Consider a two-dimensional laminar flow over a long cylinder as shown in the figure below.

The free stream velocity is ^_$U\omega$ and the free stream temperature ^_$T\omega$ is lower than the cylinder surface temperature T_s. The local heat transfer coefficient is minimum at point

In laminar flow, the heat transfer coefficient is minimum where the thickness of boundry layer is maximum. The heat transfer coefficient is maximum where the thickness is minimum. For turbulent-region thickness of boundry layer is maximum at 3. For laminar region thickness of boundry layer is maximum at 2 so it will have minimum local heat transfer coefficient.