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.
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