In this article we employ homotopy analysis method (HAM), to study the entropy analysis in an unsteady magneto-hydrodynamic nano-fluid regime adjacent to an accelerating stretching permeable surface with the water as the base fluid and four different types of nanoparticles; copper (Cu), copper oxide (CuO), aluminum oxide (Al2O3) and titanium dioxide (TiO2). The governing partial differential equations are transformed into highly nonlinear coupled ordinary differential equations consisting of the momentumand energy equations via appropriate similarity transformations. The current HAM solution demonstrates very good correlation with those of the previously published studies in the especial cases. The influences of different flow physical parameters such as the nanoparticle volume fraction parameter (φ), unsteadiness parameter (A), magnetic parameter (M), suction parameter (fw), and different types of nanoparticles on the fluid velocity component (f′(η)), the temperature distribution (θ(η)), the skin friction coefficient (CfRex 1/2), the local Nusselt number (Nux/Rex 1/2), and the averaged entropy generation function (NG,av) and also the effects of the Reynolds (Re) number, the Brinkman number (Br) and the Hartmann number (Ha) on the averaged entropy generation function (NG,av) are illustrated graphically and discussed in details. This model has important applications in heat transfer enhancement in the renewable energy systems, industrial thermal management and also materials processing.

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