  We propose solar-shaped thermal concentrators designed with orthoradial
layers and obtained in practice through the homogenization of an ideal thermal
concentrator. Considering the spectral regime of the heat equation, we
quantitatively evaluate at different pulsations the effectiveness of the
homogenized concentrators by comparing the thermal flux existing in an ideal
concentrator and the thermal flux in an homogenized concentrator. Dependence on
the pulsation is shown to be negligible and plotting the effectiveness of the
homogenized concentrators as a function of the number of orthoradial layers
$N$, we determine the number of layers needed to achieve a certain
effectiveness. Significantly high numbers $N$(ranging from a hundred to tens of
thousands layers) are found highlighting the fact that achieving high
effectiveness demands a high level of engineering of the homogenized
concentrator.
