\(u\left(x,0\right)=U_{w}\left(x\right),\text{\ \ \ }v\left(x,0\right)=0,\ \text{\ \ }-k_{f}\frac{\partial T}{\partial y}\left(x,0\right)=h_{f}\left[T_{f}-T\left(x,0\right)\right]\text{\ \ }\text{\ \ }\text{at}\ \ y=0\ \) (5)
\(u\left(x,\infty\right)\rightarrow U_{\infty}\left(x\right),\ \ \ T\left(x,\ \infty\right)\rightarrow T_{\infty}\text{\ \ \ }\text{as\ \ \ }\ \ y\rightarrow\infty\) (6)