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