Table 4 Numerical values of Nusselt number \(Re_{x}^{-1/2}Nu_{x}\) for different values of physical parameters \(A=0.3,\) \(S_{1}=0.0.2,W_{e}=0.4, \gamma _{1}=0.2\).

From: Estimation of unsteady hydromagnetic Williamson fluid flow in a radiative surface through numerical and artificial neural network modeling

\(M_{1}\)

\(E_{1}\)

\(R_{1}\)

\(P_{r}\)

\(E_{c}\)

\(Q_{1}\)

\(B_{i}\)

\(\alpha \)

\(-{\text {Re}}_{x}^{-1/2}Nu_{{\hat{x}}}\)

GWRM

ANN Prediction

\(\varpi =\pi /2\)

\(\varpi =\pi /6\)

\(\varpi =\pi /2\)

\(\varpi =\pi /6\)

0.0

0.3

0.3

1

0.5

0.5

0.2

0.2

0.417812

0.417812

0.417622065

0.417011494

0.2

       

0.417615

0.417798

0.416708272

0.417312171

0.4

       

0.413635

0.417615

0.413437193

0.416625828

0.6

       

0.409676

0.416479

0.409060414

0.415986525

0.2

0.0

0.3

1

0.5

0.5

0.2

0.2

0.401078

0.414855

0.401080763

0.414687452

 

0.1

      

0.409927

0.415234

0.409457697

0.415549836

 

0.2

      

0.411936

0.416209

0.412264956

0.415243645

 

0.3

      

0.417615

0.417798

0.416708272

0.417312171

0.2

0.3

0.0

1

0.5

0.5

0.2

0.2

0.268871

0.268210

0.268799609

0.268001409

  

0.2

     

0.365731

0.365844

0.364971655

0.365299625

  

0.4

     

0.471390

0.471922

0.47056126

0.471221267

  

0.6

     

0.583913

0.585162

0.578643641

0.580752337

0.2

0.3

0.3

0.8

0.5

0.5

0.2

0.2

0.393609

0.394120

0.393078442

0.393476331

   

0.9

    

0.378502

0.378705

0.391306506

0.387579291

   

1.0

    

0.365730

0.365836

0.356708272

0.357312171

   

1.1

    

0.355096

0.354673

0.35485935

0.354320921

0.2

0.3

0.3

1.0

0.0

0.5

0.2

0.2

0.254696

0.256038

0.256716643

0.254569521

    

0.3

   

0.352399

0.353061

0.352157083

0.352463088

    

0.6

   

0.450119

0.450186

0.449328272

0.449794601

    

0.9

   

0.547505

0.547101

0.546883625

0.546264445

0.2

0.3

0.3

1.0

0.5

\(-\)0.4

0.2

0.2

0.255003

0.254178

0.249302396

0.248048876

     

\(-\)0.2

  

0.273659

0.272779

0.281062975

0.282322934

     

0.0

  

0.297440

0.296601

0.297826133

0.296945579

     

0.2

  

0.329769

0.328813

0.330039994

0.329025368

     

0.4

  

0.378853

0.378246

0.39093441

0.391221193

0.2

0.3

0.3

1.0

0.5

0.5

0.0

0.3

0.199100

0.197921

0.20215141

0.204587407

      

0.2

 

0.403670

0.403598

0.402736781

0.403118255

      

0.4

 

0.548724

0.549310

0.548508547

0.548963569

      

0.6

 

0.655744

0.656985

0.662586879

0.638124434

0.2

0.3

0.3

1.0

0.5

0.5

0.3

0.0

0.542491

0.542391

0.542129796

0.541764069

       

0.1

0.51954

0.520165

0.519009327

0.519677028

       

0.2

0.499513

0.500135

0.499251651

0.499576203

       

0.3

0.481828

0.482317

0.481695049

0.481651657

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