A numerical study of natural convection in a horizontal enclosure with a conducting body

The physical model considered here is a horizontal layer of fluid heated below and cold above with a conducting body placed at the center of the layer. The body has dimensionless thermal conductivities of 0.1, 1 and 50. Two-dimensional solution for unsteady natural convection is obtained using an accurate and efficient Chebyshev spectral methodology for different Rayleigh numbers. Multi-domain technique is used to handle a square-shaped conducting body. The results for the case of a conducting body are also compared to those of adiabatic and neutral isothermal bodies. When the dimensionless thermal conductivity is 0.1, a pattern of fluid flow and isotherms and the corresponding surface- and time-averaged Nusselt number are almost the same as the case of an adiabatic body. When the dimensionless thermal conductivity is 50, a pattern of flow and isotherm and the corresponding surface- and time-averaged Nusselt number are similar to those of neutral isothermal body. The results for the case of dimensionless thermal conductivity of unity are also compared to those of pure natural convection.