Convective Instability in Fluids of High Thermal Diffusivity

The problem of the onset of thermal instability in heated layers of fluid is investigated in a linear approximation, assuming the confining planes to be surfaces of constant heat flux. It is shown that in the absence of time dependence a limiting point of the neutral stability curve can be obtained exactly by analytical methods. This point is evaluated for a variety of boundary conditions on the fluid motion, and it is verified that the results give criteria for the onset of instability as stationary convection. Similar calculations are made for an idealized fluid in the time-dependent case, and it is established that the combined effects of buoyancy and surface-tension gradients may lead to overstable oscillations in certain circumstances.