Effects of heights and a length on natural convection of three dimensional parallel plates with a heated bottom surface are investigated numerically. The compressibility of fluid induced by a high temperature difference is taken into consideration for simulating more realistic situations, and then the Boussinesq assumption is not necessary to be adopted. Methods of the Roe scheme, preconditioning and dual time stepping matching the method of LUSGS are simultaneously used to solve the compressible flow problem. Non-reflecting boundary conditions are held on apertures to prevent reflections from apertures induced by pressure waves. A CUDA computational platform is used to economize massive computing time. Under a low height case, the flow field is restricted by the shear force caused by the low height and displays a stable situation. Oppositely, under a high height case the flow field indicates active behaviors and an irregular situation is observed. (C) 2013 Elsevier Ltd. All rights reserved.