###### Contents  
* 1 Introduction
* 2.1 Introduction
* 2.2 Explanation of the model
* 2.3 Explanation of the model
* 2.4 Explanation of the model
* 2.5 Explanation of the model
* 2.6 Explanation of the model
* 2.7 Explanation of the model
* 2.8 Explanation of the model
* 2.9 Explanation of the model
* 3.0 Explanation of the model
* 3.1 Explanation of the model
* 3.2 Explanation of the model
* 3.3 Explanation of the model  
investigation. The average short-term CO\({}_{2}\) efficiency by crop absorption was 57.3% during the four days of daylight. For the medium term, more than 27 days, the efficiency of CO\({}_{2}\) enrichment was 45.5% on an average. The investigation demonstrated that the efficiency was not solely caused by the low levels of solar radiation or strong wind. In comparison, higher efficiency was achieved by higher solar radiation and weaker external wind. Since CO\({}_{2}\) could not be homogeneously spread far from the CO\({}_{2}\) tube (CO\({}_{2}\) source), CO\({}_{2}\) distribution depends on air circulation inside the greenhouse. Thus, the delivery system (air circulation and ventilation) must be designed to ensure an even distribution throughout the greenhouse. Additionally, [PERSON] et al. [14] showed that unequal distribution of CO\({}_{2}\) depends on temperature and location. A comparison showed that temperature is inversely proportional to the change in CO\({}_{2}\) distribution. As mentioned above, CO\({}_{2}\) enrichment plays a significant role in stable crop yield. Nevertheless, the detailed spatiotemporal distribution of CO\({}_{2}\) in foliage remains unknown. Most of time, chambers are used in experiments to readily regulate environmental conditions because of their comparatively simple design. In this study, the performance of a recently constructed photosynthesis model for CO\({}_{2}\) distribution was assessed using a photosynthetic chamber with exhaust fans on top of the chamber. The new chamber is a semi-closed hanging type chamber covering the entire plant and monitoring the real-time photosynthetic rate. The new chamber is shaped vertically because it is intended to completely cover plants, such as tomatoes. [PERSON] et al. [15] successfully tracked the time courses of tomato plants, the net photosynthetic rate, transpiration rate, and total conductance inside a monitoring system using a similar chamber. However, since measurement was conducted only for the photosynthetic rate and related environmental factors, the CO\({}_{2}\) distribution in the chamber was not well known. Computational fluid dynamics (CFD) has been applied in various research areas to predict and simulate a similar process close to the actual condition. Many researchers have analyze greenhouse designs, airflow, temperature, and radiation distribution in the agricultural field using CFD [16; 17; 18; 19; 20; 21]. Analysis of the detailed CO\({}_{2}\) distribution is rarely implemented and is still ongoing to date. [PERSON] et al. [11] showed that the efficiency of CO\({}_{2}\) distribution using CO\({}_{2}\) supplement/tube could save half of the fuel and achieve a higher CO\({}_{2}\) concentration compared with a CO\({}_{2}\) generator. CFD is a powerful tool for describing greenhouse microclimate, plant behavior [22], and photosynthesis. [PERSON] et al. [9] reported that photosynthesis could be simulated accurately using CFD in each cell of the domain corresponding to the crop. In their study, photosynthesis was computed as a function of the CO\({}_{2}\) concentration estimated by the CFD software. The CFD model made it possible to reveal airflow details above and within the canopy, effects of the different structures on water irrigation, and predicted crop transpiration [23; 24; 25]. The validity of the CFD results has been a perennial problem. However, the continuous development of computer and numerical methods enhances the accuracy of the simulation prediction and shows outstanding potential for analyzing complex airflow in a greenhouse [20].