Solutions are obtained for the concentration of radioactive nuclide on the walls and in the radially mixed fluid transporting the nuclide, when the fluid circulates in a closed loop system. The differential equations, which describe the mass balance of the nuclide in the system and on which the solutions are based, take into account nuclide sorption-desorption on the system walls (at constant rates) and a source which releases the radioactive nuclide (fission product) into the stream.