Numerical studies are made of the transient natural convection in a two dimensional square cavity of finite wall thickness. Two vertical walls are assumed to have same thickness and material. Initially, the walls of the enclosure and the fluid(air) inside the cavity are assumed to be at a constant, uniform temperature, and the fluid is taken to be stagnant. The horizontal walls are assumed to be insulated and have no thickness. At time t>0, constant but different temperatures are suddenly imposed on the outside of the walls and maintained until steady state conditions are reached. From this configuration, some important nondimensional parameters are presented; the heat capacity ratio $(ρC)^*$, the thermal conductivity ratio $k^*$, the wall thickness ratio $A_ω$, Rayleigh number Ra. By changing each parameter respectively from the reference case, the effects of the each parameter on the transient features of flow field and temperature profiles are pursued. The time scale with respect to the global adjustment and the enhancement(or the contraction) of the transient oscillatory fluctuation are also observed. The concept of thermal conductance and 1-D approximation which is generally used to treat the finite wall conductance is found to have some availabilities and limitations in the analysis of transient flow. By the existence of the finite wall conductance, the flow field and the temperature are weakened and time for the settlement to the final state becomes longer. Time scale going to the steady state are certified to be the sum of the conductive time scale at the wall and the convective time scale at the fluid. In this paper, it is tried to correlate both the heat transfer coefficient at the steady state and the effective Rayleigh number with thermal conductance and Rayleigh number.
