In this paper, obtaining the characteristics of unsteady three-dimensional incompressible flows with heat transfer along with artificial compressibility of Chorin is investigated. At first, compatibility equations and pseudo characteristics for three-dimensional flows are derived from five governing equations (continuity equation, momentum equations in three directions, and energy equation) and then results are simplified to two-dimensional flows. Pseudo Mach hyper-cone (four-dimensional cone) is found, and its cross-section with physical axis is calculated numerically. Unlike compressible flow, this is not a sphere. It is found that the pseudo-acoustic speed within the incompressible flow is a function of the artificial compressibility parameter and the directions. In two-dimensional flow, Pseudo Mach cone is obtained by numerical solution of characteristic equations. Unlike compressible flow, the cross-section of Mach cone with the x-y plane is not a circle. This shape is not oval, too. The influence of artificial compressibility parameter on convergence history and accuracy is surveyed by simulation of cavity flow as a benchmark.
