Consequence of Modified Boundary Condition On Natural Convection in a Porous Medium Saturated by Nanofluid – A Computational Approach

Abstract

In the present numerical simulation, steady, laminar, two-dimensional flow in a porous medium saturated by nanofluid [1] along an isothermal vertical plate is presented. Here we have studied a more realistic situation where the nanoparticle volume fraction at the plate (boundary condition) is passively controlled by assuming that its flux there is zero. We employ Boungiorno model [2] that treats the nanofluid as a two-component mixture, incorporating the effects of Brownian motion and thermophoresis. Darcy model is utilized for the presence of porous medium. With the help of appropriate similarity variables, the governing nonlinear partial differential equations of flow are changed to a bunch of nonlinear ordinary differential equations. Afterwards, they are reduced to a first order system and integrated using Newton Raphson and adaptive Runge-Kutta methods. The computer codes are developed for this numerical analysis in Matlab environment. Dimensionless stream function (s), longitudinal velocity (s’), temperature (θ) and nanoparticle volume fraction (f) are figured and outlined graphically for various values of four dimensionless parameters, namely, Lewis number (Le), buoyancy-ratio parameter (Nr), Brownian motion Parameter (Nb), and thermophoresis parameter (Nt). The dependence of the reduced Nusselt number on these parameters is illustrated.