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}
\[\frac{\delta u}{\delta\ x}+\frac{\delta v}{\delta\ y}=0\]
\[\begin{equation}\label{eq:1}
\begin{aligned}
u\frac{\delta u}{\delta\ x}+v\frac{\delta u}{\delta\ y}=\frac{1}{\rho_{\infty}}\frac{\delta}{\delta y}\left(\mu \frac{\delta u}{\delta y}\right)+\frac{1}{\rho_\infty}\mu_0M\frac{\delta H}{\delta x}\\
+\frac{\sigma B_0^2}{\rho_\infty}u+gB^*(T-T_\infty)
\end{aligned}
\end{equation}\]
\[\begin{equation}\label{eq:1}
\begin{aligned}
\rho_\infty c_p\left(u\frac{\delta T}{\delta\ x}+v\frac{\delta T}{\delta\ y}\right)+\mu_0T\frac{\delta M}{\delta T}\left(u\frac{\delta H}{\delta\ x}+v\frac{\delta H}{\delta\ y}\right)\\
=\frac{\delta}{\delta y}\left(k\frac{\delta T}{\delta y}\right)
\end{aligned}
\end{equation}
\]