The Rayleigh–Bénard problem for a fluid with pressure- and temperature-dependent material properties

The Rayleigh–Bénard problem in viscous fluids is one of the most intensely studied problems in fluid mechanics. The literature is rich in studies concerning Navier–Stokes fluids with constant material properties and fluids with variable viscosity and/or thermal conduction, whereas it lacks in results concerning the more realistic case in which all the material properties of the fluid are variable. In this paper, we re-examine the classical problem of the onset of thermal-convection for fluids whose material properties depend on the pressure and temperature by studying the linear stability of the conduction solution.