We investigate the effect of size on intrinsic dissipation in nano-structures. We use molecular dynamics simulation and study dissipation under two different modes of deformation: stretching and bending mode. In the case of stretching deformation (with uniform strain field), dissipation takes place due to Akhiezer mechanism. For bending deformation, in addition to the Akhiezer mechanism, the spatial temperature gradient also plays a role in the process of entropy generation. Interestingly, we find that the bending modes have a higher Q factor in comparison with the stretching deformation (under the same frequency of operation). Furthermore, with the decrease in size, the difference in Q factor between the bending and stretching deformation becomes more pronounced. The lower dissipation for the case of bending deformation is explained to be due to the surface scattering of phonons. A simple model, for phonon dynamics under an oscillating strain field, is considered to explain the observed variation in dissipation rate. We also studied the scaling of Q factor with initial tension, in a beam under flexure. We develop a continuum theory to explain the observed results.