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The condition for convection to cease is that the Rayleigh number $$\mathrm{Ra}=\frac{g\rho\alpha L^3\Delta T}{\kappa\nu}\lessapprox 10^3.$$ For the Earth's mantle I have seen estimates of $\mathrm{Ra}\approx 10^6$ to $10^8$, which naively would mean we need to reduce $\Delta T$ by a factor of $10^3$ to $10^5$ for convection to cease. In reality this is an overestimate since the thermal expansion $\alpha$, the thermal diffusivity $\kappa$ and especially the viscosity $\nu$ are temperature dependent.

However, being a non-geologist I find it hard to find easy functional forms of these parameters in the literature since they also depend on a number of other things like pressure and are subject to big empirical uncertainties. Are there any canonical estimates for the necessary temperature difference, or qualitative models?

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