Effect of agricultural covering material thickness on the overall heat transfer coefficient

Abstract

　This study evaluates the effect of the agricultural covering material thickness on the overall heat transfer coefficient in developing covering materials with high heat insulation. The thickness of a thin film, such as the covering material, minimally impacts conductive and convective heat transfer within and outside the greenhouse. Nevertheless, the effect of covering material thickness on radiative heat transfer remains unexplored. The higher the longwave radiation absorptance of the covering material, the lower the overall heat transfer coefficient due to the suppression of radiative heat transfer through the material. This study examined the relationship between the covering material thickness and the overall heat transfer coefficient for 24 types of polyolefin (PO) films in the market. An equation was used to estimate the overall heat transfer coefficients based on the longwave radiation absorptance of each covering material, which was measured using an emissivity meter. The tested PO films’ maximum, minimum, and average thicknesses were 0.16, 0.06, and 0.12 mm, respectively, with a standard deviation (SD) of 0.03 mm. The longwave radiation absorptance’s maximum, minimum, and average values were 0.74, 0.37, and 0.63, respectively, with an SD of 0.08. The maximum, minimum, and average values of the overall heat transfer coefficients were 7.22, 6.19, and 6.56 W m^-2 K^-1, respectively with an SD of 0.24 W m^-2 K^-1. A significant positive correlation was observed between film thickness and longwave radiation absorptance (R = 0.6468). There was a significant negative correlation between film thickness and the overall heat transfer coefficient (R = -0.6642). As film thickness increased, longwave radiation absorptance increased, suppressing radiative heat transfer through the covering material and decreasing the overall heat transfer coefficient. This study clarifies the mechanism by which the thickness of the covering material affects the overall heat transfer coefficient.

1. Introduction

Growing crops year-round in outdoor fields becomes challenging in regions with cold winters due to the temperature drop below the optimal range for crop growth. Conversely, greenhouse horticulture enables consistent harvesting even in winter, as greenhouses can be heated to maintain suitable crop temperatures. However, heating greenhouses demands significant energy consumption. Thus, energy efficiency in greenhouse horticulture becomes crucial, particularly given the recent surge in global energy costs (Fernández and Molnar, 2021). Because most of the energy used in cold regions is for winter heating (Dimitropoulou et al., 2023), thus improving greenhouse insulation stands out as a critical strategy for energy conservation. Not only does energy conservation offer immediate benefits, but it also contributes to the future decarbonization of greenhouse horticulture.

Among the forms of heat loss in greenhouses during winter nights, heat transfer through covering materials by radiation, conduction, and convection accounts for the largest proportion. In this study, heat transfer through the covering material is defined as overall heat transfer. Other forms of heat loss include ventilation and soil heat transfers. Generally, the overall heat transfer contributes to over 80% of the total heat loss in a greenhouse during winter nights (Hayashi, 1980). Consequently, reducing overall heat transfer is the most effective approach for enhancing greenhouse heat insulation. To enhance heat insulation of greenhouses, it is essential to develop covering materials characterized by low overall heat transfer coefficients.

The overall heat transfer coefficient varies depending on the covering material used. For instance, hot-box measurements have demonstrated that glass exhibits a lower overall heat transfer coefficient than plastic films (Feuilloley and Issanchou, 1996). Glass has a smaller overall heat transfer coefficient than plastic materials such as polyolefin (PO) films and polyethylene films due to its higher longwave radiation (3-60 µm) absorptance (Ohashi et al., 2023).

Moreover, manufacturers have been enhancing heat insulation by incorporating infrared absorbers such as glass fillers into the covering materials, which effectively block longwave radiation (Egami, 1990; Goto, 2014). However, the specific type and proportion of these infrared absorbers remain undisclosed as proprietary information. Generally, increasing the amount of infrared absorbers decreases the transmission of photosynthetically active radiation (PAR) (400-700 nm). This reduction in PAR transmittance can negatively impact crop photosynthesis, particularly for exterior covering materials, as many crops rely on the total light received for dry matter production (Monteith, 1977). Hence, a decrease in PAR transmittance leads to diminished yields. Therefore, there is a need to enhance the heat insulation of covering materials without compromising PAR transmittance.

This study focused on the impact of the thickness of the covering material. Research indicates that the thickness of thin films, such as covering materials, minimally influences conductive or convective heat transfer (Sase, 2005; Ishigami, 2022). However, the influence of covering material thickness on radiative heat transfer remains unclear. As previously discussed, longwave radiation absorptance significantly affects radiative heat transfer through the covering material. Higher longwave radiation absorptance correlates with reduced radiative heat transfer (Ohashi et al., 2023). Consequently, if the thickness of the covering material influences longwave radiation absorptance, it also affects radiative heat transfer and the overall heat transfer coefficient. Understanding the relationship between covering material thickness and the overall heat transfer coefficient is crucial for developing high heat-insulating covering materials while considering cost and ease of application.

