1. Ferromagnetic interaction parameter \(\beta=0,5,10\)    as in \cite{kafoussias2003,shit2009,tanoudis2003,vnnikiforov2007}
2. Thermal conductivity parameter  \(\alpha=0.0, 0.12, 0.2\)            as in \cite{ferdows2019}.
3. Viscosity variation parameter \(\theta_r=-0.2, -0.4, -0.6\)              as in    \cite{ferdows2019}.
4. Prandtl number  \(Pr=21, 23, 25\)                                           as in  \cite{ferdows2019}.
5. Values of dimensionless distance  \(\alpha=1\)                                  as in   \cite{kafoussias2003} .
6. Magnetic field parameter \(M=1,2,3\)                                    as in  \cite{ferdows2019} 
7. Mixed convection parameter  \(\lambda_1=-0.5, 0.0, 0.5\)              as in \cite{psdatti2010}.
8. Viscous dissipation parameter\(\lambda=1.6\times10^{-14}\)

Results and Discussion

To check the numerical accuracy we compared our present results of the rate of heat transfer \(-\theta'(0)\)   and skin friction coefficient \(-f''(0)\)  with the existing work of \cite{rashidi1992} for the values of \(Pr=0.7\)  and  \(Pr=10\) respectively while viscosity parameter \(\theta_r\)  ranging from -10 to +10. The comparison shows an excellent agreement as present in Table 1and Table 2.
Table 1 Comparison of skin friction for different values of stretching parameter with \(\beta=0,S=0,\Pr=0.72\)