Table 6 Fluid pressure and torques on upper plate with \(\xi _{rad} = 0.1\), \(\xi _{sq} = 1.5\), \(\xi _{z} = 0.2\), \(\xi _{\theta } = 0.5\), \(\xi _{mag} = 0.1\), \(\xi _{pr} = 3\), \(\xi _{hm} = 1\), \(\xi _{pm} = 0.2\), \(\xi _{sm} = 1\), \(\xi _{ec} = 2\), \(S = 1\) and various values of \(\xi _{vis}\).

From: Hydrodynamic analysis of the magnetic field dependent viscous fluid flow and thermosolutal convection between rotating channels

\(\xi _{vis}\)

HAM result

BVP4c result

%Error = \(\vert \frac{N.R - H.R}{N.R}\vert\)

 

\(F_{pres}\)

\(g'(1)\)

\(F_{pres}\)

\(g'(1)\)

\(F_{pres}\)

\(g'(1)\)

0.1

1.9722

\(-\,5.5855\)

1.9721

\(-\,5.5856\)

\(5.07074\times 10^{-4}\)

\(1.79032\times 10^{-4}\)

0.5

3.6515

\(-\,2.4989\)

3.6514

\(-\,2.4990\)

\(2.73868\times 10^{-4}\)

\(4.00160\times 10^{-4}\)

1

5.6661

\(-\,1.5789\)

5.6660

\(-\,1.5790\)

\(1.76491\times 10^{-4}\)

\(6.33312\times 10^{-4}\)

1.5

7.6712

\(-\,1.1632\)

7.6711

\(-\,1.1633\)

\(1.30359\times 10^{-4}\)

\(8.59623\times 10^{-4}\)