This study aims to elucidate the impact of covering material thickness on the overall heat transfer coefficient in developing covering materials with superior heat insulation properties.

2. Materials and methods

2.1. Measurement of covering material thickness

Twenty-four types of transparent PO films currently available were used as test materials. PO is a material made of polyethylene (PE) and ethylene-vinyl acetate (EVA) in a multilayer structure blended with additives for heat-retaining, weather-resistant, and anti-fog applications. PO films have been actively used in recent years because of their multilayered structure, facilitating the effective blending of raw materials and additives according to the usage scenario (Goto, 2014).

The thickness of each covering material was measured thrice using a micrometer (79523, Shinwa Rules Co., Ltd., Niigata, Japan), and the average value was used as the thickness of the material.

2.2. Estimation of overall heat transfer coefficient

The overall heat transfer coefficients of the covering materials were calculated using the hot-box method (Geoola et al., 2009; 2011; Hayashi et al., 2011; Ohashi et al., 2023). However, the hot-box method is complicated when there are many sample materials because of the extended measurement time per material. Ohashi et al. (2023) developed an equation describing the relationship between the overall heat transfer coefficient and longwave radiation absorptance using the hot-box method (R² = 0.924, clear weather condition) (Equation 1).

k=-2.1907ε²-0.327ε+7.6481　　　(Equation 1)

Where k is the overall heat transfer coefficient (W m^-2 K^-1). ε is the longwave radiation absorptance. In this study, the overall heat transfer coefficient was estimated by substituting the longwave radiation absorptance of the covering material into Equation 1.

The longwave radiation characteristics (transmittance, reflectance, and absorptance) of the covering material were measured using the emissivity meter proposed by Okada (1983). The longwave radiation transmittance (τ) and reflectance (γ) of the 24 covering materials were measured using the method described by Ohashi et al. (2023, 2024). The calculated τ and γ were substituted into Equation 2 to calculate the longwave radiation absorptance (ε) of the covering material.

ε=1-τ-γ 　　　(Equation 2)

The ε calculated in Equation 2 was substituted into Equation 1 to calculate k. Regression analysis was performed to determine the relationship between the thickness of the covering material and k. In addition, a regression analysis was performed to determine the relationship between the thickness and longwave radiation characteristics (absorptance, transmittance, and reflectance) of the covering materials. The presence or absence of correlation was evaluated by performing a test for no correlation. Histograms were also prepared to show the distribution of k, τ, γ, and ε for the 24 test materials.

2.3. Measurement of visible light transmittance

Despite improvements in the heat insulation of covering materials, low PAR transmittance diminishes crop photosynthesis, leading to decreased yields. Hence, maintaining high PAR transmittance is crucial in developing covering materials. This study examines the effect of covering material thickness on PAR transmittance.

The wavelength ranges of PAR (400-700 nm) and visible light (380-780 nm) were mostly coincident. The visible light transmittance of the covering materials was measured using a visible light transmittance meter (peak wavelength: 550 nm) (Model 2000, Laser Labs Inc., MA, USA) to evaluate the PAR transmittance of the covering materials. A standard plate (transmittance of 0.85) was inserted between the measured sections of the transmittance meter to confirm that the measured values were acceptable. Next, 24 different covering materials were inserted individually into the measuring section of the transmittance meter, and the transmittance of visible light was measured. Regression analysis was then conducted to determine the relationship between the thickness of the covering material and the visible light transmittance. The presence or absence of correlation was evaluated by performing a test for no correlation.

In addition, a regression analysis was performed to determine the relationship between the visible light transmittance of the covering materials and the overall heat transfer coefficient. The presence or absence of correlation was evaluated by performing a test for no correlation.

3. Results

3.1. Covering material thickness

The maximum, minimum, average, and SD of the thicknesses of the test materials are listed in Table 1. The maximum, minimum, and average thicknesses of the 24 test materials were 0.16, 0.06, and 0.12 mm, respectively, with a SD of 0.03 mm.

Table 1. Various properties of agricultural PO films (n = 24).

3.2. Relationship between covering material thickness and heat insulation properties

3.2.1. Longwave radiation characteristics

The maximum, minimum, average, and SD of the longwave radiation characteristics of the test materials are listed in Table 1. The maximum, minimum, and average longwave radiation absorptance values of the test materials were 0.74, 0.37, and 0.63, respectively, with a SD of 0.08. The maximum, minimum, and average longwave radiation transmittances of the test materials were 0.55, 0.19, and 0.30, respectively, with a SD of 0.08. The maximum, minimum, and average longwave radiation reflectances of the test materials were 0.10, 0.03, and 0.07, respectively, with a SD of 0.01.

