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Table 4 Nusselt number Nu computed for \(\mu =0.0\), \(\mu =0.5\), \(\mu =1.0\) with different viscous dissipation number D at \({\mathrm{Ra}} = 10^7\) and \(\theta _0\) = 0.1

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

\(\Delta \eta\)

Nusselt number Nu

\(\mu =0.0\)

\(\mu =0.5\)

\(\mu =1.0\)

\(D = 0.0\)

\(D = 0.3\)

\(D = 0.6\)

\(D = 0.0\)

\(D = 0.3\)

\(D = 0.6\)

\(D = 0.0\)

\(D = 0.3\)

\(D = 0.6\)

\(10^{10}\)

6.76800

3.83912

2.22500

8.06845

4.46772

2.45665

9.35884

5.22977

2.76453

\(10^{15}\)

5.36157

2.90745

1.73657

6.98490

3.62823

1.93308

8.20184

4.58926

2.25912

\(10^{20}\)

4.45036

2.34275

1.48655

6.29310

3.09495

1.63913

6.85055

4.18656

1.93551

\(10^{25}\)

3.80090

2.00320

1.34157

5.79442

2.71655

1.45780

5.43699

3.88971

1.71162

\(10^{30}\)

3.25696

1.77292

1.24780

5.39304

2.40512

1.33803

4.79113

3.64133

1.54933