Abstract: Restart process of hot oil pipeline is kind of unstable coupled flow that physical property of oil varies with oil temperature. Governing equations are available according to laws of conservation of mass, momentum and energy, which are general for unsteady flow and heat transfer in round pipelines. If oil physical property is independent on temperature, the main governing equations of unsteady coupled flow with constant physical property can be derived. On the condition of temporal affecting factor to be ignored, main governing equations of steady coupled flow are given.