The present paper describes the numerical modelling of turbulent flow and convective heat transfer for two types of two-dimensional forced unsteady flows: periodically oscillating flow through an abrupt pipe expansion, and flow over a backward facing step with periodic injection and ingestion through a slot at the separation corner. In both cases the flow Reynolds numbers are reasonably high and emphasis is placed on the resulting heat transfer rates in the separated and recovery regions of the flow. The present work tests the two-equation linear k -e (Launder and Sharma, 1974) and a modified two-equation non-linear k -e (Craft et al., 2005) turbulence model in conjunction with the Reynolds-averaged momentum (URANS) and temperature equations. The imposed unsteadiness enhances the coherence of the separated shear layers and reduces the reattachment lengths. Both models are shown to broadly capture this effect, with the non-linear scheme giving better quantitative agreement with available experimental data. Key words: Eddy-viscosity model, Convective heat transfer, Imposed unsteadiness, URANS.