This paper considers the study of electrically conducting alumina-water nanofluid flow induced by horizontal shrinking cylinder under the effect of velocity and thermal slip at the surface. The Buongiorno's non-homogenous model is implemented which accounted with the nanolayer based effective thermal conductivity and Nielsen's effective viscosity model. The governing transport model for nanofluid has been transformed into a set of nonlinear similarity equations and solved with a shooting technique using MATLAB ode solver and 'fsolve' command. The behavior of skin friction, velocity, Nusselt number and temperature are investigated numerically. The increasing trends of Nusselt number as well as skin friction are noticed as nanoparticle concentration increases at the outer surface of the boundary layer. Nusselt number is found to be decreasing nonlinearly with nanoparticle diameter ranging from 5 nm to 60 nm. Two branches of solution are also captured in some fixed range of involving parameter, namely mass transfer (suction), curvature and shrinking parameters. The physical existence of these branches is also discussed. (C) 2017 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.