I just want to convert velocity gradient in polar coordinate to velocity gradient in Cartesian one (i.e. $\frac{\partial u_r}{\partial r}=f\left(\frac{\partial v}{\partial y}\right)$). How can I convert these terms into each other?
Indeed, I have a fully developed boundary condition in the outlet of my computational domain. In the attached image, this boundary condition should be employed in the $\Gamma_2$ region. As can be seen, The domain is defined through polar coordinates. So in order to use the fully developed B.C ($\frac{\partial u}{\partial x}=\frac{\partial v}{\partial x}=0$), I should convert them in the equations based on $\frac{\partial u_r}{\partial \theta}$ or something like this. Can anybody tell me more about its equations in polar coordinates? image
