was established to evaluate fungal heat production, considering kernel breakage and vertical pressure. Based on the experimental results, it was found that breakage induced larger compression; the compression of HK was 62% and 58% higher than that of WK at 50 kPa and 150 kPa, respectively. The creep model of the Hooke spring–Kelvin model in series can be used to accurately describe the creep behavior of maize bulk. Fungi and aerobic plate counting (APC) were affected signiﬁcantly by the breakage and vertical pressure. APC in HK was 19 and 15 times that of WK under 150 and 50 kPa, respectively. The heat released by the development of fungi was found to be directly related to the APC results. The average temperatures of WK and HK under 150 and 50 kPa were 11.1%, 9.7%, 7.9%, and 7.6% higher than the room temperature, respectively. A numerical method was established to simulate the temperature increase due to fungi development. Based on the numerical results, heat production ( Q ) by fungi was estimated, and the results showed that the Q in HK was 1.29 and 1.32 times that of WK on average under 150 and 50 kPa. Additionally, the heat production results agreed very well with the APC results.


Introduction
Maize is among the major cereal crops, with a wide planting range and high harvest in China. Over 40 million hectares were sown, producing 260 million tons of maize in 2020 [1]. However, despite a massive increase in maize production, postharvest losses of maize during storage remain a significant challenge [2]. A considerable amount of maize kernel breakage is easily caused by postharvest processes such as transportation and grain loading. It reduces the quality grade of the grain and also increases the risk of grain security. The density change due to the self-weight of maize bulk further induces variation in grain properties, such as non-uniform airflow [3] and heat conductivity rate, and affects mildew on grain.
Broken kernels are more susceptible to the development of fungi, and they produce a considerable amount of heat because the physical integrity of kernels is compromised [4][5][6][7]. The distribution of fungi in broken kernels was preliminarily studied via milling and dehulling [5]. Pietri et al. [8] and Burger et al. [9] found that fungi are usually concentrated in the bran, and the damage to kernel brans often increases the risk of fungi infection. Oliveira et al. [7] analyzed the relationship between the physical properties of maize

Test Materials
The maize used in this experiment was a normal, Zhengdan 958 hybrid maize with the conventional tillage, harvested in 2021, and stored in silos. Samples of maize kernels were collected directly from the silo. In total, 10 kg of the sample was taken at 20 random sampling points and sealed in a sterile sampling bag. The maize sample was filtered through a circular sieve to remove broken kernels and foreign impurities. Four maize samples were randomly selected from the filtered grains, and the mass of each sample was 400 g. Two samples were whole kernels, as shown in Figure 1a, and the kernels of the other two samples were cut into two parts along their middle, as shown in Figure 1b. The initial moisture content of maize was determined to be 9.8%, with samples of 30 g in three replications after drying at 103 • C for 72 h, and the moisture content after the test was also determined [22]. In this study, we focused on the numerical simulation and analytical investigation of the mildew process. Thus, we increased the moisture content to about 20% to shorten the test duration, which might not be the optimum moisture content for storage in reality. To obtain the desired target moisture content, maize was rewetted by adding distilled water mixed thoroughly and then hermetically sealed in polyethylene bags and stored at 4 • C for 48 h to allow moisture equilibrium [10]. Maize was mixed well, and about 400 g was randomly drawn for each treatment. The four actual levels of adjusted moisture content of maize were 21.02 ± 0.03%, 20.97 ± 0.29%, 21.04 ± 0.06% and 20.89 ± 0.13% wet basis. Appl. Sci. 2022, 12, x FOR PEER REVIEW 3 of 13

