Parameter | Symbol | Value |
---|---|---|
Mantle depth | d | \(3\times 10^6\) m |
Thermal expansion coefficient | \(\alpha\) | \(2\times 10^{-5}\) K\(^{-1}\) |
Reference density | \(\rho _0\) | \(4\times 10^3\) kg m\(^{-3}\) |
Gravitational acceleration | g | 10 m s\(^{-2}\) |
Temperature at the top of the mantle | \(T_{\mathrm{s}}\) | 300 K |
Temperature at the base of the mantle | \(T_{\mathrm{b}}\) | 3000 K |
Temperature difference | \(\Delta T\) | 2700 K |
Thermal conductivity | k | 4 W m\(^{-1}\)K\(^{-1}\) |
Specific heat at constant pressure | \(C_{\mathrm{p}}\) | \(10^3\) J kg\(^{-1}\) K\(^{-1}\) |
Activation energy | E | 300–525 kJ mol\(^{-1}\) |
Activation volume | V | \(6\times 10^{-6}\) m\(^3\) mol\(^{-1}\) |
Gas law constant | R | 8.31 J mol\(^{-1}\) K\(^{-1}\) |
Viscous rate constant | A | \(10^5\) MPa\(^{-1}\) s\(^{-1}\) |
Thermal diffusivity | \(\kappa\) | \(1\times 10^{-6}\) m\(^2\) s\(^{-1}\) |
Rayleigh number | Ra | \(10^7-10^9\) |
Viscous temperature parameter | \(\varepsilon\) | \(0.042-0.083\) |
Viscous pressure number | \(\mu\) | \(1.2-2.4\) |
Boussinesq number | \({\bar{B}}\) | 0.06 |
Dimensionless surface temperature | \(\theta _0\) | 0.1 |
Dissipation number | D | 0.6 |