Low-temperature shear viscosity of a spin polarized two-component quasi-2D dipolar Fermi gas with long-range 1/r interaction in the Bose-Einstein condensation (BEC) limit, where the system can be considered as dimers and the unpaired fermions, is calculated by means of the Kubo formalism. By taking into account the dimer-atom, dimer-dimer, and atom-atom interactions in the self-energies the viscous relaxation time (tau(eta) = (tau(-1)(D A) + tau(-1)(D D) + tau(-1)(A A))(-1)) is determined. Since the relaxation rates due to these interactions tau(-1)(D A) , tau(-1)(D D) and tau(-1)(A A) varies, respectively, as T, T-2, and T in the low-temperature limit T -> 0, the dimer-atom and atom-atom interactions play the dominant role to the shear viscosity and the shear viscosity varies as T-1. For small polarization the effect of dimer-dimer interaction is important (tau(D A), tau(A A) >> tau(D D)), and the shear viscosity changes as the standard T-2 behviour. In this case, the temperature behavior of the dimer relaxation rate unaffected by 1/r interaction and the contact, dipole-dipole, and 1/r interactions play the same role in the temperature dependence of the shear viscosity. Our results have important consequences for developing experiments and theoretical researches on the transport properties of ultracold gases with repulsive or attractive long range 1/r interaction.
