Green–Naghdi fluid with non-thermal equilibrium effects

Abstract

A. E. Green, FRS and P. M. Naghdi developed a new theory of continuum mechanics based on an entropy identity rather than an entropy inequality. In particular, within the framework of this theory, they developed a new set of equations to describe viscous flow. The new theory additionally involves vorticity and spin of vorticity. We here develop the theory of Green and Naghdi to be applicable to thermal convection in a fluid in which is suspended a collection of minute metallic-like particles. Thus, we develop a non-Newtonian theory we believe capable of describing a nanofluid. Numerical results are presented for copper oxide or aluminium oxide particles in water or in ethylene glycol. Such combinations are used in real nanofluid suspensions.