JJMIE
Volume 9 Number 2, April.2015
ISSN 1995-6665
Pages 149 - 157
Jordan Journal of Mechanical and Industrial Engineering
Heatline Visualization of Buoyancy-Driven Flow inside a
Nanofluid-Saturated Porous Enclosure
Iman Zahmatkesh
*
Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran
Received 15 Jan 2015 Accepted 27 April 2015
Abstract
In the present paper, the heatline visualization technique is utilized to understand heat transport path for buoyancy-driven
flow inside a rectangular porous enclosure saturated with nanofluids. For this purpose, the mass, momentum and energy
conservation equations are solved numerically adopting a control-volume based computational procedure. Moreover, the
dimensionless heat function equation is utilized to determine the heat flow pattern inside the enclosure. Computations are
undertaken for Cu, Al
2
O
3
, and TiO
2
nanoparticles in the base fluid of water and corresponding results in terms of
dimensionless distributions of streamlines, isothermal lines, and heatlines as well as numerical values for flow strength and
the average Nusselt number are compared with those of pure water under different Darcy-Rayleigh numbers. Additionally,
the consequences of the nanoparticle fraction and the enclosure aspect ratio on the buoyancy-driven flow are analyzed.
Inspection of the presented results indicates that among Cu-water, Al
2
O
3
-water, and TiO
2
-water nanofluids, the Cu-water
one produces higher heat transfer rates that is attributed to higher thermal conductivity of the Cu nanoparticles.
© 2015 Jordan Journal of Mechanical and Industrial Engineering. All rights reserved
Keywords: Nanofluid, Porous Media, Buoyancy-Driven Flow, Heatline, Enclosure.
*
Corresponding author. e-mail: zahmatkesh5310@mshdiau.ac.ir.
Nomenclature
AR aspect ratio of the enclosure
Cv constant-pressure specific heat
Da Darcy number
g gravitational acceleration
h heat function
H enclosure height
k thermal conductivity
K medium permeability
L enclosure length
Nu local Nusselt number
average Nusselt number
Ra Darcy-Rayleigh number
T temperature
u,v velocity components in x- and y-directions
x,y Cartesian coordinates
X,Y dimensionless coordinates
Greek symbols
α thermal diffusivity
thermal expansion coefficient
θ dimensionless temperature
μ dynamic viscosity
dimensionless heat function
ρ density
ϕ nanoparticle fraction
ψ stream function (m
2
s-1)
dimensionless stream function
Subscripts
bf base fluid
C cold
nf nanofluid
p nanoparticle
1. Introduction
Recent years have witnessed extensive research on
convective heat transfer of nanofluids in the view of their
abnormally better thermophysical properties. Thereby, it is
not surprising to see some previous interests on the
analysis of buoyancy-driven flow inside nanofluid-
saturated porous enclosures. Sun and Pop [1], Chamkha
and Ismael [2], Ahmed et al. [3], Rashidi et al. [4],