Energy and Power En gi neering, 2011, 3, 174-180
doi:10.4236/epe.2011.32022 Published Online May 2011 (http://www.SciRP.org/journal/epe)
Copyright © 2011 SciRes. EPE
Investigation of Natural Convection Heat Transfer
Coefficient on Extended Vertical Base Plates
Mahdi Fahiminia1, Mohammad Mahdi Naserian2, Hamid Reza Goshayeshi1, Davood Majidian3
1Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran
2Young Researchers Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran
3Department of Systems Engineering, Virginia Polytechnic Institute and State University, USA
E-mail: MFahiminia@Gmx.com, Mmahnas@yahoo.com, Goshayshi@yahoo.com, DMajidian@yahoo.com
Received December 21, 2010; revised April 8, 2011; accepted April 15, 2011
Abstract
In this research, computational analysis of the laminar natural convection on vertical surfaces has been in-
vestigated. Natural convection is observed when density gradients are present in a fluid acted upon by a
gravitational field. Our example of this phenomenon is the heated vertical plate exposed to air, which, far
from the plate, is motionless. The CFD simulations are carried out using fluent software. Governing equa-
tions are solved using a finite volume approach. Coupling between the velocity and pressure is made with
SIMPLE algorithm. The resultant system of discretized linear algebraic equations is solved with an alternat-
ing direction implicit scheme. Then a configuration of rectangular fins is put in different ways on the surface
and natural convection heat transfer coefficient on these no slope surfaces is studied and finally optimization
is done.
Keywords: Natural Convection, Vertical Surfaces, Simple Algorithm, Rectangular Fins
1. Introduction
In this document Natural convection is observed as a
result of fluid movement which is caused by density gra-
dient. A radiator which is used for warming the house is
an example of practical equipment for natural convection.
The movement of fluid, whether gas or liquid, in natural
convection is caused by buoyancy force due to density
reduction beside to surfaces in heating process. When an
external force such as gravity, has no effect on the fluid
there would be no buoyancy force, and mechanism
would be conduction. But gravity is not the only force
causing natural convection. When a fluid is confined in
the rotating machine, centrifugal force is exerted on it
and if one or more than one surfaces, with more or less
temperature than that of the fluid are in touch with the
fluid, natural convection flows will be experienced. The
fluid which is adjacent to the vertical surface with con-
stant temperature, the fluid temperature is less than the
surface temperature, forms a velocity boundary layer.
The velocity profile in this boundary layer is completely
different with the velocity profile in forced convection.
The velocity is zero on the wall due to lack of sliding.
Then the velocity goes up and reaches its maximum and
finally gets zero on the external border of velocity
boundary layer. Since the factor that causes the natural
convection, is temperature gradient, the heating bound-
ary layer appears too. The temperature profile has also
the same value as the temperature of wall due to the lack
of particles sliding on the wall, and temperature of parti-
cles goes down as approaching to external border of
temperature boundary layer and it would reach the tem-
perature of far fluid. The initial enlargement of boundary
layer is laminar, but in the distance from the uplifting
edge, depending on fluid properties and the temperature
difference of the wall and the environment, eddies will
be formed and movement to turbulent zone will be
started.
However, relatively little information is available on
the effect of complex geometries on natural convection.
Numerous experimental [1-4] and numerical [5] studies
of rectangular fin heat sinks have been carried out [1].
Since the pioneering experimental work of Ray in 1920,
natural or free convection has developed into one of the
most studied topics in heat transfer. Jofre and Barron
obtained data for heat transfer to air from vertical ex-
tended surface [2]. At RaL = 109 they quoted an im-
provement in the average Nusselt number of about 200%