The heat transfer performance of a 5 mm internal diameter (I.D.) mesoscale continuous oscillatory flow crystalliser with smooth periodic constrictions (herein called SPC meso-tube) is herein reported for the first time for both steady flow and unsteady oscillatory flow conditions. Experimental values of the tube-side Nusselt number, Nu(t), accompanied by an estimability analysis, emphasized the key role played by smooth constrictions and bulk flow velocity in controlling tube-side heat transfer, while revealing a weaker influence of oscillatory flow on heat transfer enhancement in the SPC meso-tube. Although the presence of smooth constrictions provided an increased surface area to volume (SAV) ratio, and recirculation zones which promoted heat transfer rates, a maximum 1.7-fold heat transfer augmentation was obtained when fluid oscillations were combined with smooth constrictions. The behaviour of the SPC meso-tube was such that increasing the net flow Reynolds number, Re-n, from 11 up to 54 with the combination of smooth constrictions and oscillatory flow resulted in the attainment of higher rates of heat transfer up to a maximum Nu(t) of 3.09. The Strouhal number, St, was also found to have a more significant effect on the heat transfer performance than oscillatory frequency, f. An empirical correlation was for the first time developed to describe the heat transfer characteristics of the SPC meso-tube, and predict Nu(t) based on experimental data for the range of net flow and oscillatory flow conditions investigated. A parameter estimability approach was also implemented to enhance the prediction capability of the correlation. The approach was based on a sequential orthogonalisation, thanks to which the most influential factors affecting the tube-side heat transfer were identified given the available experimental data. Overall, the results accentuate the efficient heat transfer capabilities of the SPC meso-tube in the laminar flow regime, and its suitability for performing cooling crystallisations where tight temperature control of supersaturation is essential. (C) 2018 Elsevier Ltd. All rights reserved.