  We have observed seven nearby large angular sized galaxies at 0.33 GHz using
GMRT with angular resolution of $\sim10''$ and sub-mJy sensitivity. Using
archival higher frequency data at 1.4 or $\sim$6 GHz, we have then determined
their spatially resolved non-thermal spectrum. As a general trend, we find that
the spectral indices are comparatively flat at the galaxy centres and gradually
steepen with increasing galactocentric distances. Using archival far infrared
(FIR) MIPS 70 ${\mu} m$ data, we estimate the exponent of radio-FIR
correlation. One of the galaxy (NGC 4826) was found to have an exponent of the
correlation of $\sim1.4$. Average exponent from 0.33 GHz data for the rest of
the galaxies was 0.63$\pm$0.06 and is significantly flatter than the exponent
0.78$\pm$0.04 obtained using 1.4 GHz data. This indicates cosmic ray electron
(CRe) propagation to have reduced the correlation between FIR and 0.33 GHz
radio. Assuming a model of simple isotropic diffusion of CRe, we find that the
scenario can explain the frequency dependent cosmic ray electron propagation
length scales for only two galaxies. Invoking streaming instability could,
however, explain the results for the majority of the remaining ones.
