Table 2 Assessment of the values of \(F^{\prime\prime}\left( c \right)\) when \(\phi = M = We = 0\).

From: Dual solutions of nanomaterial flow comprising titanium alloy (Ti6Al4V) suspended in Williamson fluid through a thin moving needle with nonlinear thermal radiation: stability scrutinization

\(c\)

\(\lambda = 0\)

\(\lambda = - 1\)

\(\lambda = - 1\)

Soid et al.8

Present

Soid et al.8

Present

Present

First solution

Second solution

First solution

Second solution

0.01

8.491454

8.4915

26.599394

2.805533

26.6021

2.8031

0.1

1.288778

1.2888

3.703713

0.389103

3.7162

0.3884

0.2

0.751665

0.7515

2.005424

0.227837

2.0055

0.2278

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