Test Methods
To evaluate the effect of kernel breakage and compression on the mildew effect, a testing system was used in this study, which was modified from a conventional oedometer, normally used for soil testing, as shown in Figure 2. The testing system consists of a loading frame, a testing box, and a measuring system. The box is made of high-strength aluminum alloy and plexiglass, with a size of 120 by 120 by 55 mm. The metal loading plate is highly stiff, with a flexible rubber pad pasted below it [23]. A vertical loading screw is located in the groove so as to distribute the pressure applied to the maize bulk below. The extension length of the screw was adjusted according to the height of the maize bulk. The compression amount (s) of maize bulk under different vertical pressure levels and temperatures (T) were obtained by using a dial indicator and two T-type thermocouples (Applent Instruments Inc., Changzhou, China). The dial indicator was set on the loading screw. One thermocouple was placed in the geometric center of the maize sample, and another was attached to the external side of the box to observe the room temperature. The temperature results were recorded with an AT4508 temperature testing system (Applent Instruments Inc., China) and an automatic acquisition system. The walls of the testing box were coated with a thin layer of vaseline to eliminate side friction, and a 400 g sample of maize kernels was randomly taken and deposited in the testing box. As the sample area in this study was different from that of a conventional oedometer test, the vertical stress applied followed a sequence of 3, 8, 18, 28, 50, 75, 100, 125, and 150 kPa according to the calculation beforehand. In this study, two WK samples were loaded to 50 kPa and 150 kPa on multi-stages, respectively (i.e., WK50 and WK150), and two HK samples were loaded in the same way (i.e., HK50 and HK150). It is worth noting that each loading stage lasted for 20 min before reaching the final stress. Then, the four samples were continued for 7 d at constant stress. After the loading test, the APC test was performed to check mildew and grain quality.

Test Methods
To evaluate the effect of kernel breakage and compression on the mildew effect, a testing system was used in this study, which was modified from a conventional oedometer, normally used for soil testing, as shown in Figure 2. The testing system consists of a loading frame, a testing box, and a measuring system. The box is made of high-strength aluminum alloy and plexiglass, with a size of 120 by 120 by 55 mm. The metal loading plate is highly stiff, with a flexible rubber pad pasted below it [23]. A vertical loading screw is located in the groove so as to distribute the pressure applied to the maize bulk below. The extension length of the screw was adjusted according to the height of the maize bulk. The compression amount (s) of maize bulk under different vertical pressure levels and temperatures (T) were obtained by using a dial indicator and two T-type thermocouples (Applent Instruments Inc., Changzhou, China). The dial indicator was set on the loading screw. One thermocouple was placed in the geometric center of the maize sample, and another was attached to the external side of the box to observe the room temperature. The temperature results were recorded with an AT4508 temperature testing system (Applent Instruments Inc., China) and an automatic acquisition system.

Test Methods
To evaluate the effect of kernel breakage and compression on the mildew e testing system was used in this study, which was modified from a conventional oe ter, normally used for soil testing, as shown in Figure 2. The testing system consi loading frame, a testing box, and a measuring system. The box is made of high-s aluminum alloy and plexiglass, with a size of 120 by 120 by 55 mm. The metal l plate is highly stiff, with a flexible rubber pad pasted below it [23]. A vertical l screw is located in the groove so as to distribute the pressure applied to the mai below. The extension length of the screw was adjusted according to the height of the bulk. The compression amount (s) of maize bulk under different vertical pressure and temperatures (T) were obtained by using a dial indicator and two T-type therm ples (Applent Instruments Inc., Changzhou, China). The dial indicator was set on th ing screw. One thermocouple was placed in the geometric center of the maize samp another was attached to the external side of the box to observe the room temperatu temperature results were recorded with an AT4508 temperature testing system (A Instruments Inc., China) and an automatic acquisition system. The walls of the testing box were coated with a thin layer of vaseline to elimina friction, and a 400 g sample of maize kernels was randomly taken and deposited testing box. As the sample area in this study was different from that of a conve oedometer test, the vertical stress applied followed a sequence of 3, 8, 18, 28, 50, 125, and 150 kPa according to the calculation beforehand. In this study, two WK s were loaded to 50 kPa and 150 kPa on multi-stages, respectively (i.e., WK50 and and two HK samples were loaded in the same way (i.e., HK50 and HK150). It is worth that each loading stage lasted for 20 min before reaching the final stress. Then, t samples were continued for 7 d at constant stress. After the loading test, the APC t performed to check mildew and grain quality. The walls of the testing box were coated with a thin layer of vaseline to eliminate side friction, and a 400 g sample of maize kernels was randomly taken and deposited in the testing box. As the sample area in this study was different from that of a conventional oedometer test, the vertical stress applied followed a sequence of 3, 8, 18, 28, 50, 75, 100, 125, and 150 kPa according to the calculation beforehand. In this study, two WK samples were loaded to 50 kPa and 150 kPa on multi-stages, respectively (i.e., WK 50 and WK 150 ), and two HK samples were loaded in the same way (i.e., HK 50 and HK 150 ). It is worth noting that each loading stage lasted for 20 min before reaching the final stress. Then, the four samples were continued for 7 d at constant stress. After the loading test, the APC test was performed to check mildew and grain quality.

