  We numerically study the Rayleigh-B\'enard (RB) convection in two-dimensional
model emulsions confined between two parallel walls at fixed temperatures. The
systems under study are heterogeneous, with finite-size droplets dispersed in a
continuous phase. The droplet concentration is chosen to explore the convective
heat transfer of both Newtonian (low droplet concentration) and non-Newtonian
(high droplet concentration) emulsions, the latter exhibiting shear-thinning
rheology, with a noticeable increase of viscosity at low shear rates. It is
well known that the transition to convection of a homogeneous Newtonian system
is accompanied by the onset of steady flow and time-independent heat flux; in
marked contrast, the heterogeneity of emulsions brings in an additional and
previously unexplored phenomenology. As a matter of fact, when the droplet
concentration increases, we observe that the heat transfer process is mediated
by a non-steady flow, with neat heat-flux fluctuations, obeying a non-Gaussian
statistics. The observed findings are ascribed to the emergence of space
correlations among distant droplets, which we highlight via direct measurements
of the droplets displacement and the characterisation of the associated
correlation functions.
