Table 4 Calculation of Nusselt Number \(={N}_{u}R{e}_{x}^{\frac{-1}{2}}\) for \(Pr=6450\).

From: RETRACTED ARTICLE: Thermal cooling efficacy of a solar water pump using Oldroyd-B (aluminum alloy-titanium alloy/engine oil) hybrid nanofluid by applying new version for the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

\({\alpha }_{1}\)

\({\alpha }_{2}\)

\(\phi /{\phi }_{h}\)

\(S\)

\(Q\)

\({N}_{r}\)

\(Bi\)

\(Ec\)

\({\gamma }^{*}\)

\(K\)

\({N}_{u}R{e}_{x}^{\frac{-1}{2}}\) mono

\({N}_{u}R{e}_{x}^{\frac{-1}{2}}\) hybrid

Relative \(\frac{{Nu}_{hybrid}-{Nu}_{nano}}{N{u}_{hybrid}}\times 1\) 00

0.1

0.1

\(0.02\)

0.1

0.1

0.1

0.1

1.0

0.1

0.1

0.08041

0.10582

24.21%

0.2

         

0.08078

0.11885

32.12%

0.3

         

0.08139

0.12706

35.21%

 

0.1

        

0.08041

0.10582

24.21%

 

0.2

        

0.08095

0.11632

30.31%

 

0.3

        

0.08106

0.12372

34.37%

  

\(0.02\)

       

0.08041

0.10582

24.21%

  

\(0.06\)

       

0.08048

0.10799

25.48%

  

\(0.1\)

       

0.08084

0.10994

26.37%

   

0.1

      

0.08041

0.10582

24.21%

   

0.3

      

0.08060

0.10699

24.66%

   

0.5

      

0.08080

0.10809

25.14%

    

0.1

     

0.08041

0.10582

24.21%

    

0.3

     

0.08080

0.10699

24.47%

    

0.5

     

0.08139

0.10978

25.75%

     

0.1

    

0.08041

0.10582

24.21%

     

0.2

    

0.08133

0.10796

24.48%

     

0.3

    

0.08244

0.10999

25.15%

      

0.1

   

0.08041

0.10582

24.21%

      

0.2

   

0.08080

0.10799

25.17%

      

0.3

   

0.08085

0.10891

25.76%

       

1

  

0.08041

0.10582

24.21%

       

3

  

0.08050

0.10691

24.70%

       

5

  

0.08066

0.10777

25.15%

        

0.1

 

0.08041

0.10582

24.21%

        

0.3

 

0.08040

0.10482

23.29%

        

0.5

 

0.08039

0.10382

22.56%

         

0.1

0.08041

0.10582

24.21%

         

0.2

0.08047

0.10784

25.28%

         

0.3

0.08052

0.10892

26.25%