Table 3 The comparison of \(-{\theta }^{^{\prime}}(0)\) values with the increasing Prandtl Number, \(\phi =0\), \({\phi }_{h}=0\), \(Q=0\), \({\gamma }^{*}=0\), \({E}_{c}=0{, N}_{r}=0\), \(Q=0\), \({E}_{c}=0\), \(S=0\), and \(Bi=0\).

From: RETRACTED ARTICLE: Thermal cooling efficacy of a solar water pump using Oldroyd-B (aluminum alloy-titanium alloy/engine oil) hybrid nanofluid by applying new version for the model of Buongiorno

\(Pr\)

Ref. 17

Ref. 76

Ref. 77

Ref. 78

Ref. 79

Ref. 80

Present

0.72

0.80876181

0.8086

0.8086

0.80863135

0.80876122

0.80876181

0.80876181

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

3.0

1.92357420

1.9237

1.9236

1.92368259

1.92357431

1.92357420

1.92357420

7.0

3.07314651

3.0723

3.0722

3.07225021

3.07314679

3.07314651

3.07314651

10

3.72055429

3.7207

3.7006

3.72067390

3.72055436

3.72055429

3.72055429