The influence of buoyancy on vortex shedding from a heated square cylinder and its effects on the heat transfer of mixed convection were simulated.The flow equations, based on the velocity and the pressure, were solved along with the energy equation by a modified SIMPLER algorithm-the Quick Scheme and small Control Volume (QSCV) algorithm developed by the authors of the present paper.A set of optimized computational domain and artificial lateral boundary conditions were used along with the QSCV algorithm.Several cases were simulated for the Grashof numbers up to 1.8×105, the Reynolds numbers up to 500, and a range of angles between free stream velocity and gravity from 0 to 1.5π.In opposing flow, the results distinguish two different flow patterns: periodic flow for Gr＜Grc and steady flow with attached twin vortices for Gr＞Grc, and a precise correlation between Grc and Re expressed as Grc=0.00166(Re)2.97795 for Re up to 500 was firstly obtained.In cross flow, it could be seen that the Ri=Gr/Re2 plays a great role in the wake vortex patterns and the temperature fields.In aiding flow, it is found that the main flow currents cause a large expansion of the streamlines and isotherms in the direction normal to the free stream velocity.These changes in the wake vortex patterns and the temperature fields greatly modify the heat flux along the surface of the square cylinder and consequently, the heat transfer rate is strongly dependent upon the Reynolds numbers, the Grashof numbers, and the gravity direction.