\(u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}=\upsilon\frac{\partial^{2}u}{\partial y^{2}}-\frac{\sigma B_{0}^{2}}{\rho}u+g\beta\left(T-T_{\infty}\right)+g\beta^{*}\left(C-C_{\infty}\right)\) |
(2) |
\(u\frac{\partial T}{\partial x}+v\frac{\partial T}{\partial y}=\frac{1}{\rho c_{p}}\left[\frac{\partial}{\partial y}\left(\kappa\left(T\right)\frac{\partial T}{\partial y}\right)-\left(\frac{\partial q_{r}}{\partial y}\right)+q\left(T-T_{\infty}\right)\right]+\frac{Dk_{t}}{c_{p}c_{s}}\left(\frac{\partial^{2}C}{\partial y^{2}}\right)+\frac{\mu}{c_{p}}\left(\frac{\partial u}{\partial y}\right)^{2}\) |
(3) |
\(u\frac{\partial C}{\partial x}+v\frac{\partial C}{\partial y}=D\frac{\partial^{2}C}{\partial y^{2}}+\frac{Dk_{t}}{T_{m}}\ \left(\frac{\partial^{2}T}{\partial y^{2}}\right),\) |
(4) |