Delayed cooling of the Earth's mantle due to variable thermal conductivity and the formation of a low conductivity zone

The thermal conductivity of mantle materials decreases with higher temperatures and increases with greater pressure due to phonon mechanism, but increases with temperature for radiative transfer. This trade-off attribute allows for the formation of a low conductivity zone (LCZ) within the top thermal boundary layer in mantle convection. We have studied with a two-dimensional (2-D) cartesian model the potential of this low conductivity zone in retarding secular cooling of the mantle for a longer period of time than models with constant thermal conductivity. Using a recently proposed model for thermal conductivity and an adiabatic boundary condition for the bottom of the mantle, we have carried out a set of numerical experiments within the framework of the extended Boussinesq approximation for constant viscosity, depth-dependent thermal expansivity and variable thermal conductivity with surface Rayleigh numbers between around 10⁶ and around 10⁷. We have employed internal heating between two and four times the chondritic level and half-life time values of 2.5 Ga and 5 Ga. The cooling rate of the mantle can be decreased by the feedback interaction between mantle conductivity and internal heating, which gives rise to slower sinking cold currents. The retardation time increases with the strength of radiogenic heating and can be as long as a couple of billion years for high initial heating rates, four times the chondritic value. However, increasing the radiative contribution of the conductivity speeds up the cooling process. The less the radiative contribution is, the more mantle cooling would be retarded. In the course of adiabatic cooling we find the paradoxical situation in which the effective Rayleigh number of the mantle can actually increase with time. We suggest then that, because of the possibilities for the formation of low conductivity zones adjacent to the thermal boundary layers, which bring forth unexpected consequences, mantle thermal conductivity should be considered as a fundamentally important factor in constraining the thermal evolution of both the core and mantle.