Fig. 1 shows the relationship between the thickness of the test material and the longwave radiation characteristics. A significant positive correlation (R² = 0.4183, R = 0.6468) was detected at p < 0.01 between the thickness of the test material and the longwave radiation absorptance. A significant negative correlation (R² = 0.417, R = -0.6458) was detected at p < 0.01 between the thickness of the test materials and the longwave radiation transmittance. No correlation was detected between the thickness of the test materials and longwave radiation reflectance (R² = 0.0175, R = -0.1323).

A histogram of the distribution of the longwave radiation characteristics of the test materials is shown in Fig. 2. The longwave radiation absorptance of the test materials was distributed between 0.35 and 0.75, with the largest distribution between 0.65 and 0.70. The longwave radiation transmittance of test materials ranged from 0.15 to 0.60, with the largest distribution between 0.25 and 0.30. The longwave radiation reflectance of the test materials was distributed between 0.00 and 0.10, with the largest distribution between 0.05 and 0.10.

Fig. 1.Effect of the thickness of covering materials on the longwave radiation absorptance, transmittance, and reflectance (n = 24). The presence or absence of correlation was evaluated by performing a test of no correlation. * indicate a significant correlation at p < 0.01 between them.

Fig. 2.Histograms of longwave radiation absorptance, transmittance, and reflectance of covering materials (n = 24).

3.2.2. Overall heat transfer coefficient

The maximum, minimum, average, and SD values of the overall heat transfer coefficients of the test materials are listed in Table 1. The maximum, minimum, and average overall heat transfer coefficients of the test materials were 7.22, 6.19, and 6.56 W m^-2 K^-1, respectively, with the SD of 0.24 W m^-2 K^-1.

The relationship between the thicknesses of the test materials and the overall heat transfer coefficients is shown in Fig. 3. A significant negative correlation was detected at p < 0.01 between the thickness of the test material and the overall heat transfer coefficient (R² = 0.4411, R = -0.6642).

A histogram of the distribution of the overall heat transfer coefficients of the test materials is shown in Fig. 4. The overall heat transfer coefficients of the test materials were distributed between 6.0 and 7.4 W m^-2 K^-1, with the largest distribution between 6.4 and 6.6 W m^-2 K^-1.

Fig. 3.Relationship between covering material thicknesses and overall heat transfer coefficient (n = 24). The presence or absence of correlation was evaluated by performing a test of no correlation. * indicates a significant correlation at p < 0.01 between them.

Fig. 4.Histogram of overall heat transfer coefficient of covering materials (n = 24).

3.3. Visible light transmittance

Table 1 lists the maximum, minimum, average, and SD values of the visible light transmittance of the test materials. The maximum, minimum, and average transmittances of the test materials were 0.93, 0.87, and 0.91, respectively, with an SD of 0.02.

Fig. 5 shows the relationship between the thickness of the test material and the visible light transmittance. No correlation was detected between the thickness of the test materials and the visible light transmittance (R² = 0.0591, R = -0.2431).

Fig. 6 shows the relationship between the visible light transmittance and the overall heat transfer coefficient of the test materials. No correlation was detected between the visible light transmittance of the test materials and the overall heat transfer coefficient (R² = 0.072, R = 0.2683).

Fig. 5.Relationship between covering material thicknesses and visible light transmittance (n = 24). The peak wavelength for visible light transmittance measurement is 550 nm. The presence or absence of correlation was evaluated by performing a test of no correlation.

Fig. 6.Relationship between visible light transmittance of covering materials and overall heat transfer coefficient (n = 24). The peak wavelength for visible light transmittance measurement is 550 nm. The presence or absence of correlation was evaluated by performing a test of no correlation.

4. Discussion

4.1. Relationship between covering material thickness and the longwave radiation characteristics

The positive correlation between the thickness of the covering material and the longwave radiation absorptance (Fig. 1) occurs because, as the thickness increases, the optical path length also increases, and the probability of longwave radiation striking the plastic molecules and being absorbed increases. Therefore, increasing the thickness of the covering material is an effective way to increase longwave radiation absorptance.

The negative correlation between the thickness of the covering material and the longwave radiation transmittance (Fig. 1 is due to the effect of the light path length, as previously discussed.