Inspection of APC
Maize kernels at the center of the box, as shown in Figure 3, were selected to conduct the APC test. The sample was prepared using a rectangular plastic sampler with a size of 29 by 29 mm, which was used to take out about 30 g of maize.

Inspection of APC
Maize kernels at the center of the box, as shown in Figure 3, were selected the APC test. The sample was prepared using a rectangular plastic sampler wi 29 by 29 mm, which was used to take out about 30 g of maize. The specific preparation process for the APC test is as follows: 1. Preparation of the plate counting agar (PCA): First, the tryptone, yeast ex cose, and agar were mixed thoroughly and dissolved fully, and the pH trolled at 7.0 ± 0.2. The mixed solution was autoclaved at 121 °C for 15 min flask; 2. Preparation of the bacterial suspension: Briefly, 25 g maize sample and 225 water were put into a 500 mL conical flask. The conical flask was placed lator and vibrated for 30 min at a speed of 10,000 r•min −1 . The aim of this p to fully diffuse the microorganisms on the surface of the maize kernels into water. By this process, a homogenate with a concentration of 1:10 was obt 3. Preparation of homogenates with different concentrations by serial dilutio step, 1 mL of 1:10 sample homogenate, drawn by a 1000 µL pipette, was test tube containing 9 mL sterile water to obtain a sample homogenate, concentration. The above steps were repeated several times to obtain a ser tions with different concentrations. Normally, two homogenates with dif centrations should be prepared for later fungus culture depending on th nation conditions. In this study, sample homogenates with concentrations 1:100 were selected for maize before testing, and 10 −5 and 10 −6 were selecte test; 4. Fungus culture: Briefly, 1 mL of sample homogenate with desired concent taken and mixed with 15-20 mL PCA. Then, the mixture was cooled to 46 injecting into 3 pre-sterilized Petri dishes. After the agar was coagulated, were turned over and cultured at 30 ± 1 °C for 72 h (MJPS-150, Shanghai Laboratory Instrument Co., Ltd., Shanghai, China); 5. Colony counting: For each sample, one from the 3 dishes with mold colon ranging from 100 to 150 colony-forming units (cfus) were selected, and th number of colonies were recorded by observing under a microscope. The The specific preparation process for the APC test is as follows: 1.
Preparation of the plate counting agar (PCA): First, the tryptone, yeast extract, glucose, and agar were mixed thoroughly and dissolved fully, and the pH was controlled at 7.0 ± 0.2. The mixed solution was autoclaved at 121 • C for 15 min in a conical flask; 2.
Preparation of the bacterial suspension: Briefly, 25 g maize sample and 225 mL sterile water were put into a 500 mL conical flask. The conical flask was placed in an oscillator and vibrated for 30 min at a speed of 10,000 r·min −1 . The aim of this process was to fully diffuse the microorganisms on the surface of the maize kernels into the sterile water. By this process, a homogenate with a concentration of 1:10 was obtained; 3.
Preparation of homogenates with different concentrations by serial dilution: For this step, 1 mL of 1:10 sample homogenate, drawn by a 1000 µL pipette, was mixed in a test tube containing 9 mL sterile water to obtain a sample homogenate, with 1:100 concentration. The above steps were repeated several times to obtain a series of solutions with different concentrations. Normally, two homogenates with different concentrations should be prepared for later fungus culture depending on the contamination conditions. In this study, sample homogenates with concentrations of 1:10 and 1:100 were selected for maize before testing, and 10 −5 and 10 −6 were selected after the test; 4.
Fungus culture: Briefly, 1 mL of sample homogenate with desired concentration was taken and mixed with 15-20 mL PCA. Then, the mixture was cooled to 46 • C before injecting into 3 pre-sterilized Petri dishes. After the agar was coagulated, the dishes were turned over and cultured at 30 ± 1 • C for 72 h (MJPS-150, Shanghai Jing Hong Laboratory Instrument Co., Ltd., Shanghai, China); 5.
Colony counting: For each sample, one from the 3 dishes with mold colony number ranging from 100 to 150 colony-forming units (cfus) were selected, and the type and number of colonies were recorded by observing under a microscope. The number of colonies was calculated as follows: where N is the aerobic plate count; ΣC is the sum of bacterial colony number; n 1 is the number of colonies for 1:10 homogenate; n 2 is the number of colonies for 1:100 homogenate; d is the dilution. In this study, d is equal to 10 −1 for maize before the test, and 10 −5 after the test [24]. The procedure for the APC test is shown in Figure 4.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 5 of 13 where N is the aerobic plate count; C  is the sum of bacterial colony number; 1 n is the number of colonies for 1:10 homogenate; 2 n is the number of colonies for 1:100 homogenate; d is the dilution. In this study, d is equal to 10 −1 for maize before the test, and 10 −5 after the test [24]. The procedure for the APC test is shown in Figure 4.

