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%