Finite element analysis for steady state natural convection in an open square cavity having partially heated circular cylinder

Abstract

Natural convection in open cavities has received considerable attention because of its importance in several thermal 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. In this thesis under the title “Finite Element Analysis for Steady State Natural Convection in a Square Open Cavity Having Partially Heated Circular Cylinder” two problems have been studied. The study as well depending on various kinds of cylinder and boundary conditions are abstracted below. Firstly, Numerical analysis of two-dimensional laminar steady-state natural convection in a tilted square open cavity with a partially heated circular cylinder has been investigated. A partially heated circular cylinder is placed at the center of the cavity and the opposite wall to the aperture is placed at iso-flux heat source. The other two remaining walls were kept cooled with Temperature Tc (Top wall) and heated with temperature Th (bottom wall). The fluid is concerned with Prandtl numbers 0.72, 1.0 and 7.0. The properties of the fluid were assumed to be constant. The physical problems are represented mathematically by different sets of governing equations along with the corresponding boundary conditions. The non-dimensional governing equations are discretized by using Galerkin weighted residual method of finite element formulation. The obtained results are presented in terms of streamlines and isotherms, heat transfer characteristics Nusselt numbers for Grashof numbers from 103 to 106 and for inclination angles of the cavity from 0º to 45º. The obtained results are also presented with the variation of different diameter ratios of the cylinder. The results show that the Nusselt numbers increase with the increase of Grashof numbers. Also the average Nusselt number changes substantially with the inclination angle of the cavity while better thermal performance is also sensitive to the boundary condition of the heated wall. The computational results also indicate that the average Nusselt number at the hot wall of the cavity is depending on the dimensionless parameters. Finally, Numerical analysis of two-dimensional laminar steady-state natural convection in a tilted square open cavity with a partially heated square cylinder has been investigated. A partially heated square cylinder is placed at the center of the cavity and remains all of properties unchanged. The obtained results are presented in terms of streamlines and isotherms, heat transfer characteristics Nusselt numbers for Grashof