Double diffusive convection in nanofluids analytical and computational studies

Abstract

The effect of a vertical magnetic field on the stability of a horizontal binary nanofluid layer is investigated using the normal mode technique and one-term Galerkin approximation. The results are encapsulated in Eq. (2.53) for stationary convection and Eqs. (2.57)-(2.58) for oscillatory motions. Complex expressions for Rayleigh number are simplified using valid approximations for analytical study and numerical investigations are made using alumina-water nanofluid. Darcy-Brinkman model for porous medium is used to study the impact of vertical magnetic field on double-diffusive convection in a nanofluid layer. The analysis is carried out within the framework of linear stability theory, normal mode analysis and single-term Galerkin approximation. The present chapter investigates the double-diffusive convection in a rotating nanofluid layer for both types of configurations: top-heavy and bottom-heavy. It has been found that the critical values of wave number and Rayleigh number exhibit a significant rise in their values with the rise in Taylor number. Darcy-Brinkman model is applied to study double-diffusive convection problems to consider the impact of rotation/Coriolis force and porosity. The relevant partial differential equations are solved using the methodologies of superposition of basic possible modes and single-term Galerkin approximation. The critical wave number and critical Rayleigh number show a significant rise with a rise in rotation parameters for nanofluid flow in a porous medium. A modified model incorporating differential conductivity effects of nanoparticles is used to investigate the instability of a binary nanofluid layer analytically and numerically. The partial differential equations based on conservation laws are translated into an eigenvalue problem using normal modes and the Galerkin type weighted residual method. The nanoparticle volume fraction is assumed to be constant in the initial state which leads to an expression for Rayleigh number T R as given by Eq. (7.35). newline