Under the above assumption we explore the idea of [28] and hence the governing boundary layer equations i.e. continuity, momentum and energy equations are in following  \cite{radiation2015}
\[\frac{\delta u}{\delta\ x}+\frac{\delta v}{\delta\ y}=0\]
\[\begin{equation}\label{eq:1} \begin{aligned} u\frac{\delta u}{\delta\ x}+v\frac{\delta u}{\delta\ y}=\frac{1}{\rho_{\infty}}\frac{\delta}{\delta y}\left(\mu \frac{\delta u}{\delta y}\right)+\frac{1}{\rho_\infty}\mu_0M\frac{\delta H}{\delta x}\\ +\frac{\sigma B_0^2}{\rho_\infty}u+gB^*(T-T_\infty) \end{aligned} \end{equation}\]
\[\begin{equation}\label{eq:1} \begin{aligned} \rho_\infty c_p\left(u\frac{\delta T}{\delta\ x}+v\frac{\delta T}{\delta\ y}\right)+\mu_0T\frac{\delta M}{\delta T}\left(u\frac{\delta H}{\delta\ x}+v\frac{\delta H}{\delta\ y}\right)\\ =\frac{\delta}{\delta y}\left(k\frac{\delta T}{\delta y}\right) \end{aligned} \end{equation} \]