Table 7 Fluid pressure and torques on upper plate with \(\xi _{sq} = 0.1\), \(\xi _{z} = 0.2\), \(\xi _{\theta } = 0.5\), \(\xi _{mag} = 0.3\), \(\xi _{pr} = 3\), \(\xi _{hm} = 1\), \(\xi _{pm} = 0.2\), \(\xi _{sm} = 1\), \(\xi _{ec} = 2\), \(\xi _{vis} = 0.3\), \(S = 1\) and various values of \(\xi _{a}\).

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

\(\xi _{a}\)

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

19.2024

\(-\,0.4561\)

19.2023

\(-\,0.4562\)

\(5.20771\times 10^{-6}\)

\(2.19202\times 10^{-3}\)

0.5

6.9653

\(-\,0.4723\)

6.9652

\(-\,0.4724\)

\(1.43571\times 10^{-4}\)

\(2.11775\times 10^{-3}\)

1

\(-\,34.0176\)

\(-\,0.5127\)

\(-34.0175\)

\(-\,0.5128\)

\(2.93966\times 10^{-6}\)

\(1.95008\times 10^{-3}\)

1.5

\(-\,268.29\)

\(-\,0.3399\)

\(-268.28\)

\(-\,0.3400\)

\(3.72745\times 10^{-4}\)

\(2.94204\times 10^{-3}\)