A method has been proposed for the prediction of velocity radial profiles and axial profiles of the local heat fluxes supplied through the wall in nonadiabatic tubular apparatus with bed packed randomly with regular solid elements (spheres, cylinders, Raschig rings) through which air is flowing. The velocity profiles can be predicted by means of equation (16) and fig. 5, and the heat flux profiles, by means of equations (17), (21), (27), (28). The profiles predicted agree well with those obtained experimentally under exothermic and endothermic conditions. In the first case, the apparatus with cooled wall has been supplied with the air previously heated, and in the second case, the apparatus wall has been heated and cold air has been passed through it. The experiments have been performed in the equipment, the scheme of which is presented in fig. 1. The velocity and temperature profiles have been determined by the thermoanemometry techniques with the probe moved continously at constant speed along individual circumferences, with the density of measurement points of 1/mm2. The instability of the system under nonadiabatic conditions has been observed, revealing a sudden rise of temperature when the local heat flux at 1/3 of the height of the apparatus wall has been equal to that averaged over the whole wall.