Solutions of the equations describing the motion of a straight horizontal magnetic flux tube in the convection zone of the sun including inertial term and radiative exchange with the surroundings are presented. Cases where the tube is initially both in thermal or in mechanical equilibrium with the surroundings are considered. It is shown that the superadiabatic stratification of the convection zone affects greatly the time scale for the rise of tubes with weak field strength (less than the equipartition value), reducing it by a large factor compared with tubes in permanent thermal equilibrium with the surroundings. The various possible regimes for the rise starting from a state of initial mechanical equilibrium are discussed. It is shown that all tubes with magnetic fluxes approximately equal to or greater than 10 to the 20th Mx will cross the convection zone in time scales of less than two years.