  We present mesoscale numerical simulations of Rayleigh-B\'{e}nard convection
in a two-dimensional concentrated emulsion, confined between two parallel
walls, heated from below and cooled from above, under the effect of buoyancy
forces. The systems under study comprise finite-size droplets, whose
concentration $\Phi_0$ is varied, ranging from the dilute limit up to the point
where the emulsion starts to be packed and exhibits non-Newtonian rheology. We
focus on the characterisation of the convective heat transfer properties close
to the transition from conductive to convective states. The convective flow is
confined and heterogeneous, which causes the emulsion to exhibit concentration
heterogeneities in space $\phi_0(y)$, depending on the location in the
wall-to-wall direction ($y$). With the aim of assessing quantitatively the heat
transfer efficiency of such heterogeneous systems, we resort to a side-by-side
comparison between the concentrated emulsion system and a single-phase (SP)
system, whose local viscosity $\eta^{\mbox{SP}}(y)$ is suitably constructed
from the shear rheology of the emulsion. Such comparison highlights that a
suitable degree $\Lambda$ of coarse-graining needs to be introduced in the
local viscosity $\eta_{\Lambda}^{\mbox{SP}}(y)$, in order for the single-phase
system to attain the same heat transfer efficiency of the emulsion.
Specifically, it is shown that a quantitative matching between the two systems
is possible whenever the coarse-graining is performed over a scale of the order
of the droplet size.
