Eur. Phys. J. Plus (2017) 132: 187
https://doi.org/10.1140/epjp/i2017-11454-4

Regular Article

A bioconvection model for a squeezing flow of nanofluid between parallel plates in the presence of gyrotactic microorganisms

¹ Department of Mathematics, College of Science, King Saud University, PO. Box 2455, 11451, Riyadh, Saudi Arabia
² Department of Mathematics, Faculty of Sciences, HITEC University Taxila Cantt, Taxila, Pakistan
³ Department of Mathematics, Mohi-ud-Din Islamic University, Nerian Sharif, Azad Jammu and Kashmir, Pakistan
⁴ Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan

^* e-mail: umar_jadoon4@yahoo.com

Received: 24 February 2017
Accepted: 14 March 2017
Published online: 26 April 2017

Abstract

This article deals with the bioconvection flow in a parallel-plate channel. The plates are parallel and the flowing fluid is saturated with nanoparticles, and water is considered as a base fluid because microorganisms can survive only in water. A highly nonlinear and coupled system of partial differential equations presenting the model of bioconvection flow between parallel plates is reduced to a nonlinear and coupled system (nondimensional bioconvection flow model) of ordinary differential equations with the help of feasible nondimensional variables. In order to find the convergent solution of the system, a semi-analytical technique is utilized called variation of parameters method (VPM). Numerical solution is also computed and the Runge-Kutta scheme of fourth order is employed for this purpose. Comparison between these solutions has been made on the domain of interest and found to be in excellent agreement. Also, influence of various parameters has been discussed for the nondimensional velocity, temperature, concentration and density of the motile microorganisms both for suction and injection cases. Almost inconsequential influence of thermophoretic and Brownian motion parameters on the temperature field is observed. An interesting variation are inspected for the density of the motile microorganisms due to the varying bioconvection parameter in suction and injection cases. At the end, we make some concluding remarks in the light of this article.