Table 6 Values of skin friction \(= C_{f} Re_{x}^{\frac{1}{2}}\) and Nusselt number \(= Nu_{x} Re_{x}^{{\frac{ - 1}{2}}}\) for \(P_{r} = 7.38\), and \(n = 0.2\)

From: RETRACTED ARTICLE: A brief comparative examination of tangent hyperbolic hybrid nanofluid through a extending surface: numerical Keller–Box scheme

\(W_{e}\)

\(M\)

\(\phi\)

\(\phi_{{TiO_{2} }}\)

\({\Upsilon }\)

\(N_{r}\)

\(B_{i}\)

\(E_{c}\)

\(\lambda\)

\(S\)

\(C_{f} Re_{x}^{\frac{1}{2}}\) Cu–EG

\(C_{f} Re_{x}^{\frac{1}{2}}\)

TiO2–Cu/EG

\(N_{u} Re_{x}^{{\frac{ - 1}{2}}}\)

Cu–EG

\(N_{u} Re_{x}^{{\frac{ - 1}{2}}}\)

TiO2–Cu/EG

0.1

0.1

0.18

0.09

0.3

0.3

0.3

0.3

0.2

0.1

2.3839

2.7558

1.2114

1.2589

0.2

         

2.3654

2.7355

1.1972

1.2368

0.3

         

2.3343

2.7124

1.1716

1.1942

 

0.1

        

2.3839

2.7558

1.2114

1.2589

 

0.3

        

2.4065

2.7704

1.1946

1.2333

 

0.4

        

2.4202

2.7928

1.1717

1.2147

  

0.09

       

2.3839

-

1.2114

-

  

0.15

       

2.4025

-

1.2273

-

  

0.18

       

2.4242

–

1.2392

–

   

0.0

      

–

2.3839

–

1.2114

   

0.06

      

–

2.7339

–

1.2439

   

0.09

      

–

2.7558

–

1.2589

    

0.1

     

2.4245

2.7953

1.2523

1.2992

    

0.2

     

2.4024

2.7721

1.2325

1.2778

    

0.3

     

2.3839

2.7558

1.2114

1.2589

     

0.1

    

2.3839

2.7558

1.1969

1.2336

     

0.3

    

2.3839

2.7558

1.2114

1.2589

     

0.5

    

2.3839

2.7558

1.2388

1.2793

      

0.1

   

2.3839

2.7558

1.1745

1.2129

      

0.3

   

2.3839

2.7558

1.2114

1.2589

      

0.4

   

2.3839

2.7558

1.2368

1.2945

       

0.1

  

2.3839

2.7558

1.2358

1.2718

       

0.3

  

2.3839

2.7558

1.2114

1.2589

       

0.4

  

2.3839

2.7558

1.1989

1.2346

        

0.1

 

2.3839

2.7558

1.2114

1.2589

        

0.2

 

2.3839

2.7558

1.1946

1.2365

        

0.3

 

2.3839

2.7558

1.1729

1.2146

         

0.1

2.3839

2.7558

1.2114

1.2589

         

0.2

2.4034

2.7746

1.2337

1.2754

         

0.3

2.4226

2.7952

1.2582

1.2972

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