If a greenhouse in the temperate and subtropical regions is maintained in a closed condition, the indoor temperature commonly exceeds that required for optimal plant growth, even in the cold season. This study considered this excess energy as surplus thermal energy (STE), which can be recovered, stored and used when heating is necessary. To use the STE economically and effectively, the amount of STE must be estimated before designing a utilization system. Therefore, this study proposed an STE model using energy balance equations for the three steps of the STE generation process. The coefficients in the model were determined by the results of previous research and experiments using the test greenhouse. The proposed STE model produced monthly errors of 17.9%, 10.4% and 7.4% for December, January and February, respectively. Furthermore, the effects of the coefficients on the model accuracy were revealed by the estimation error assessment and linear regression analysis through fixing dynamic coefficients. A sensitivity analysis of the model coefficients indicated that the coefficients have to be determined carefully. This study also provides effective ways to increase the amount of STE.

Modern greenhouses control plant growth conditions, such as temperature, humidity, carbon dioxide concentration, light and nutrients, and produce high-quality products irrespective of the outdoor climate. However, controlling the climate requires a large amount of energy, especially for heating during the cold season. The energy costs diminish the benefits of greenhouse farming, and the use of fossil fuels for the energy contributes to global warming. Therefore, many studies have been conducted to reduce the use of fossil fuels and conserve energy for greenhouse operation. Solar energy is a representative renewable and sustainable energy for greenhouse heating (

This study concentrates on the utilization of surplus thermal energy (STE) in greenhouses. Even in the cold season, the thermal energy input from solar radiation easily exceeds the required amount for heating on a clear day in the temperate or subtropical regions. This excessive solar energy is regarded as STE. There are several studies related to the STE energy (^{2} floor area and recovered 8.71 GJ for 3 months in a cold season (

The test greenhouse was single span, and the covering material was double-layer glass with 7 mm thickness. The floor area was 99.36 m^{2} with a width of 6.9 m and 14.4 m in length. The wall and the ridge were 3.4 m and 5.1 m high, respectively. Accordingly, the covering area was 267.33 m^{2}, and the interior volume was 422.28 m^{3}. The greenhouse was at latitude 37.2° N, in an east-west orientation rotated 20° clockwise.

The STE utilization system consists of a heat pump, low and high temperature heat storage tanks (LST and HST, respectively), and 10 fan-coil units (FCUs) as shown in

The test greenhouse system was operated during the winter (December 2010 – February 2011). The cultivated plants were roses (

where _{gr} is the energy amount that supplied for or recovered from the greenhouse; _{wt} is the water flow rate (m^{3}/min); _{wt} and _{wt} are the specific heat of water (J/kg/K) and the water density (kg/m^{3}), respectively; _{en} and _{lv} are the temperature (°C) entering and leaving the greenhouse at time _{m-s} is the unit factor for converting from minute to second (60 s/min).

The water flow rate and the water temperature were measured using a water flow meter (HMD40-1b, Shinil meter tech, Korea), accuracy ±2%, and temperature sensors (NTC-10kΩ), accuracy ±0.3°C. For the greenhouse indoor and outdoor temperatures, temperature sensors (PT-100Ω), accuracy ±0.3°C, with the fan-aspirated radiation shield (

The elements of the greenhouse energy balance for the STE model are shown in _{s}) transmits through the greenhouse covers, and its energy reduces. Total solar energy transmitted into the greenhouse (_{so}) is converted to sensible heat by the plants and floor (_{input}). If this sensible heat is greater than thermal energy loss of the greenhouse (_{loss}), the greenhouse contains the STE (_{sp}) as their difference. The detailed calculation procedure is elaborated in the following section.

The energy input from solar radiation was determined by the covering areas, the ratios of the direct and the diffuse radiation to the global radiation, and light transmissivity of the covers. The ratios of the direct and the diffuse radiation to global radiation display a stable value at a specific location on a clear day (_{so}, is expressed as

where _{drt} and _{dff} are the areas affected by direct and diffuse radiation, respectively; _{drt} and _{dff} are the ratios of direct and diffuse radiation to global radiation, respectively; _{s} is the intensity of global solar radiation; _{gh} is the solar radiation transmissivity of greenhouse-covering materials; and _{dff}) is equal to the total covering area (_{cv}),

where, _{r }
_{drt}
_{cv}
_{drt}
_{dff}. In winter, when the solar altitude is low, direct radiation reaches approximately half of the total covering area, _{drt} = 0.5_{cv}. The ratio of diffuse radiation to global radiation (_{dff}) is 0.15 on a clear day, and thus, _{drt} = 0.85 (_{r} becomes 0.575.

The greenhouse covers _{gh} varies according to the type, orientation and covering material of the greenhouse. The solar position and outside weather conditions also contribute to the _{gh}. A variety of studies on the _{gh} have considered the incidence angle of solar radiation (_{gh }vary from 25% to 59%, according to experimental conditions, applying a specific _{gh} for the energy input equation was difficult. To resolve this difficulty in _{gh} determination, factors affecting the _{gh} were divided into the incidence angle of solar radiation and the dust/dirt of the covering. Thus, the overall _{gh} of a greenhouse is expressed by

where _{pd} is the solar radiation transmissivity for the perpendicular beam on the surface, and _{ang} and _{dd} are the incidence angle factor and the dust/dirt factor for the solar radiation transmissivity, respectively.

