Table 4 The computational output values of the local heat flux for sundry values of the mentioned parameters.

From: Forced convection flow of water conveying AA7072 and AA7075 alloys-nanomaterials on variable thickness object experiencing Dufour and Soret effects

\(\phi_{1} ,\phi_{2}\)

\(R_{d}\)

\(Du\)

\(- 2\sqrt c \left( {\frac{{k_{hnf} }}{{k_{bf} }} + \frac{4}{3}R_{d} } \right)\theta ^{\prime}(a)\)

Upper branch solution

Lower branch solution

0.022

2.0

0.4

4.4442242

1.9299000

0.026

  

4.4927471

1.9325963

0.030

  

4.5420482

1.9345058

0.034

  

4.5921239

1.9356261

 

1.0

 

2.5715016

0.9095888

 

1.5

 

3.5824305

1.3683308

 

2.0

 

4.6047635

1.9357822

 

2.5

 

5.6261206

2.5854656

  

0.1

4.1057667

1.1847094

  

0.3

4.4311727

1.6870532

  

0.5

4.7860747

2.1823139

  

0.7

5.1731712

2.6670956

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