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Table 1 Typical parameter values for mantle convection with variable viscosity

From: Mathematical modelling of mantle convection at a high Rayleigh number with variable viscosity and viscous dissipation

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