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We solve numerically the ideal MHD equations with an external gravitationalfield in 2D in order to study the effects of impulsively generated linear andnon-linear Alfv\'en waves into isolated solar arcades and coronal funnels. Weanalyze the region containing the interface between the photosphere and thecorona. The main interest is to study the possibility that Alfv\'en wavestriggers the energy flux transfer toward the quiet solar corona and heat it,including the case that two consecutive waves can occur. We find that in thecase of arcades, short or large, the transferred fluxes by Alfv\'en waves aresufficient to heat the quiet corona only during a small lapse of time and in acertain region. In the case of funnels the threshold is achieved only when thewave is faster than 10 km/s, which is extremely high. We conclude from ouranalysis, that Alfv\'en waves, even in the optimistic scenario of having twoconsecutive Alfv\'en wave pulses, cannot transport enough energy as to heat thequiet corona.

Estimating the contribution of Alfv\'en waves to the process of heating the quiet solar corona