The mechanism of the solar corona heating still remains unexplained, almost 80 years after the discovery of the million degree hot solar corona. Observations show that the temperature increases more than one order of magnitude in the transition region (TR), the boundary between the solar chromosphere and the solar corona. We are giving a detailed magnetohydrodynamic (MHD) calculation of the height dependence of the temperature and solar wind velocity. The temperature and solar wind velocity profiles are calculated for static frequency dependent spectral density of incoming MHD waves, no time dependent computer simulations have been performed. In our calculation we take into account only Alfvén wave (AW) polarization. The other modes (slow- and fast-magnetosonic waves) do not create cooling. A self-consistent calculation of MHD wave propagation through a static background of fully ionized hydrogen plasma in weak magnetic field is performed. Heated by the MHD waves, the background plasma temperature increases leading to strong plasma viscosity increase, which results in more efficient MHD wave absorption. Within this calculation, the width of the TR is also evaluated by maximal value of the logarithmic derivative of the temperature. Comparison of the calculated temperature profile with the available observational data show qualitative agreement and this gives the final answer to the problem of the solar corona heating. There are no alternative explanations of the narrow width of the TR. In such a way, after more than 70 years we have returned to the original Alfvén idea [Alfvén, H. 1947, MNRAS, 107, 211] that the solar corona is heated by AW.

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