Proceedings of the
International Conference on Mechanical Engineering 2011
(ICME2011) 18-20 December 2011, Dhaka, Bangladesh
ICME11-FL-050
© ICME2011 1 FL-050
1. INTRODUCTION
Natural convection in enclosures has attracted
considerable interest of investigators. Such type of flow
has a wide range of applications, for example, multi-pane
windows, cooling of electronic equipment, solar thermal
central receiver design, aircraft break-housing systems
design and in other building and equipment components.
Especially recently, sloped windows and skylights have
been more and more frequently applied in buildings,
which makes it necessary to gain more understanding on
the natural convection in the cavities.
A large numbers of literatures are available which deal
with the study of natural convection in enclosures [1-3]
with either vertical or horizontal imposed heat flux or
temperature difference. Hadjisophocleous et al. [4]
solved the natural convection of a square cavity problem
by no orthogonal boundary fitted coordinate system.
However, they compared their results with that of de Vahl
Davis [5] and Markatos and Perikleous [6] which is a
regular geometry problem. Chan and Tien [7] studied
numerically shallow open cavities and also made a
comparison study using a square cavity in an enlarged
computational domain. They found that for a square open
cavity having an isothermal vertical side facing the
opening and two adjoining adiabatic horizontal sides,
satisfactory heat transfer results could be obtained,
especially at high Rayleigh numbers. In a similar way,
Mohamad [8] studied inclined open square cavities, by
considering a restricted computational domain. Different
from those by Chan and Tien [9], gradients of both
velocity components were set to zero at the opening
plane. It was found that heat transfer was not sensitive to
inclination angle and the flow was unstable at high
Rayleigh numbers and small inclinations angles. G. Saha
et al [10] investigated a numerical simulation of
two-dimensional laminar steady-state natural convection
in a square tilt open cavity. The results show that the
Nusselt numbers increases with the Rayleigh numbers.
Also the average Nusselt number changes substantially
with the inclination angle of the cavity while better
thermal performance was also sensitive to the boundary
condition of the heated wall.
Finite element (FE) analysis is a method to
numerically solve partial differential equations which
can be applied to many problems in engineering. The
method has been extended to solve problems in several
other fields such as in the field of heat transfer,
electromagnetic, biomechanics, complex structural
problems [11-13]. In spite of the great success of the
method in these fields, its application to fluid mechanics
is still under intensive research. This is due to the fact
that the governing differential equations for general flow
problems consist of several coupled equations that are
inherently nonlinear. Accurate numerical solutions thus
require a vast amount of computer time and data storage.
One-way to minimize the amount of computer time and
data storage used is to employ an adaptive meshing
technique [14]. The technique places small elements in
the regions of large change in the solution gradients to
increase solution accuracy, and at the same time, uses
large elements in the other regions to reduce the
computational time and computer memory.
The objective of the present study is to investigate
the effects of diameter ratio of adiabatic cylinder on
ABSTRACT
A numerical analysis is carried out to study the performance of natural convection inside a square open
cavity. An adiabatic circular cylinder is placed at the center of the cavity and the sidewall in front of the
breathing space is heated by a constant heat flux. The top and bottom walls are kept at the ambient constant
temperature. Two-dimensional forms of Navier-Stokes equations along with the energy equations are
solved using Galerkin finite element method. Results are obtained for a range of Grashof number from 10
3
to 10
6
at Pr = 0.71 with constant physical properties. The parametric studies for a wide range of governing
parameters show consistent performance of the present numerical approach to obtain as stream functions
and temperature profiles. The computational results indicate that the heat transfer coefficient is strongly
affected by Grashof number. An empirical correlation is developed by using Nusselt number and Grashof
number.
Keywords: Open Cavity, Natural Convection, Finite Element, Grashof Number.
EFFECT OF DIAMETER RATIO OF ADIABATIC CYLINDER ON
NATURAL CONVECTION FROM A SQUARE OPEN CAVITY
Fariza Tul Koabra
1
and Md. Abdul Alim
2
1
Department of Mathematics, Eden Mohila College, Dhaka,Bangladesh,
2
Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh