08-13U

A limit to the smooth continuous potential for equations of the kinetic theory of mixtures with the multi-step interaction potential is considered. When the kinetic equation reduces to that of the kinetic mean-field theory (KMFT), the limiting equation for the kinetic energy density differs from its KMFT counterpart. To elucidate this, the derivation of the KMFT transport equations is analyzed. As a result, the modified kinetic energy transport equation is proposed, which is consistent with the limiting one and with the standard form of transport equations in terms of a flux and a source. It is shown that the derived modification does not influence on previous calculations of the KMFT thermal conductivity coefficient.