Natural Convection in Parabolic Enclosure Heated from Below

The effects of vertical parabolic walls on natural convection in a parabolic enclosure have investigated numerically in this paper. The bottom wall is heated isothermally, while the other vertical parabolic walls are maintained at constant cold temperature and the top wall is well insulated. The flow and temperature fields are studied numerically for three values (C = 0.1, 0.5, 1.0) of the parabolic equation constant. The laminar flow field is analyzed numerically by solving the steady, two-dimensional incompressible Navier-Stokes and energy equations. The Cartesian velocity components and pressure on a collocated (non-staggered) grid are used as dependent variables in the momentum equations, which discretized by finite volume method, body fitted coordinates are used to represent the complex parabolic wall geometry accurately, and grid generation technique based on elliptic partial differential equations is employed. SIMPLE algorithm is used to adjust the velocity field to satisfy the conservation of mass. The range of Rayleigh number is (103? Ra ?105) and Prandtl number is 0.7. The results show that the heat transfer rates decrease with increase the parabolic equation constant.