dissipation of magnetohydrodynamic waves in the solar stratified flux tubes

Chromosphere is the second layer of the sun with high variability. the increase of the temperature and the decrease of the density are observed in this layer. this unusual behavior is one of the most important problems in the solar corona. between the solar chromosphere and the corona, there is a thin transition zone in which the temperature rises very rapidly. magnetohydrodynamic waves are thought to play an important role in this heating. the dissipation of alfven waves has been investigated due to phase mixing in the presence of steady flow and sheared magnetic field in a solar stratified flux tube. the temperature variations with height (t0(z)) in the flux tube has been considered. the numerical calculations showed that the amplitude of the tube oscillations decreases with time. hence, the wave damping takes place in the flux tubes. the temperature and the density variations enhances the wave damping rate compared to the case without temperature effect.