This study of thermal convection uses the following geometry: a horizontal layer of fluid heated from below of solid lid at bottom and cooled from above. A variety range of thermal conductivity ratio, k is considered to investigate the interface temperature, theta(i) between solid and fluid region. Periodic boundary conditions are employed in the horizontal direction to allow for lateral freedom for the convection cells. A two-dimensional solution for unsteady natural convection is obtained, using an accurate and efficient Chebyshev spectral multi-domain methodology, for different effective Rayleigh numbers, Ra-eff varying over the range of 10(4)-10(7). A concept for the effective Rayleigh number is to take into account an effect of existence of solid lid. The solid lid at bottom affects the flow pattern that the flow is restricted to increase of dimensionless thermal conductivity. The root mean square of time- and surface-averaged interface temperature decreases as dimensionless thermal conductivity increases. That is, the lateral motion of circulating cell of flow is fixed to arbitrary position at which the minimum solid temperature is obtained. The analysis has been further extended to three-dimensional geometry with periodic boundary condition. The span-wise direction is discretized by Fourier serious expansion with uniform mesh configuration. The thermal flow field has been captured by visualizing three-dimensional vortical structure. The flow behavior at a provided effective Rayleigh number shows coherent pattern regardless of a magnitude of the thermal conductivity ratio. (C) 2017 Elsevier Ltd. All rights reserved.