  For a thermal conductivity that is spatially uniform and independent of
temperature, Fourier's law of heat transfer predicts a curl-free heat-flux. In
the quasi-ballistic phonon transport regime, where the Fourier law breaks down,
it has been proven starting from the Boltzmann transport equation that the
constitutive relation for the heat-flux contains a solenoidal (circulatory)
term with zero divergence and non-zero curl. In this paper we show how to
reduce the effective thermal conductivity of a material with dimensions on the
same scale as the phonon mean-free path, by exploiting the solenoidal term in
the constitutive relation.