Creep Behavior
Creep deformation analysis (i.e., creep) is considered a valuable method in the quality assessment of grain/food products [12]. The deformation of maize under vertical load (i.e., gravity or weight of machine) results in a reduction in void ratio and ultimately impacts the moisture content, temperature, and biochemical functions. The deformation curve of maize bulk is shown in Figure 5a. Kernel breakage and vertical pressure affected the vertical compression of maize. Compression deformations of WK50 and HK50 after compression were 3.73 and 6.04 cm when loading was 50 kPa, and compression deformations of WK150 and HK150 after compression were 6.15 and 9.72 cm when loading was 150 kPa. The vertical compression of maize bulk increased with time under constant load. The compression of WK was small under the same vertical pressure. The compression deformations of HK were 62% and 58% higher than those of WK at 50 kPa and 150 kPa, respectively. The reason is that the grain skeleton composed of WK was not easily compressed, whereas HK easily slid and filled the pores, resulting in large compression deformation.

Creep Behavior
Creep deformation analysis (i.e., creep) is considered a valuable method in the quality assessment of grain/food products [12]. The deformation of maize under vertical load (i.e., gravity or weight of machine) results in a reduction in void ratio and ultimately impacts the moisture content, temperature, and biochemical functions. The deformation curve of maize bulk is shown in Figure 5a. Kernel breakage and vertical pressure affected the vertical compression of maize. Compression deformations of WK 50 and HK 50 after compression were 3.73 and 6.04 cm when loading was 50 kPa, and compression deformations of WK 150 and HK 150 after compression were 6.15 and 9.72 cm when loading was 150 kPa. The vertical compression of maize bulk increased with time under constant load. The compression of WK was small under the same vertical pressure. The compression deformations of HK were 62% and 58% higher than those of WK at 50 kPa and 150 kPa, respectively. The reason is that the grain skeleton composed of WK was not easily compressed, whereas HK easily slid and filled the pores, resulting in large compression deformation.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 5 of 13 where N is the aerobic plate count; C  is the sum of bacterial colony number; 1 n is the number of colonies for 1:10 homogenate; 2 n is the number of colonies for 1:100 homogenate; d is the dilution. In this study, d is equal to 10 −1 for maize before the test, and 10 −5 after the test [24]. The procedure for the APC test is shown in Figure 4.

Creep Behavior
Creep deformation analysis (i.e., creep) is considered a valuable method in the quality assessment of grain/food products [12]. The deformation of maize under vertical load (i.e., gravity or weight of machine) results in a reduction in void ratio and ultimately impacts the moisture content, temperature, and biochemical functions. The deformation curve of maize bulk is shown in Figure 5a. Kernel breakage and vertical pressure affected the vertical compression of maize. Compression deformations of WK50 and HK50 after compression were 3.73 and 6.04 cm when loading was 50 kPa, and compression deformations of WK150 and HK150 after compression were 6.15 and 9.72 cm when loading was 150 kPa. The vertical compression of maize bulk increased with time under constant load. The compression of WK was small under the same vertical pressure. The compression deformations of HK were 62% and 58% higher than those of WK at 50 kPa and 150 kPa, respectively. The reason is that the grain skeleton composed of WK was not easily compressed, whereas HK easily slid and filled the pores, resulting in large compression deformation.  The s~log (t) curve follows a reversed s-shape, and the deformation mainly underwent three stages: (1) Instantaneous deformation: the deformation was mainly affected by the magnitude of the load. The compression deformation occurred almost at the moment of load application, and the kernels slipped along the contact surface due to shear stress overcoming the friction at the contact surface. The kernels filled the large pores between kernels; (2) rapid deformation: the curve in this stage is mainly a section near the inflection point; the kernels were compressed, the pores between the kernels were filled, the resistance of the kernels increased, and the deformation rate decreased; (3) steady-state creep: the pores between kernels were basically filled, the resistance of kernels was greater, and the creep curve tended to be flat, roughly parallel to the abscissa axis.
Although s~log t can reflect the deformation trend of maize, it cannot clearly explain the internal characteristics and compression mechanism of grain, and it is not convenient to calculate the settlement of grain bulk in the process of long-term grain storage. To avoid this defect and consider the practicability of the model, a three-element model was used in this study, as seen in Figure 5b. The first region is represented by the Hooke spring unit, which shows the initiation of elastic deformation in a very short time frame, known as the instantaneous elastic deformation. The second region is represented by the Kelvin element, which indicates the retarded elastic deformation [14]. The Kelvin element is composed of Hooke spring and dashpot in parallel and can be expressed as where σ is the applied stress (MPa); ε is the total strain (dimensionless); E 1 is the deformation modulus of creep stage (MPa); η 1 is the viscosity coefficient of Kelvin (MPa·h). When the pressure is applied to the model, the spring will not be compressed immediately, due to the dashpot, and deformation gradually develops. Hooke spring is connected to the Kelvin element in series, and the creep model can be expressed as where E 0 is the instantaneous elastic modulus (MPa); ε 0 = σ/E 0 ; t is the storage time (h). The creep model of Hooke spring and Kelvin model in series can accurately describe the creep behavior of maize bulk under uniaxial compression. The fitting curve agreed very well with the test results, and all regression parameters had the coefficient of determination R 2 > 0.97, suggesting that the creep model can represent the creep behavior of maize bulk. Moreover, only three parameters-E 0 , E 1 , and η 1 -need to be determined when the vertical stress σ, time t, and strain ε are known; the model parameters are relatively few, which is convenient to describe the creep behavior of grain bulk.

