\(\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=0\) (2)
\(u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}=U_{\infty}\frac{dU_{\infty}}{\text{dx}}+\ \upsilon\left(1+\frac{1}{\beta}\right)\frac{\partial^{2}u}{\partial y^{2}}+\beta g\left(T-T_{\infty}\right)-\frac{\sigma B_{0}^{2}\left(x\right)}{\rho}\left(u-U_{\infty}\right)\) (3)
\(u\frac{\partial T}{\partial x}+v\frac{\partial T}{\partial y}=\alpha\frac{\partial^{2}T}{\partial y^{2}}+\frac{\text{μα}}{k}\left(1+\frac{1}{\beta}\right)\left(\frac{\partial u}{\partial y}\right)^{2}+\frac{\text{ασ}B_{0}^{2}\left(x\right)}{k}\left(u-U_{\infty}\right)^{2}.\) (4)