The longwave radiation reflectance of the covering materials was less than 0.10, which was smaller than the absorptance and transmittance values (Figs. 1and 2). No correlation was detected between thickness and reflectance, as there was no difference in the longwave radiation reflectance between materials of different thicknesses (Table 1 and Fig. 1). A previous study also determined the longwave radiation reflectance was around 0.10 for several types of transparent covering materials (Ohashi et al., 2023), which was consistent with the trend observed in the present study. These results indicate that the thickness of the covering material does not affect the longwave radiation reflectance.

However, the aluminum-evaporated film used for thermal screens has high longwave radiation reflectance (reflectance: ~0.5) and, thereby, high heat insulation (Bailey, 1977; Okada, 1981; Ohashi et al., 2024). Until now, no attention has been paid to longwave radiation reflectance as a factor in improving the heat insulation of transparent covering materials. Therefore, developing technologies that increase the longwave radiation reflectance of transparent covering materials will lead to the development of materials with improved heat insulation.

4.2. Effect of covering material thickness and the overall heat transfer coefficient

A negative correlation was detected between the thickness of the covering material and the overall heat transfer coefficient (Fig. 3), indicating that the thickness of the covering material affected the overall heat transfer coefficient. Although the thickness of a thin film, such as the covering material, has little effect on conductive and convective heat transfer (Sase, 2005; Ishigami, 2022), the thickness of the covering material affects the overall heat transfer coefficient as follows.

There was a positive correlation between the thickness of the covering material and longwave radiation absorptance (Fig. 1), and the longwave radiation absorptance tended to increase as the thickness of the covering material increased. The higher the longwave radiation absorptance of the covering material, the lower the overall heat transfer coefficient, owing to decreased radiative heat transfer through the film (Ohashi et al., 2023). Therefore, as the thickness of the covering material increases, the overall heat transfer coefficient decreases (Fig. 3). The results of this study clarify the mechanism by which the thickness of the covering material affects the overall heat transfer coefficient.

The histogram in Fig. 4 reveals that the overall heat transfer coefficient varied even among films made of polyolefin materials. Almost all technical books list only one overall heat transfer coefficient value for each type of material. The overall heat transfer coefficient directly influences the heating energy consumption of greenhouses on winter nights. Therefore, when selecting materials, it is best to measure the longwave radiation characteristics in advance and select materials with high heat insulation.

In addition, the results of our previous studies have shown that, for PO films, the overall heat transfer coefficient decreases by about 15% when the weather changes from sunny to cloudy (Ohashi et al., 2023). Therefore, if it is necessary to calculate the overall heat transfer coefficient on cloudy days, the equation relating longwave radiation absorptance and overall heat transfer coefficient on cloudy days should be used instead of Equation 1.

4.3. Relationship between covering material thickness and the visible light transmittance

There was no significant correlation between the thickness of the covering material and the visible light transmittance (Fig. 5). This means the thickness of covering materials had little effect on visible light transmittance in the thickness range of the covering material used in this study (0.06-0.16 mm) because of the physical properties that allow visible light to pass through them easily. As the thickness of the film increases to an extreme value, the visible light transmittance will also decrease.

Table 1 and Fig. 5 showing the distribution of the visible light transmittance of the covering materials shows that all the materials had a transmittance between 0.87 and 0.93. Because crop dry matter production is generally determined by the total amount of light received (Monteith, 1977), the covering materials currently on the market were developed with an emphasis on transmittance in the visible light range for crop photosynthesis.

No correlation was found between the visible light transmittance of covering materials and the overall heat transfer coefficient (Fig. 6) because the wavelength range (3 to 60 µm) affecting the radiative heat transfer through the film is differs from the visible light range.

Another method to reduce the overall heat transfer coefficient is adding an infrared absorber to the film. Reducing the overall heat transfer coefficient while maintaining transparency is generally difficult because the visible light transmittance decreases as the infrared absorber content increases. Contrastingly, no decrease in the visible light transmittance was observed for the range of covering material thickness used in this study (Fig. 5). Therefore, increasing the thickness of the covering material is one way to reduce the overall heat transfer coefficient without decreasing visible light transmittance.

5. Conclusions

A significant negative correlation was detected between the thickness of the covering material and the overall heat transfer coefficient (R = -0.6642). The overall heat transfer coefficient decreased with increasing covering material thickness owing to the following mechanism.

A significant positive correlation (R = 0.6468) was found between the thickness of the covering material and longwave radiation absorptance, and the longwave radiation absorptance also increased as the thickness of the covering material increased. Since the overall heat transfer coefficient decreased with increasing longwave radiation absorptance of the covering material, the overall heat transfer coefficient decreased with increasing thickness of the covering material. This study clarified the mechanism by which thickness affects the overall heat transfer coefficient.

Acknowledgments

This work was supported by the MAFF-Commissioned project study entitled “Pilot research project for materializing low-carbon agriculture” (Grant Number JPJ009819).

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