SUMMARYA local block reÿnement procedure for the e cient computation of transient incompressible ows with heat transfer is presented. The procedure uses patched structured grids for the blockwise reÿnement and a parallel multigrid ÿnite volume method with colocated primitive variables to solve the NavierStokes equations. No restriction is imposed on the value of the reÿnement rate and non-integer rates may also be used. The procedure is analysed with respect to its sensitivity to the reÿnement rate and to the corresponding accuracy. Several applications exemplify the advantages of the method in comparison with a common block structured grid approach. The results show that it is possible to achieve an improvement in accuracy with simultaneous signiÿcant savings in computing time and memory requirements.