A model interpreting variations of EUV brightness upward propagating in sol
ar coronal loops as slow magnetoacoustic waves is developed. A loop is cons
idered to have a non-zero plane inclination angle and offset of the circula
r loop centre from the baseline. The model also incorporates effects of dis
sipation and gravitational stratification. A linear evolutionary equation i
s derived and applied to investigations of slow wave dynamics. Both the non
-zero plane inclination and the offset decrease the growth of the wave ampl
itude due to stratification. It is shown that wide-spectrum slow magnetoaco
ustic waves, consistent with currently available observations in the low fr
equency part of the spectrum, can provide a rate of heat deposition suffici
ent to heat the loop. In this scenario, the heat would be deposited near th
e loop footpoints, which agrees with the current observational data.