On the interaction between the external magnetic field and nanofluid inside a vertical square duct

Kashif Ali,Shabbir Ahmad,Shahzad Ahmad,Muhammad Ashraf,Muhammad Asif

doi:10.1063/1.4934484

Abstract

In this paper, we numerically study how the external magnetic field influences the flow and thermal characteristics of nanofluid inside a vertical square duct. The flow is considered to be laminar and hydrodynamically as well as thermally developed, whereas the thermal boundary condition of constant heat flux per unit axial length with constant peripheral temperature at any cross section, is assumed. The governing equations are solved using the spectral method and the finite difference method. Excellent comparison is noted in the numerical results given by the two methods but the spectral method is found to be superior in terms of both efficiency and accuracy. We have noted that the flow reversal due to high Raleigh number may be controlled by applying an external magnetic field of suitable strength. Moreover, the Nusselt number is found to be almost a linear function of the nanoparticle volume fraction parameter, for different values of the Raleigh number and the magnetic parameter.

Highlights

An interaction between the hydrodynamic boundary layer and the electromagnetic field exhibits the magnetohyrodynamics (MHD) phenomenon
We have noted that the flow reversal due to high Raleigh number may be controlled by applying an external magnetic field of suitable strength
We numerically investigate the mixed convection in the hydrodynamically as well as thermally developed flow of a silver-water nanofluid in a vertical square duct, using the spectral method and the finite difference method (FDM)

Summary

INTRODUCTION

An interaction between the hydrodynamic boundary layer and the electromagnetic field exhibits the magnetohyrodynamics (MHD) phenomenon. The study has been extended to the case of two or more walls kept at a higher temperature by Lee.[14] Hwang et al.[15] has utilized the velocity–vorticity formulation to numerically solve the balance equations in the case of natural convection in a vertical rectangular duct with three adiabatic walls and the last one isothermal or subjected to a uniform heat flux. In Ref. 16 employed the stream function method to solve numerically the governing equations for mixed convection in a horizontal square duct or in a horizontal circular tube. We numerically investigate the mixed convection in the hydrodynamically as well as thermally developed flow of a silver-water nanofluid in a vertical square duct, using the spectral method and the finite difference method (FDM). F Re is found to be more sensitive to nanoparticle volume fraction parameter for the smaller values of the later

MATHEMATICAL FORMULATION

NUMERICAL SOLUTION

RESULTS AND DISCUSSION

Spectral Method f Re

CONCLUSIONS