Numerical investigation on natural convection from an open rectangular cavity containing a heated circular cylinder

Abstract

Natural convection in open cavity becomes very important in many scientific and engineering problems, for example, in the design of electronic devices, solar thermal receivers, uncovered flat plate solar collectors having rows of vertical strips, geothermal reservoirs, etc. Several experiments and numerical investigation have been presented for describing the phenomenon of natural convection in open cavity for two decades. Finite Element Simulation of two-dimensional laminar steady state natural convection in a rectangular open cavity has been investigated. A heated circular cylinder is placed at the centre of the cavity where the left sidewall to the cavity is heated by a constant heat flux. The top wall is kept cool and the bottom wall is kept at a hot temperature. The fluid is concerned with different Prandtl numbers. The properties of the fluid are assumed to be constant. The physical problems are represented mathematically by different sets of governing equations along with the corresponding boundary conditions. In this study, finite element method for steady state incompressible natural convection flows is used to find the numerical results. The Galerkin Weighted Residual method of finite element formulation is applied to discretize the non-dimensional governing equations. The results of the investigation are obtained in terms of streamlines, isotherms and heat transfer characteristics Nusselt numbers for different Grashof numbers and different inclination angles of the cavity ranges from 0o to 45o It is observed that the heat transfer rate increases as the increase of the inclination angle of the cavity for lower Prandtl numbers and lower temperature at the bottom wall. The average Nusselt number increase mainly for higher angles and for higher Grashof number. It is observed that fluid moves clockwise around the cylinder. Thermal boundary layer thickness becomes thinner for higher Grashof number. The heat transfer rate decreases for Gr = 10. The results are obtained for the diameter ratio 0.2 of the cylinder. A comparative study has been done on the obtained results. The numerical results are presented graphically as well as in tabular form. The software FEMLAB is used to present numerical data graphically. 3 and increases gradually for increasing of Grashof number . Various vortices and recirculations are formed into the flow field for higher Prandtl number and higher temperature at the bottom wall.