Diverging supersonic flows are accelerating, as in the case of a de Laval nozzle, and the same concept has been applied for acceleration of magnetohydrodynamic flows in the universe. Here, we study the dynamics of "non-diverging" cylindrical supersonic flows and show that they can be accelerated by effects of radiative cooling and the tangled magnetic field... In addition to radiative cooling of the jet materials (cooling effect), conversion of the ordered magnetic field into the turbulent one (conversion effect) and dissipation of the turbulent magnetic field (dissipation effect) are formulated according to our study on pulsar wind nebulae. Although each of the cooling and conversion effects is an ineffective acceleration process, the terminal velocity of magnetized cylindrical jets attains about half of the maximum possible value when the cooling, conversion and dissipation effects work simultaneously. The radiation efficiency is also about half of the total luminosity of the jet in the case of maximal acceleration. The concept for flow acceleration by the non-ideal MHD effects may be useful for studying relativistic jets in active galactic nuclei, in which the region near the jet axis is expected to be cylindrical and kink unstable. (read more)