Table 2 Numerical study of mesh-free for concentration, velocity and heat energy profiles via mid of 300 elements when \(\alpha =0.5, m=0.3, Re=4.0, we=3.0, M=3.0, Pr=206, {H}_{t}=-2.0, Sc=0.0, {\delta }_{1}=0.4, ph1=0.003, {\phi }_{1}=0.004, {\phi }_{2}=0.0075, {K}_{c}=-3.0, {\varphi }_{1}=0.003.\)

From: Thermal and solute aspects among two viscosity models in synovial fluid inserting suspension of tri and hybrid nanomaterial using finite element procedure

Number of elements

\(F{^{\prime}}\left(\frac{{\eta }_{max}}{2}\right)\)

\(\theta \left(\frac{{\eta }_{max}}{2}\right)\)

\(\phi \left(\frac{{\eta }_{max}}{2}\right)\)

30

0.02294303658

0.5407391166

0.5331705542

60

0.01376586145

0.5245896500

0.5165094221

90

0.01198065198

0.5191518648

0.5109559950

120

0.01124242297

0.5164233899

0.5081778903

150

0.01084212050

0.5147803839

0.5065116330

180

0.01059108809

0.5136848805

0.5054008033

210

0.01041887658

0.5129035893

0.5046079652

240

0.01029345534

0.5123159218

0.5040134244

270

0.01019938656

0.5118566461

0.5035502943

300

0.01012545524

0.5114903521

0.5031791373

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