Rayleigh-Bénard Convection for Nanofluids for More Realistic Boundary Conditions (Rigid-Free and Rigid-Rigid) Using Darcy Model

Jyoti Ahuja,Urvashi Gupta

doi:10.33889/ijmems.2019.4.1-013

Abstract

In this article, Rayleigh-Bénard convection for nanofluids for more realistic boundary conditions (rigid-free and rigid-rigid) under the influence of the magnetic field is investigated. Presence of nanoparticles in base fluid has introduced one additional conservation equation of nanoparticles that incorporates the effect of thermophoretic forces and Brownian motion and the inclusion of magnetic field has introduced Lorentz’s force term in the momentum equation along with Maxwell’s equations. The solution of the Eigen value problem is found in terms of Rayleigh number by implementing the technique of normal modes and weighted residual Galerkin approximation. It is found that the stationary as well as oscillatory motions come into existence and heat transfer takes place through oscillatory motions. The critical Rayleigh number for alumina water nanofluid has an appreciable increase in its value with the rise in Chandrasekhar number and it increases moderately as we move from rigid-free to both rigid boundaries. The effect of different nanofluid parameters on the onset of thermal convection for two types of boundaries is investigated.

Highlights

The thermal instability of a fluid layer in a porous medium has emerged as an evident problem considering its widespread usage across various utility applications such as enhanced oil recovery, storage of agricultural products, geothermal reservoirs and the underground pollutant transport
The present article investigates Rayleigh-Bénard convection for nanofluids under the influence of magnetic field for more realistic boundary conditions: rigid-free and rigid-rigid
The solution of the eigen value problem is found in terms of Rayleigh number by implementing the technique of normal modes and weighted residual Galerkin approximation

Summary

Introduction

The thermal instability of a fluid layer in a porous medium has emerged as an evident problem considering its widespread usage across various utility applications such as enhanced oil recovery, storage of agricultural products, geothermal reservoirs and the underground pollutant transport. A nanofluid is basically a fluid that is formed by suspending particles of nano-sized such as ceramics, metals, oxides, nitrides, and semiconductors in base fluids like water, ethylene glycol, oil etc. The usefulness of these suspensions is revealed in the study (Choi, 1995) which emphasizes the importance of nanofulids in enhancing the heat transfer mechanism because of exhibiting enormously high thermal conductivity. The present formulation of the thermal convection problem introduces the impact of permeability and vertical magnetic field using the Darcy model for a porous medium for two types of boundaries: bothrigid and rigid-free. Elimination of these unknowns from the obtained set of equations gives the Eigen value equation

Results and Discussion

13 Pr1 35 2520 5 35

Conclusions