Chapter 14.1, Problem 5E

To determine

The steady state temperature in the circular plate with the boundary condition as ${\frac{\partial u}{\partial \theta }|}_{\theta =0}=0,{\frac{\partial u}{\partial \theta }|}_{\theta =\pi }=0$ and $u\left(2,\theta \right)=\{\begin{array}{l}{u}_{0}0<\theta <\frac{\pi }{2}\\ 0\frac{\pi }{2}<\theta <\pi \end{array}$.