  We developed a model for the enhancement of the heat flux by spherical and
elongated nano- particles in sheared laminar flows of nano-fluids. Besides the
heat flux carried by the nanoparticles the model accounts for the contribution
of their rotation to the heat flux inside and outside the particles. The
rotation of the nanoparticles has a twofold effect, it induces a fluid
advection around the particle and it strongly influences the statistical
distribution of particle orientations. These dynamical effects, which were not
included in existing thermal models, are responsible for changing the thermal
properties of flowing fluids as compared to quiescent fluids. The proposed
model is strongly supported by extensive numerical simulations, demonstrating a
potential increase of the heat flux far beyond the Maxwell-Garnet limit for the
spherical nanoparticles. The road ahead which should lead towards robust
predictive models of heat flux enhancement is discussed.
