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This paper reports the development of a refined wall-function strategy for the modelling of forced convection turbulent heat transfer over smooth and rough surfaces. In order to include the effects of fine-grain surface roughness, the present study extends a more fundamental work on the development of advanced wall functions of general applicability. The presently proposed model is validated through comparisons with heat transfer data available for internal flows through channels and for external flows over flat and curved plates with both smooth and rough surfaces. The validation results suggest that the presently proposed form is successfully applicable to a wide range of heat transfer problems over smooth and fine-grain rough surfaces.