Temperature and APC
Due to respiration in wet maize kernels and microorganisms, a considerable amount of heat is released, thus raising the grain temperature [11,25]; therefore, the temperature difference is a sensitive indicator of maize mold activity [11]. The temperatures of maize bulk are shown in Figure 6. By observing the room temperature, we found that heating intensity was high during daytime and low during nighttime. The temperature of maize bulk was significantly influenced by the laboratory environment and was higher than the room temperature. There were considerable differences caused by vertical pressure and kernel breakage. The temperature was the highest in HK 50 and lowest in WK 150 . The average temperatures of HK 50 , HK 150 , WK 50 , and WK 150 were 11.1%, 9.7%, 7.9%, and 7.6%, respectively, higher than the room temperature. The reason i believed to be the higher respiration process in broken kernels and sufficient oxygen between kernels under low vertical pressure, thereby developing heat energy and leading to the rise in grain bulk temperature.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 7 of 1 respiration process in broken kernels and sufficient oxygen between kernels under low vertical pressure, thereby developing heat energy and leading to the rise in grain bulk temperature. APC of maize kernels is an important parameter to evaluate the bacterial reproduc tive dynamics and bacterial contamination during storage [6]. The APC values in the cen ter of the maize sample were 3.0 × 10 6 , 1.9 × 10 6 , 0.2 × 10 6 , and 0.1 × 10 6 cfu g −1 for HK50 HK150, WK50, and WK150, respectively, as seen in Figure 7. The endosperm of maize had celadon hyphae and strong musty off-odor in half kernels. In addition, the color of les moldy samples was relatively bright in WK150. These results indicated that the broken ker nels were more likely to be contaminated, compared with whole kernels. The larger ver tical pressure compressed and deformed the maize bulk, reducing the pores between ker nels; the oxygen concentration was also low, which inhibited the development of stored grain fungi. This result corresponded very well to the temperature change shown in Fig  ure 6. Fewer molds produced a smaller amount of respiratory heat.

