Eur. Phys. J. Plus (2017) 132: 425
https://doi.org/10.1140/epjp/i2017-11680-8

Regular Article

Presence of different shapes of ZrO₂ nanoparticles in the melting heat transfer of a Casson flow

¹ Dept. of Mathematics, A. B. N. Seal College, Pin: 736101, West Bengal, India
² Department of Mathematics, Jadavpur University, 700032, Kolkata, India

^* e-mail: tausifdropbox@gmail.com

Received: 27 July 2017
Accepted: 28 August 2017
Published online: 16 October 2017

Abstract

In the present paper, we figured the MHD boundary layer emanation of a Casson fluid with suspended ZrO₂ nanoparticles of four different shapes over a flat surface with melting heat transfer. In this study, two diverse cases of controlling nanoparticle (i.e. active and passive control) have been considered. The concerned governing equations with appropriate boundary conditions and similarity transformations are solved analytically using the optimal homotopy analysis method and numerically using the Runge-Kutta 5th-order method, to develop an optimized solution. In the relevant governing equations we have blended the single-phase and two-phase model to detect the heat transportation development at the nanoscale as well as the distribution of nanoparticles in the flow system. Several tables and figures have been drawn to show the consequence of particular shapes of nanoparticles, Casson parameter, melting process, Brownian motion, thermophoresis and the presence of nanoparticles on the properties of the current flow system. We show that our outcomes have an admirable level of agreement with experimental results from the literature.