  In this work we analyze plasma and magnetic field data provided by the Parker
Solar Probe (\emph{PSP}) and Solar Orbiter (\emph{SO}) missions to investigate
the radial evolution of the heating of Alfv\'enic slow wind (ASW) by imbalanced
Alfv\'en-Wave (AW) turbulent fluctuations from 0.06 au to 1 au. in our analysis
we focus on slow solar-wind intervals with highly imbalanced and incompressible
turbulence (i.e., magnetic compressibility $C_B=\delta B/B\leq 0.25$, plasma
compressibility $C_n=\delta n/n\leq 0.25$ and normalized cross-helicity
$\sigma_c\geq 0.65$). First, we estimate the AW turbulent dissipation rate from
the wave energy equation and find that the radial profile trend is similar to
the proton heating rate. Second, we find that the scaling of the empirical AW
turbulent dissipation rate $Q_W$ obtained from the wave energy equation matches
the scaling from the phenomenological AW turbulent dissipation rate $Q_{\rm
CH09}$ (with $Q_{\rm CH09}\simeq 1.55 Q_W$) derived by~\cite{chandran09} based
on the model of reflection-driven turbulence. Our results suggest that, as in
the fast solar wind, AW turbulence plays a major role in the ion heating that
occurs in incompressible slow-wind streams.
