AbstractThis study develops the stability analysis of a double-diffusive convection system in a penetrating layer of internally heated fluid, where the variable gravity and coupled stress influence, in conjunction with the influences of the slip and Robin border conditions of the velocity, temperature, and salinity concentration fields. Two different changing gravity functions are tested: the decreasing function and the function that implies a change in sign in the layer’s upper and lower halves. The linear instability theory and non-linear stability theory have been investigated, and the D 2 Chebyshev tau technique has been used to compute the related eigenvalue systems for both theories depending on the border conditions. The computational and graphical outcomes demonstrate that important impacts determine both the stabilizing threshold and destabilizing threshold of double-diffusive convection when the changing gravity, coupled stress, and interior heat source impacts apply, along with the impacts of the slip and Robin border conditions of velocity field, temperature field, and concentration of salt field.