Effect of an uniform magnetic field on unsteady natural convection of nanofluid

Abstract

In this work, the problem of the unsteady natural convection in an ${\rm Al}_2{\rm O}_3 $-water filled nanofluids influenced by an uniform magnetic field is analysed numerically. Governing equations are given in terms of the streamlines, the vorticity and the temperature of the fluid. Dual Reciprocity Boundary Element Method (DRBEM) is performed as a solution technique. Both the fundamental solutions of Laplace equation $(({1}/{2 \pi })\ln (x)) $ and modified Helmholtz equation $({1}/{2 \pi })K_0(x)) $ are used in the derivation of the method. The numerical analysis are done for physical parameters Rayleigh number ( $10^3\leq Ra\leq ~10^6 $), Hartmann number ( $0\leq Ha \leq ~75 $) and particle volume fraction ( $0\leq \phi \leq ~0.2 $). From the results, it is observed that the behaviours of all the variables are influenced by the changing values of parameters. The solution procedure of the all variables needs considerably small number of iterations and large time increments with suitable values of relaxation parameters which occur in the argument of Bessel function $K_0(x) $.

Keywords

• drbem
• natural convection flow
• nanofluid
• magnetic field