Three-dimensional numerical simulations, for confined flows and unconfined flows, have been carried out to study the Karman vortex street inversion in the wake of a square cylinder. This paper is aimed to analyze the cause of the vortex inversion and to investigate the physical mechanisms. As two independent factors for the inversion, the wall confinement and the incoming flow conditions have been proved in a more rigorous way. It is shown that the interaction between the primary vortex and the incoming flow or the wall vortex layer is the fundamental cause. In order to compare the thermal transport phenomenon between the inversion and non-inversion cases, the top wall of a channel is kept at the free stream temperature and the bottom wall is set heated, while the cylinder is maintained adiabatic. The results indicate that the inversion phenomenon is not good for the heat transfer. Additionally, the effects of streamwise magnetic field on the vortex street inversion has been considered. (C) 2017 Elsevier Ltd. All rights reserved.