The Degree of Adaptation for the Establishment and Orientation of the Old and New Educational Buildings of Dezful City with the Climatic Conditions Based on the Law of Cosines

ABSTRACT
This study aimed to identify the degree of adaptation for the establishment and orientation of old and new educational buildings in Dezful city with the climatic conditions to use the climatic capabilities during school activities and reduce the use of heating and cooling equipment. The law of cosines method and Q Basic software were used to extract the most appropriate pattern of establishing schools based on the climatic conditions. First, the amount of radiant energy received on vertical surfaces was theoretically and realistically calculated for 24 geographical directions based on the climate data of Dezful weather station in the period (1986-2019). Subsequently, the most appropriate direction and other preferred routes were identified and presented, culminating in an examination of the educational buildings in the field. Fifteen examples from old, new, and refurbished schools were selected to compare the general orientation of the buildings with the pattern derived from the law of cosines. Based on the results of Kisnos law and considering the climatic conditions of Dezful city, both in two-sided buildings, and in four-sided buildings, the south direction is the most suitable direction for the installation of walls and openings. When the orientation of these schools is compared to the proper model derived from the study, it becomes clear that the appropriate model has been seen in both new and ancient cases. Of course, openings were built in all geographical directions, as shown in several examples. However, the compatibility with the desired pattern in new schools is generally higher than in old schools.
 
Extended Abstract
Introduction
One of the important topics in architectural studies is the role of climate factors in each region. In Iran, the climatic diversity has led to the formation of different spaces due to architecture. In addition to adapting and coordinating structures with climate conditions, paying attention to climatic designs also lowers the use of fossil fuels and saves energy. This study aimed to determine the appropriate orientation for the educational buildings of this city so that the best living conditions are provided for the comfort and learning of students in the classrooms.
 
Methodology
For the law of cosines, in the first step, the angle of radiation and the angle of the direction of radiation were calculated using calculation relationships, and Q-Basic software for the latitude of Dezful city. Subsequently, the angle of deviation (Mdarmil) and the duration of daylight for each month in Dezful city were computed. Utilizing the cosine law and effective temperature calculation methods, the theoretical and empirical amounts of direct energy radiated hourly on vertical surfaces across 24 geographical orientations were determined, based on the climatic data from the Dezful meteorological station from 1986 to 2019.  Using the effective temperature output for twelve hours each month, the hot and cold periods of the year were separated. Finally, the most suitable directions for the establishment of two- and four-sided educational buildings were introduced based on the largest difference in energy received in Dezful city. Then, old and new schools of Dezful city were examined, and the degree of adaptation of these buildings to the region's climatic conditions was examined.
 
Results and discussion
Hourly temperature was obtained using the average of maximum and minimum temperature and the monthly average temperature. Then, using the law of cosines, the amount of direct solar radiation reaching a level on the Earth's surface was calculated. To obtain theoretical hours, the amount of energy radiated on vertical walls was calculated for all geographical directions at a distance of 15 degrees and in all 12 months of the year in Dezful city. However, in some months and at certain hours of the day, the weather is cloudy and prevents sunlight when rain systems enter the region. Therefore, radiation energy calculated for different directions for different months should be made more realistic. The percentage of sunny hours in a given month is calculated by dividing the statistics of sunlit hours at the Dezful meteorological station by the duration of the day in that month in order to obtain values that are close to the actual amount of solar energy. Subsequently, each month's theoretical values of solar energy are multiplied by the percentage of sunny hours in the month in question to arrive at the closest possible value of solar energy.  The highest amount of energy belongs to +135 degrees (southeast) and -135 degrees (southwest). The lowest amount of energy belongs to the north direction. It can also be seen that in the cold season, the southern geographical direction received the highest amount of energy by receiving 4755 BTUs of energy, on the contrary, in the hot summer months, the direction of windows and openings, as well as the walls exposed to radiation to the southwest, is completely unfavorable and will greatly aggravate the summer heat conditions.
In buildings with 2 opposite main facades and receiving energy from these two facades, the total energy radiated to both facades was calculated. Based on the climatic conditions of Dezful city, the intensity of heat in the hot period, especially in June to August, is much higher than the intensity of cold in December to February.
As a result of choosing a two-way direction that receives the least energy throughout the year, the south-north directions with 6440 BTUs (57.6%) are more favorable than the west-east direction with 11169 BTUs (100%).
Hence, the building can receive thermal energy from four sides. The optimal direction of four-sided buildings is based on the lowest amount of energy intake throughout the year based on the climatic conditions of Dezful city in the north-southeast-west direction.
Conclusion
Despite Dezful city being tropical at first glance, considering that most of the school activity period is in the second half of the year, in which the air temperature, especially in the morning hours, is below the comfort threshold of students. The orientation of schools and windows, as well as the design pattern of schools, should be configured to optimize the utilization of solar radiation to provide the interior spaces of the classrooms with heat and illumination.  Additionally, the law of cosines indicates that the optimal orientation for schools is south in one-sided structures and south-north in two-sided structures. The direction of north-south and west-east is the best and most appropriate for four-sided buildings, and Dezful schools are generally of this type. Based on the orientation table of old and new schools selected as examples, both in the orientation of old schools and in the newly established schools, a combination of south, north, and west and east directions can be seen. However, in general, in the newly established schools, the direction of the south was observed more.
 
Funding
There is no funding support.
 
Authors’ Contribution
All of the authors approved the content of the manuscript and agreed on all aspects of the work.
 
Conflict of Interest
Authors declared no conflict of interest.
 
Acknowledgments
We are grateful to all the scientific consultants of this paper.