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Galaxy clusters are promising probes of precision cosmology. Their ability to deliver precise, unbiased, results depends on a better understanding of the intracluster medium (ICM). Active galactic nuclei (AGN) powered by the central Super-Massive Black Holes (SMBHs) play a major role in modifying the thermal properties of the ICM. Therefore, understanding the AGN feedback mechanism is essential for cluster cosmology. In this work, we implement two AGN heating models: (i) by buoyant cavities rising through stratified ICM (Effervescent model) and, (ii) by viscous and conductive dissipation of sound waves (Acoustic model). Our aim is to determine whether these heating models are consistent with ICM observables and if one is preferred over the other. We study the evolution of ICM thermal profiles with effervescent and acoustic models of AGN heating. We assume an initial entropy profile of ICM expected from the purely gravitational infall of the gas in the potential of the dark matter halo. We then incorporate heating, radiative cooling, and thermal conduction over the age of the clusters. Our results are: (i) We find that both heating processes match well with observations, with some tuning of relevant parameters. (ii) Thermal conduction is crucially important, even at the level of 10% of the Spitzer values, in transferring the injected energy beyond the central regions, and without which the temperature/entropy profiles do not match with observations. (iii) We show that the required injected AGN power scales with cluster mass as for both models. (iv) Moreover, the required AGN luminosity is comparable with the observed radio jet power, reinforcing …