  We explore in the present work the near-field radiative heat transfer between
two semi-infinite parallel nonlocal dielectric planes by means of fluctuational
electrodynamics. We use atheory for the nonlocal dielectric
permittivityfunction proposed byHalevi and Fuchs. This theory has the advantage
to includedifferent models performed in the literature. According to this
theory, the nonlocal dielectric function is described by a Lorenz-Drude like
single oscillator model, in which the spatial dispersion effects are
represented by an additional term depending on the square of the total
wavevector k. The theory takes into account the scattering of the
electromagneticexcitation at the surface of the dielectric material, which
leads to the need of additional boundary conditions in order to solve Maxwell's
equations and treat the electromagnetic transmission problem. The additional
boundary conditions appear as additional surface scattering parameters in the
expressions of the surface impedances. It is shown that the nonlocal modeling
deviates from the classical $1/d^2$ law in the nanometerrangeat distances still
larger than the ones where quantum effects are expected to come into play.
