Abstract Heat and mass transport phenomena in a binary mixture compressible supercritical fluid around the pseudo-critical line were investigated theoretically and numerically. In this study, we focused on supercritical artificial air with a composition of 79% nitrogen and 21% oxygen, and investigated the piston effect, the soret effect, and the interactions between these effects. We derived thermo-fluid dynamic equations, in which the compressibility of the fluid, the temperature, the pressure, and the concentration dependences of the entropy were taken into account. The governing equations were solved numerically by using the finite difference method. We could verify that the thermal energy was propagated by the piston effect in a binary mixture supercritical fluid, and the concentration change certainly occurred due to the soret effect. Moreover, we could also estimate the thermal diffusion ratio, which made a direct correlation between the temperature gradient and the concentration gradient.