Physical Modeling of Heat Transfer and Verification
To investigate heat transfer due to physical factors during the testing process, finit element (FE) software COMSOL Multiphysics was used to establish numerical modeling APC of maize kernels is an important parameter to evaluate the bacterial reproductive dynamics and bacterial contamination during storage [6]. The APC values in the center of the maize sample were 3.0 × 10 6 , 1.9 × 10 6 , 0.2 × 10 6 , and 0.1 × 10 6 cfu g −1 for HK 50 , HK 150 , WK 50 , and WK 150 , respectively, as seen in Figure 7. The endosperm of maize had celadon hyphae and strong musty off-odor in half kernels. In addition, the color of less moldy samples was relatively bright in WK 150 . These results indicated that the broken kernels were more likely to be contaminated, compared with whole kernels. The larger vertical pressure compressed and deformed the maize bulk, reducing the pores between kernels; the oxygen concentration was also low, which inhibited the development of stored grain fungi. This result corresponded very well to the temperature change shown in Figure 6. Fewer molds produced a smaller amount of respiratory heat.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 7 of 13 respiration process in broken kernels and sufficient oxygen between kernels under low vertical pressure, thereby developing heat energy and leading to the rise in grain bulk temperature. APC of maize kernels is an important parameter to evaluate the bacterial reproductive dynamics and bacterial contamination during storage [6]. The APC values in the center of the maize sample were 3.0 × 10 6 , 1.9 × 10 6 , 0.2 × 10 6 , and 0.1 × 10 6 cfu g −1 for HK50 HK150, WK50, and WK150, respectively, as seen in Figure 7. The endosperm of maize had celadon hyphae and strong musty off-odor in half kernels. In addition, the color of less moldy samples was relatively bright in WK150. These results indicated that the broken kernels were more likely to be contaminated, compared with whole kernels. The larger vertical pressure compressed and deformed the maize bulk, reducing the pores between kernels; the oxygen concentration was also low, which inhibited the development of stored grain fungi. This result corresponded very well to the temperature change shown in Figure 6. Fewer molds produced a smaller amount of respiratory heat.

Physical Modeling of Heat Transfer and Verification
To investigate heat transfer due to physical factors during the testing process, finite element (FE) software COMSOL Multiphysics was used to establish numerical modeling

Physical Modeling of Heat Transfer and Verification
To investigate heat transfer due to physical factors during the testing process, finite element (FE) software COMSOL Multiphysics was used to establish numerical modeling. For simplicity, the maize kernels were assumed as porous media with isotropic properties and in local thermodynamic equilibrium with their surrounding air. Additionally, the laminar air in the void between kernels was incompressible under vertical load. However, the buoyant force and natural convection due to temperature gradient can be considered. The flow rate is assumed to be unchanged, and the 3D flow field can be expressed as where u j (j = 1,2,3) is the air flow rate in the direction x j , u 1 = u, u 2 = u 3 = v. In rectangular Cartesian coordinate system, x 1 = x, x 2 = y, x 3 = z. The Brinkman-Darcy formulation was incorporated with the maize domain to represent the air flow. Additionally, the momentum satisfies the Boussinesiq's approximation, then where ρ a is the density of air, u i is the speed of airflow, t is the storage time, p is the air pressure, φ is the porosity of maize bulk, K is the permeability of maize bulk, T is the temperature of the air and maize kernels, ρ 0 is the density of air at the reference temperature (T 0 ), g is the gravity vector, β is the coefficient of volumetric expansion of the air, and µ is the viscosity of air.
As there is a local thermodynamic equilibrium between maize kernels and the surrounding air, the governing conservation equation of thermal energy is where c a is the specific heat of air; ρ b , c b , and k b are the dry density, specific heat, and the effective thermal conductivity of maize bulk, respectively; h s is the heat sorption of water on maize, and W is the moisture content of maize in dry basis. Maize is a living organism with water absorption and desorption feature. Thus, the moisture balance formula is written as where τ is the tortuosity factor of maize bulk, D v is a dimensionless rate coefficient for moisture exchange between air and maize kernels, and w is the moisture content of water vapor in the air on a dry basis.
To verify the effectiveness of the numerical model, physical heat transfer for maize was investigated with both testing and FE methods. The test was conducted by placing the sample within the model box (including the top plate) in a freezer. Before testing, the model box, top plate, and spread-open kernels were placed in the freezer, with the door open for hours to reach a uniform initial temperature. Then, the whole maize kernels were put into the box and covered by the top plate. The tests were begun after closing the door, and the temperature of the freezer was set at 6 • C. The test lasted for 350 min only. Therefore, biochemical heat production could be ignored, and only physical heat transfer occurred during the test. Two T-type thermocouples were set at the central point of the sample and in the freezer to monitor the temperature change. The material parameters of the model box and maize used in FE analysis are listed in Table 1, and the sources of the parameters are specified as well. As seen in Figure 2, the maize bulk was basically sealed by the box and top plate during the test. Thus, there was almost no air convection between the pores, and the maize moisture content slightly changed during the test. As a result, the flow rate of air was assumed to be zero, and water evaporation was not considered. A comparison of the tested and numerical results of T at the central point is shown in Figure 8. After placing in the freezer, the temperature of the freezer E F gradually decreased from around 30 • C to 6 • C. It is worth noting that the maize tested T was slightly higher than the numerical value for in the late stage, e.g., after 300 min. The reason is that the biochemical heat production is not zero even under the very low freezer temperature of 6 • C. In conclusion, the heat transfer considering various physical factors, such as air convection, water migration and evaporation, and local thermodynamic equilibrium, could be well simulated using the established FE model.  the flow rate of air was assumed to be zero, and water evaporation was not considere comparison of the tested and numerical results of T at the central point is shown in Fi 8. After placing in the freezer, the temperature of the freezer EF gradually decreased f around 30 °C to 6 °C. It is worth noting that the maize tested T was slightly higher the numerical value for in the late stage, e.g., after 300 min. The reason is that the bioch ical heat production is not zero even under the very low freezer temperature of 6 °C conclusion, the heat transfer considering various physical factors, such as air convec water migration and evaporation, and local thermodynamic equilibrium, could be simulated using the established FE model.

