With the development of building construction engineering and the way to obtain energy from natural sources, the sun has become an important source to avail from thermal energy. In this research, the study of the long-term thermal performance of a passive solar heating system containing an absorber and storage wall was done by using the general design utilizability Method The equations of the mathematical model for this system were solved using the MATLAB environment program. In order to calculate the values of the solar refractive index (f) for this system for the four months of the winter season (November to February). The climatic conditions during these months are the daily values based on the monthly average in the city of Kut (Iraq). Since the best type of wall is the concrete wall, changes are made to this type of wall. A number of variables that affect the performance of the wall have been changed, including in it = wall area, wall thickness. The results showed that increasing the wall area and decreasing the thickness leads to an increase in the value of the solar refractive index, and the maximum values of the solar refractive factor were found during November, and the concrete material is the best performing material among brick and stone material, according to previous studies.