Solution: method of image for a circle in a free stream near a wall - boundary condition at the wall.

We check if a 2D dipole oriented in the $+x$ direction in a free stream of speed $U$ plus its mirror image with respect to a wall at $y = 0$ satisfy the no flux boundary condition at the wall. First, we obtain the $\frac{\partial \phi}{\partial y}$, given by the equation

$$\frac{\partial \phi}{\partial y} = Ux\left(-\frac{2a^{2}(y-b)... ...^2)^2}-\frac{2a^{2}(y+b)}{(x^{2}+(y+b)^{2})^{2}}\right) \notag$$

Next, we set $y = 0$, and

$$\frac{\partial \phi}{\partial y} = Ux\left(\frac{2a^{2}b}{(x^2+b^2)^2}-\frac{2a^{2}b}{(x^{2}+b^{2})^{2}}\right) = 0 \notag$$