The present investigation reveals the impact of mixture of nanoparticles (Al2O3 and Cu) in basefluid and convective heating on the power-law shrinking curved surface with radius of curvature (K). The homogeneous hybrid nanoliquid (0.1% of Al2O3 - Cu/water) model with theoretical and fitted (predicted) experimental correlations is transformed into coupled system of non-linear ordinary differential equations for finding possible branches of the solution. The critical values (c(c), beta(c) and chi(c)) have been evaluated for some cases, beyond these values there is either no solution or multiple solutions exist. Two different nanofluid models (Model I and II) are compared and found to be contradictory for skin friction and Nusselt number in current physical model. Linear stability analysis for finding stable branch, is also performed through construction of eigenvalue (EV) problem. The MATLAB built-in package LinearFit.model is used for multiple regression estimation (MRE) in case of stable branch which shows that nanoparticle concentration has maximum contribution towards the heat transfer. Moreover, the wall skin friction has strong dependence on curvature parameter. As Prandtl number increases, the linearly fitted model is found to be more suitable for convective boundary case (gamma = 0.5). (C) 2019 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.