  Observations from past missions such as RXTE and Beppo-SAX suggested the
presence of inverse Compton (IC) scattering at hard X-ray energies within the
intracluster medium of some massive galaxy clusters. In subsequent years,
observations by, e.g., Suzaku, and now NuSTAR, have not been able to confirm
these detections. We report on NuSTAR hard X-ray searches for IC emission in
two massive galaxy clusters, Abell 665 and Abell 2146. To constrain the global
IC flux in these two clusters, we fit global NuSTAR spectra with three models:
single (1T) and two-temperature (2T) models, and a 1T plus power law component
(T$+$IC). The temperature components are meant to characterize the thermal ICM
emission, while the power law represents the IC emission. We find that the 3-30
keV Abell 665 and 3-20 keV Abell 2146 spectra are best described by thermal
emission alone, with average global temperatures of $kT = (9.15\pm 0.1)$ keV
for Abell 665 and $kT = (8.29\pm 0.1)$ keV for Abell 2146. We constrain the IC
flux to $F_{\rm NT} < 0.60 \times 10^{-12}$ erg s$^{-1}$ cm$^{-2}$ and $F_{\rm
NT} < 0.85 \times 10^{-12}$ erg s$^{-1}$ cm$^{-2}$ (20-80 keV) for Abell 665
and Abell 2146, respectively both at the 90% confidence level. When we couple
the IC flux limits with 1.4 GHz diffuse radio data from the VLA, we set lower
limits on the average magnetic field strengths of $>$0.14 $\mu$G and $>$0.011
$\mu$G for Abell 665 and Abell 2146, respectively.
