Eur. Phys. J. Plus (2020) 135: 178
https://doi.org/10.1140/epjp/s13360-019-00069-0

Regular Article

Investigation of entropy generation in stratified MHD Carreau nanofluid with gyrotactic microorganisms under Von Neumann similarity transformations

¹ Department of Applied Mathematics and Statistics, Institute of Space Technology, 2750, Islamabad, 44000, Pakistan
² Center of Excellence in Theoretical and Computational Science (TaCS-CoE), SCL 802 Fixed Point Laboratory Science Laboratory Building, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, Thailand
³ Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, Pakistan

^* e-mail: zahir1987@yahoo.com

Received: 16 July 2019
Accepted: 20 October 2019
Published online: 1 February 2020

Abstract

In this article Carreau nanofluid over a flat cylinder in the presence of suspended gyrotactic microorganisms and an inclined magnetic field is premeditated. The conversion of physical representation to mathematical form results in coupled partial differential equations which are compact to higher-order coupled ordinary differential equations using Von Neumann similarity transformations. Since the arising system of equations are coupled and highly nonlinear and cannot be solved for the exact solution. The system of nonlinear transformed differential equations are solved by using optimal homotopic scheme. The mathematical scheme is explained numerically through the software Mathematica. Influence of involved parameters is noted on the silhouettes of velocity, temperature, concentration and density number of motile microorganisms and fluxes using different forms of graphical representations. Moreover, the entropy generation is premeditated through contour portraits. Important observations are made that the bioconvection parameters and curvature augment the mass transfer rate of microorganisms. Also, the temperature difference parameter can be used to uplift the system’s efficiency.