  The ratio of the shear viscosity ($\eta$) to entropy density ($s$) for the
intermediate energy heavy-ion collisions has been calculated by using the
Green-Kubo method in the framework of the quantum molecular dynamics model. The
theoretical curve of $\eta/s$ as a function of the incident energy for the
head-on Au+Au collisions displays that a minimum region of $\eta/s$ has been
approached at higher incident energies, where the minimum $\eta/s$ value is
about 7 times Kovtun-Son- Starinets (KSS) bound (1/4$\pi$). We argue that the
onset of minimum $\eta/s$ region at higher incident energies corresponds to the
nuclear liquid gas phase transition in nuclear multifragmentation.
