  Observations have revealed that a significant number of hot Jupiters have
anomalously large radii. Layered convection induced by compositional
inhomogeneity has been proposed to account for the radius anomaly of hot
Jupiters. To reexamine the impact of the compositional inhomogeneity, we
perform an evolutionary calculation by determining convection regime at each
evolutionary time step according to the criteria from linear analyses. It is
shown that the impact is limited in the case of the monotonic gradient of heavy
element abundance. The layered convection is absent for the first 1 Gyr from
the formation of hot Jupiters and instead overturning convection develops. The
super-adiabaticity of the temperature gradient is limited by the neutrally
stable state for the Ledoux stability criterion. The effect of the increased
mass of heavy elements essentially compensates the effect of the delayed
contraction on the planetary radius caused by compositional inhomogeneity. In
addition, even in the case where the layered convection is artificially
imposed, this mechanism requires extremely thin layers (~ 10^1-10^3 cm) to
account for the observed radius anomaly. The long-term stability of such thin
layers remains to be studied. Therefore, if the criteria adopted in this paper
are adequate, it might be difficult to explain the inflated radii of hot
Jupiters by monotonic gradient of heavy element abundance alone.
