Table 4 Numerical consequences of mass diffusion rate, divergent velocity and heat energy rate versus impacts of heat source, Weissenberg, Schmidt and magnetic parameters when \(\alpha =0.5, m=0.3, Re=4.0, Pr=206, {\delta }_{1}=0.4, ph1=0.003, {\varphi }_{1}=0.003, {\varphi }_{2}=0.004, {\varphi }_{3}=0.0075.\)

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

Change in parameters

\(-Cf{Re}^\frac{1}{2}\)

\(-Nu{Re}^{-\frac{1}{2}}\)

\(-Sh{Re}^{-\frac{1}{2}}\)

\({H}_{t}\)

− 1.8

0.5819082531

1.704545484

0.1251079132

0.7

0.5509136062

1.696530334

0.1251079132

1.4

0.5240101703

1.685344690

0.1251079132

\(we\)

0.0

0.5949186967

1.631731458

0.1251079132

0.7

0.5819212062

1.641203201

0.1281250122

1.3

0.5631126602

1.670330253

0.1290020237

\(Sc\)

0.0

0.5949186967

1.691723859

0.1249999995

0.3

0.5949186967

1.722068872

0.5886630903

0.7

0.5949186967

1.740594028

0.9412612184

\(M\)

0.0

0.7621803004

1.693933394

0.1253751105

0.01

0.7852799081

1.684292106

0.1233774407

0.08

0.8216289994

1.664644057

0.1213796206