Simulation Results and Analysis
The current method normally assumed that maize is an isotropic porous medium, and the model for simulating heat and moisture transfer in grain bulk was also developed. However, the current model did not consider the effect of compression deformation on heat and moisture coupling transfer. Using the verified model mentioned in the previous section and considering vertical pressure, the variation in temperature (T) at the central point was simulated. The parameters involved in the FE simulation for maize are shown in Table 2. During the simulation, vertical-pressure-induced compression (∆h), considered by the input value of density (ρ b ), was calculated using ∆h step by step, according to the loading procedure. Similarly, the variation in porosity and thermal conductivity during the test were considered step by step as well. The experimental result and simulated result are designated as T E and T N , respectively. Figure 9 presents the temperature variations in T E and T N for the four groups of maize bulk (HK 50 , HK 150 , WK 50, and WK 150 ). Clearly, it can be observed that T E is higher than T N . Compared with numerical T N , which only includes physical effect, the test T E resulted from physical heat transfer and biochemical effect (e.g., mildew). The temperature difference/rise actually is a consequence of heat accumulation due to a biochemical effect. Generally, half kernels under low vertical pressure, e.g., HK 50 , yield larger ∆T, and WK 150 yields smaller ∆T. The average values of ∆T were 2.7 • C, 2.4 • C, 1.9 • C, and 1.8 • C in HK 50 , HK 150 , WK 50 , and WK 150 , respectively. This result is proportional to the APC in Figure 7, which indicates that mildew is one of the main reasons for temperature rise in grain storage. Owing to the low thermal conductivity of air between the pores of the kernels, heat conduction is slow, and the heat generated by initial fungi inside the grain bulk cannot be quickly dissipated. Increased temperature in grain bulk further provides a favorable environment for subsequent fungal growth [10,16]. This cycle of "heat conduction-temperature rise-fungal growth" accounts for the initial condition significantly. The temperature differences ∆T of HK samples were larger than those in WK, and the result is consistent with the above APC test results.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 10 of 13 section and considering vertical pressure, the variation in temperature (T) at the central point was simulated. The parameters involved in the FE simulation for maize are shown in Table 2. During the simulation, vertical-pressure-induced compression (Δh), considered by the input value of density (ρb), was calculated using Δh step by step, according to the loading procedure. Similarly, the variation in porosity and thermal conductivity during the test were considered step by step as well. The experimental result and simulated result are designated as TE and TN, respectively. Figure 9 presents the temperature variations in TE and TN for the four groups of maize bulk (HK50, HK150, WK50, and WK150). Clearly, it can be observed that TE is higher than TN. Compared with numerical TN, which only includes physical effect, the test TE resulted from physical heat transfer and biochemical effect (e.g., mildew). The temperature difference/rise actually is a consequence of heat accumulation due to a biochemical effect. Generally, half kernels under low vertical pressure, e.g., HK50, yield larger ΔT, and WK150 yields smaller ΔT. The average values of ΔT were 2.7 °C, 2.4 °C, 1.9 °C, and 1.8 °C in HK50, HK150, WK50, and WK150, respectively. This result is proportional to the APC in Figure 7, which indicates that mildew is one of the main reasons for temperature rise in grain storage. Owing to the low thermal conductivity of air between the pores of the kernels, heat conduction is slow, and the heat generated by initial fungi inside the grain bulk cannot be quickly dissipated. Increased temperature in grain bulk further provides a favorable environment for subsequent fungal growth [10,16]. This cycle of "heat conduction-temperature rise-fungal growth" accounts for the initial condition significantly. The temperature differences ΔT of HK samples were larger than those in WK, and the result is consistent with the above APC test results.

