The influence of variable viscosity on delayed cooling due to variable thermal conductivity

Recently it was found for constant viscosity models that variable thermal conductivity can delay significantly the secular cooling of the mantle. We have verified that this same effect also holds up well for variable viscosity, in which we have used up to a factor of 3000 in the lateral viscosity variations due to temperature and a factor of 100 increase from pressure effects. A purely pressure-dependent thermal conductivity does not exert any effect on retarding the secular cooling. The amount of time for the delay is decreased a little by the presence of variable viscosity, but its influence on retarded cooling still remains. We have also found that the cooling predicted by parameterized convection is faster than for the corresponding two-dimensional (2D) solution taken from solving the complete convection equations.