Solar radiation transmitted into a greenhouse reaches plants or the floor and converts to thermal energy. In here, coefficients to convert solar energy into thermal energy are considered, and they are designated the sensible heat emission factors (SHEFs). In particular, this factor for plants is related to the Bowen ratio, which is the ratio of the sensible heat loss to the evaporative heat loss (

where _{sn-plt} and _{sn-flr} are SHEFs for the plant and the floor, respectively; and m

For greenhouses with closed windows, thermal energy loss, _{loss}, occurs by convection, conduction and infiltration through the cover and the floor, which is expressed by

where _{gh} is the overall heat transfer coefficient of the greenhouse including the infiltration effect, and _{wind} is the wind effect factor, which was set to 1.0 in this study. Although the wind effect factor is a linear function of wind speed, the effect of the wind speed is very small in the case of closed greenhouses with the double-layered glass covers except in strong winds (_{flr} is the heat transfer coefficient through the floor, and _{in}, _{out} and _{flr} are the temperatures of the greenhouse inside, outside and floor, respectively.

The STE model consists of three steps. The first step is to find the time that greenhouse heating is stopped by solar energy input. This relationship is expressed by

where inside temperature (_{in}) in the thermal energy loss element (_{loss}) becomes the heating temperature if the heating system normally operates;

After the first step is satisfied, the indoor temperature is raised by the increase of solar energy. This is the second step, expressed by

where the indoor temperature (_{in}) in the thermal energy loss element (_{loss}) equals _{in}(_{gh} is the heat capacity within the greenhouse.

When the difference between the thermal energy input and loss is a positive value, STE exists. The amount of STE is calculated by

where _{1} starts with the final _{2} is the time before the amount of STE calculated between _{1} and _{2} can be observed.

The incidence angle factor for the solar radiation transmissivity was determined based on

The incidence angle of solar radiation on the greenhouse covering, _{i}, was calculated using

where _{day} the day of the year, for example, _{day} on March 1 is 60; _{h} is the solar altitude angle; _{t} the hour angle (noon = 0); and _{a} is the surface azimuth angle; and _{b} the solar azimuth angle.

The overall heat transfer coefficient through the cover, _{gh}, and the heat transfer coefficient through the floor, _{flr}, were determined using the energy balance equation, _{gr}, was determined by

where _{flr} is the floor area, and _{flr} the floor temperature.

The projected leaf area was measured by assuming that it was a circular disc with diameter equal to the average length between the ends of leaves. The projected leaf area in a pot fluctuated from 0.00785 m^{2} to 0.0616 m^{2} between pinching and blooming as shown in

where _{pot} the number of pots. The arrangement of the pots is shown in

The SHEF coefficients were determined using _{gr}, _{so} and _{loss} were collected from Eqs. _{gr} in _{sn-plt} and _{sn-flr} were obtained.

After the STE model was determined for the test greenhouse, it was evaluated through the error between the measured and estimated amounts of STE and linear regression analysis. Moreover, the STE model includes dynamic coefficients that are changed by time or temperature, and they complicate the calculation of the model. Thus, through fixing these dynamic coefficients, the effects of the coefficients on the model accuracy were investigated.

A sensitivity analysis on the model coefficients was also conducted. When the coefficients in the model were considered as input and the estimated amounts of STE were considered as output, the effect of the coefficient on the estimation result was assessed. Among several methods for sensitivity analysis of building energy (

where _{base} is base output, equal to the estimated value, and _{base} is base input, which is equal to the coefficient.

The incidence angle of the solar radiation changes according to the date and time as shown in

The dirt/dust factor for the solar radiation transmissivity has been reported as 0.98 for 18 months and 0.95 for 24 months for glass covers (

where the incidence angle factor, _{ang}, is the dynamic coefficient as shown in

The overall heat transfer coefficient through covers, _{cv}, was determined to be 2.98 W/m^{2}/K (_{cv} is similar to the coefficient (3 W/m^{2}/K) presented by

A total of 198 data points of temperature and supplied thermal energy were collected and regression analysis was conducted using ^{2} of 0.502 and ^{2} of 0.844, respectively.

These results show that plants and floor contribute to increase the greenhouse temperature. However, according to temperature increase, the plants retain the SHEF between 0.35 and 0.40, whereas the SHEF of the floor keeps decreasing, which means the floor works as a heat sink at high indoor temperature. In addition, if it is assumed that the floor works as a heat source at low indoor temperature, the result that the SHEF of the floor was maximum at 16°C could be explained. These results provide a hint that greenhouses have to be operated at low temperature to recover the STE effectively.

Using the SHEF, the relation of sensible and latent heat in the greenhouse indoor air, and the relation of heat transfer between the greenhouse indoor air and plants or floor were simply solved.

The coefficients determined for the test greenhouse are listed in ^{2} value was 0.850. In this study, because the STE data higher than 200 MJ/day were not collected sufficiently, the proposed STE model has an applicable limitation for the high STE condition.

where

As shown in _{ang}), the SHEFs (_{sn-plt} and _{sn-flr}) and

Similar results were obtained through the linear regression analysis (^{2} values were sensitively changed because of the SHEFs and the m

The results of the sensitivity analysis of the STE model are shown in

As conclusions, this study was conducted to propose a model to estimate the surplus thermal energy (STE). Energy balance equations were basically used, and the sensible heat emission factor (SHEF) from plants and floor was newly introduced to develop the STE model. Monthly errors of the model were evaluated to be 17.9%, 10.4% and 7.4% for December, January and February, respectively. The STE model shows that the solar radiation transmissivity and the overall heat transfer coefficient of greenhouse covers are sensitively influenced to the amount of STE. Because this model was developed and verified through a small glass greenhouse, it must be tested in a larger greenhouse. As future research, it is necessary to find the coefficients in the STE model for different conditions of greenhouses.