Estimation of Fungal Heat Production
Fungal growth decomposes organic matter in maize, thereby developing heat energy, and biochemical heat production is assumed to be heat production due to fungi development [21]. In the estimation of fungal heat production, some of the heat (E T ) is used to raise the temperature of the system, some heat is likely lost due to conduction (E C ) and convection (E V ), and some may be consumed during the water phase change (E E ), e.g., from liquid to vapor. In this study, E C was not considered, as the sample was nearly sealed. E E was also considered ignorable because the moisture content of the four samples lost only 1.1%~1.3% after being stored for 7 d. Therefore, the heat produced by fungi in the maize bulk can be determined as follows: where ∆T' is the temperature difference in the maize bulk before and after fungus emergence. Heat absorbed by maize and the specific heat capacity of maize bulk were calculated using the following formula [21,26]: where ∆V is the spatial range affected by fungal activity (m 3 ). The conduction heat loss (E C ) was determined by considering heat transfer from the geometric center of the maize sample to the wall of the testing box. The calculation space is ∆x = 0.12 m,∆y = 0.12 m, and ∆z is the height of the sample at the corresponding time (∆V = ∆x∆y∆z). Taking into account the sum of the conduction heat loss on the six sides of the testing box, according to Fourier's law, E C can be calculated as follows: where ∆t is the storage time, A i is the area of one of the six faces of the testing box, and ∆T i is the temperature difference between the center of the geometric center of the maize sample and the corresponding face A i measured at a given time t. l i is the distance between the center of the geometric center of the maize sample and the corresponding face A i . In this investigation, the value of temperature difference before and after fungi emergence (∆T') can be equivalently regarded as the difference between the test and numerical results (∆T). As mentioned above, the reason for ∆T between test and simulation is whether the biochemical effect or fungi was considered. The numerical result from COMSOL Multiphysics can only include the physical factors in the simulation. Using the test and numerical temperature difference, heat production (Q) by fungi was evaluated, as shown in Figure 10. Q was the least in WK 150 , and in HK 50 , HK 150 , and WK 50 , the values were 33.7%, 29.7%, and 1.4% higher than it on average. Additionally, it is clear that this variation in Q with time agreed very well with the APC and temperature results (Figures 7 and 9).

Conclusions
The deformation of maize under vertical load and kernel breakage of maize hav important impact on the biochemical functions of maize bulk. Maize bulk appeare creep deformation under stable load, and the creep model of Hooke spring-Kelvin m in series can accurately describe the creep behavior of maize bulk. There was a signifi difference between the compression of the whole kernel and half kernel-namely compression of the half kernel was 62% and 58% higher than that of the whole kern 50 kPa and 150 kPa, respectively. Broken kernels increase the risk of fungi infection, deformation under vertical load results in a reduction in void ratio, thus affecting f development. The APC values in HK were 19 and 15 times those of WK under 150 an kPa, respectively. The temperature and heat rates agreed very well with the APC res The average temperatures of HK50, HK150, WK50, and WK150 were 11.1%, 9.7%, 7.9%, 7.6% higher than the room temperature, respectively. The heat production rate by f in HK was 1.29 and 1.32 times that of WK on average under 150 and 50 kPa.

Conclusions
The deformation of maize under vertical load and kernel breakage of maize have an important impact on the biochemical functions of maize bulk. Maize bulk appeared to creep deformation under stable load, and the creep model of Hooke spring-Kelvin model in series can accurately describe the creep behavior of maize bulk. There was a significant difference between the compression of the whole kernel and half kernel-namely, the compression of the half kernel was 62% and 58% higher than that of the whole kernel at 50 kPa and 150 kPa, respectively. Broken kernels increase the risk of fungi infection, and deformation under vertical load results in a reduction in void ratio, thus affecting fungi development. The APC values in HK were 19 and 15 times those of WK under 150 and 50 kPa, respectively. The temperature and heat rates agreed very well with the APC results. The average temperatures of HK 50 , HK 150 , WK 50 , and WK 150 were 11.1%, 9.7%, 7.9%, and 7.6% higher than the room temperature, respectively. The heat production rate by fungi in HK was 1.29 and 1.32 times that of WK on average under 150 and 50 kPa.

Data Availability Statement:
The data presented in this study are available in the article.

Conflicts of Interest:
The authors declare no conflict of interest.