\begin{multline}
\left(1+K_{1}\right)\begin{pmatrix}f^{{}^{\prime\prime\prime}}+\frac{1}{\eta+K}f^{{}^{\prime\prime}}\\
-\frac{1}{\left(\eta+K\right)^{2}}f^{{}^{\prime}}\\
\end{pmatrix}-A\left(\frac{\eta}{2}f^{{}^{\prime\prime}}+f^{{}^{\prime}}\right)+\frac{K}{\eta+K}\left({f^{{}^{\prime}}}^{2}-ff^{{}^{\prime\prime}}\right)+\frac{K}{\left(\eta+K\right)^{2}}\text{ff}^{{}^{\prime}}-
\end{multline}
\begin{multline}
\ \frac{\text{βK}}{\eta+K}\begin{bmatrix}gg^{{}^{\prime\prime}}-{g^{{}^{\prime}}}^{2}\\
+\frac{gg^{{}^{\prime}}}{\eta+K}\\
\end{bmatrix}-K_{1}h^{{}^{\prime}}=\frac{2KP}{\eta+K},
\end{multline}
|
(10)
|
\(\lambda\begin{pmatrix}g^{{}^{\prime\prime\prime}}+\frac{1}{\eta+K}g^{{}^{\prime\prime}}\\
-\frac{1}{\left(\eta+K\right)^{2}}g^{{}^{\prime}}\\
\end{pmatrix}+\frac{K}{\eta+K}\left(fg^{{}^{\prime\prime}}-gf^{{}^{\prime\prime}}\right)+\frac{K}{\left(\eta+K\right)^{2}}\left(\frac{1}{\gamma}ff^{{}^{\prime}}-\gamma gg^{{}^{\prime}}\right)-A\left(\frac{\eta}{2}g^{{}^{\prime\prime}}+g^{{}^{\prime}}\right)=0,\) |
(11) |
\(\left(1+\frac{K_{1}}{2}\right)\left(h^{{}^{\prime\prime}}+\frac{1}{\eta+K}h^{{}^{\prime}}\right)+\frac{K}{\eta+K}\left(fh^{{}^{\prime}}-hf^{{}^{\prime}}\right)-K_{1}\left(2h+\frac{1}{\eta+K}f^{{}^{\prime}}+f^{{}^{\prime\prime}}\right)-A\left(\frac{\eta}{2}h^{{}^{\prime}}+\frac{3}{2}h\right)=0,\) |
(12) |
\(\frac{1}{\Pr}\left(\theta^{{}^{\prime\prime}}+\frac{1}{\eta+K}\theta^{{}^{\prime}}\right)+\frac{K}{\eta+K}\left(f\theta^{{}^{\prime}}-f^{{}^{\prime}}\theta\right)+A\left(\frac{\eta}{2}\theta^{{}^{\prime}}+2\theta\right)=0,\) |
(13) |