Table 5 Fluid pressure and torques on upper plate with \(\xi _{rad} = 0.1\), \(\xi _{z} = 0.2\), \(\xi _{\theta } = 0.5\), \(\xi _{mag} = 0.1\), \(\xi _{pr} = 3\), \(\xi _{hm} = 1\), \(\xi _{pm} = 0.2\), \(\xi _{sm} = 1\), \(\xi _{ec} = 2\), \(\xi _{vis} = 0.3\), \(S = 1\) and various values of \(\xi _{sq}\).

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

\(\xi _{sq}\)

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

19.2226

\(-\,0.4558\)

19.2225

\(-\,0.4562\)

\(5.20224\times 10^{-6}\)

\(2.19346\times 10^{-3}\)

0.5

5.2753

\(-\,1.7021\)

5.2752

\(-\,0.4724\)

\(1.89566\times 10^{-4}\)

\(5.87475\times 10^{-4}\)

1

3.4494

\(-\,2.6614\)

3.4493

\(-\,0.5128\)

\(2.89914\times 10^{-4}\)

\(3.75728\times 10^{-4}\)

1.5

2.8340

\(-\,3.3410\)

2.8339

\(-\,0.3400\)

\(3.52871\times 10^{-4}\)

\(2.99303\times 10^{-4}\)