In this study, a different design of passive air Solar Chimney(SC)was tested by installing it in the south wall of insulated test room in Baghdad city. The SC was designed from vertical and inclined parts connected serially together, the vertical SC (first part) has a single pass and Thermal Energy Storage Box Collector (TESB (refined paraffin wax as Phase Change Material(PCM)-Copper Foam Matrix(CFM))), while the inclined SC was designed in single pass, double passes and double pass with TESB (semi refined paraffin wax with copper foam matrix) with selective working angle ((30^o, 45^o and 60^o). A computational model was employed and solved by Finite Volume Method (FVM) to simulate the air induced through the test room by SC effect. The governing equation of Computational Fluid Dynamic (CFD) model was developed by the effective heat capacity method equation to describe the heat storage and release from PCM-CFM. Practical and computational Results referred to increase in thermal conductivity of the paraffin wax that supported by CFM than 10 times, while the ventilation effect is still active for hours after sun set amount. The maximum ventilation mass flow rate with TESB collector was 36.651 kg/hr., when the overall discharge coefficient equals 0.371. Also, the experimental results referred to the best working angle range 45~60^o, while the highest approaching temperature (between air and collector) was appeared for the double passes flat plate collector. Results gave higher heat storage efficiency 47% when the maximum solar radiation 780 W/m² at 12.00 pm, and the energy summation through duration of charging time was 18460 kJ. Double passes SC at 60^o angle presented the highest efficiency with value approaching to 73%, while TESB collector efficiency depicted highest efficiency value 70% at 12:00 pm.