An accurate numerical method for the solution of the two-dimensional, time-dependent incompressible fluid flow and heat transfer in complex geometries is described. The main features of the method are space discretization with the covolume approach of the governing equations on unstructured triangular grids, and the time discretization with the fractional step method. The method is successfully applied on geometries commonly used in compact heat exchangers, e.g. a sinusoidal and an arc-shaped wavy channel.