Two-dimensional and unsteady natural convection in a horizontal enclosure with a square body

A two-dimensional solution for unsteady natural convection in an enclosure with a square body is obtained using an accurate and efficient Chevyshev spectral collocation method. A spectral multidomain methodology is used to handle a square body located at the center of the computational domain. The physical model considered here is that a square body is located at the center between the bottom hot and top cold walls. To see the effects of the presence of a body on natural convection between the hot and cold walls, we considered the cases that the body maintains the adiabatic and isothermal thermal boundary conditions for different Rayleigh numbers varying in the range of 10(3) to 10(6). When the Rayleigh number is small, the flow and temperature distribution between the hot and cold walls shows a symmetrical and steady pattern. At the intermediate Rayleigh number, the fluid flow and temperature fields maintain the steady state but change their shape to the nonsymmetrical pattern. When the Rayleigh number is high, the flow and temperature fields become time dependent, and their time-averaged shapes approach the symmetric pattern again. The Rayleigh number for the fluid flow and temperature fields to become nonsymmetrical and time dependent depends on the thermal boundary conditions of a body. The variation of time- and surface-averaged Nusselt numbers on the hot and cold walls and at the body surfaces for different Rayleigh numbers and thermal boundary conditions are also presented to show the overall heat transfer characteristics in the system.