Eur. Phys. J. Plus (2020) 135: 106
https://doi.org/10.1140/epjp/s13360-020-00181-6

Regular Article

Entropy analysis for an MHD nanofluid with a microrotation boundary layer over a moving permeable plate

¹ Physics and Engineering Mathematics Department, Faculty of Engineering at Mataria, Helwan University, Cairo, Egypt
² Basic Sciences Department, Faculty of Engineering at Benha, Benha University, Cairo, Egypt
³ Basic Sciences Department, Faculty of Engineering, BADR University in Cairo BUC, Cairo, Egypt

^* e-mail: AHMED_BADR@m-eng.helwan.edu.eg

Received: 13 August 2019
Accepted: 28 October 2019
Published online: 23 January 2020

Abstract

Entropy analysis of an electrically conducting boundary layer of a nanofluid with microrotation elements over a moving plate is presented in this article by applying the second law of thermodynamics. Two types of nanoparticles, copper oxide (CuO) and aluminum oxide (Al₂O₃), are considered in addition to microstructure elements within a base fluid. The analysis is based on governing boundary layer equations associated with the linear and angular momentum as well as the energy transformed by introducing a suitable similarity transformation into a system of triple nonlinear differential equations that are solved analytically. On the physical side, this article examines the effect of the nanoparticle type and its concentration as well as the type of base fluid, whether Newtonian or non-Newtonian, on the rate of entropy generated and the rate of heat flux from the surface. This simulation involves the cooling stage of the metals during the heat treatment process, which controls the final mechanical properties of the plate, so controlling the entropy of the cooling system plays a great role on the results. The results obtained confirm that the entropy generation of the non-Newtonian fluids (fluids with microrotation elements) is higher than that of the Newtonian fluids and that the presence of nanoparticles in the cooling system increases the rate of entropy by 1–4% according to the type and concentration of the nanoparticles.