Eur. Phys. J. Plus (2016) 131: 101
https://doi.org/10.1140/epjp/i2016-16101-0

Regular Article

Nonlinear convective analysis of a rotating Oldroyd-B nanofluid layer under thermal non-equilibrium utilizing Al₂O₃-EG colloidal suspension

¹ Department of Mathematics, Amity Institute of Applied Sciences, Amity University, Noida, Uttar Pradesh, India
² Department of Mathematics, Jaypee Institute of Information Technology, Noida, Uttar Pradesh, India

^* e-mail: drshilpimath@gmail.com

Received: 17 September 2015
Accepted: 17 February 2016
Published online: 18 April 2016

Abstract

In this paper, we examine a layer of Oldroyd-B nanofluid for linear and nonlinear regimes under local thermal non-equilibrium conditions for the classical Rayleigh-Bénard problem. The free-free boundary condition has been implemented with the flux for nanoparticle concentration being zero at edges. The Oberbeck-Boussinesq approximation holds good and for the rotational effect Coriolis term is included in the momentum equation. A two-temperature model explains the effect of local thermal non-equilibrium among the particle and fluid phases. The criteria for onset of stationary convection has been derived as a function of the non-dimensionalized parameters involved including the Taylor number. The assumed boundary conditions negate the possibility of overstability due to the absence of opposing forces responsible for it. The thermal Nusselt number has been obtained utilizing a weak nonlinear theory in terms of various pertinent parameters in the steady and transient mode, and has been depicted graphically. The main findings signify that the rotation has a stabilizing effect on the system. The stress relaxation parameter inhibits whereas the strain retardation parameter exhibits heat transfer utilizing Al₂O₃ nanofluids.