In this study, exergy destruction is studied theoretically in a methodological manner for flow systems. The equation of the rate of flow exergy destruction is derived beginning from the definition of exergy for forced convective flow through a duct. The second law of thermodynamics is applied on convective systems to investigate the irreversibilities which are the indicator of the destruction of available work named also as exergy destruction. Explicit form of exergy destruction equation for incompressible Newtonian fluid flow in two-dimensional Cartesian coordinates is presented as an example. A new term for dimensional quantitative results of flow exergy destruction, named exergy destruction factor, is also introduced. The study, being important for all academic researchers as well as engineers in efforts of research and development, will be helpful for understanding exergy destruction with the physics of incompressible transient laminar convection in ducts. The study addresses the fundamentals of thermodynamics.