Authors:
K. K. Dhar,A. Mitra,P. Bhattacharya,DOI NO:
https://doi.org/10.26782/jmcms.2020.09.00008Keywords:
Brownian Motion,Isothermal Vertical Plate,Nano Fluid,Natural Convection,Thermophoresis,Two-Phase Model,Abstract
A numerical algorithm is presented for the laminar natural convection flow of a nanofluid along with an isothermal vertical plate. Nanofluid is treated as a two-component mixture as per Boungiorno model, and as such, the effects of Brownian motion and thermophoresis is incorporated. The equations governing the flow are higher-order nonlinear partial differential equations, and subsequently, they are transformed into a set of nonlinear ordinary differential equations using similarity transformation. Finally, they are reduced to a first-order system and we integrate them using Newton Raphson and adaptive Runge-Kutta methods. For the whole numerical procedure, computer codes are developed in the Matlab environment. We compute dimensionless stream function (s), longitudinal velocity (s′), temperature (θ), and nanoparticle volume fraction (f) and illustrate them graphically for various values of five pertinent dimensionless parameters, namely, Prandtl number (Pr), Lewis number (Le), buoyancy-ratio parameter (Nr), Brownian motion Parameter (Nb), and thermophoresis parameter (Nt). The reduced Nusselt number (Nur) is found to be a decreasing function of each of Nr (buoyancy-ratio parameter), Nb (Brownian motion parameter), and Nt (Thermophoresis parameter). The results of the present simulation agreeRefference:
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