The research studies the prediction of thermal characteristics for open designer shape of solar collector of flat plate of area 2.34m2, connected to water tank of 85 liter capacity . Mathematical model was represented and made the system of private accounts, transactions and through the creation of mathematical equations and solved numerically using the method of Finite Difference Method (FDM).The results of research is to obtain hot water at average temperatures up to 520C at mid-day during February month, as the water temperature is at its lowest value in this month in Baghdad city, with an average efficiency of the system up to 53.6% .This predictive study is compared with a previous measurement work and confirmed that the results match well.