Within the framework of the classical availability of heterogeneous nucleation, a scaled exergetic model has been developed to elucidate the two-dimensionality effects on the potency factor which is an explicit dimensionless scaled parameter for the nucleation barrier height. The effects of system geometry and substrate wettability on the thermodynamics of heterogeneous nucleation on a two-dimensional curved substrate are studied. The difference in the potency factor between two-dimensional nucleation on a convex and a flat substrate is always positive and has a maximum value for a given size factor. The regime of the associated contact angle related to maxima are in the cluster-phase-philic regime irrespective of the substrate size or the three phases associated with heterogeneous nucleation. On the other hand, the difference in the potency factor between heterogeneous nucleation on a concave and a planar substrate is always negative and has a minimum value for a given size factor. In this case, the regime of the associated contact angle related to maxima are in the cluster-phase-phobic regime irrespective of the substrate size or the three phases associated with heterogeneous nucleation. The potency factor has lower values in case of concave substrate and has higher values in case of convex substrate and heterogeneous nucleation on a flat substrate is always in between that of the convex substrate and the concave substrate. (C) 2019 Elsevier Ltd. All rights reserved.