Thermal convection of non-Fourier fluids. Linear stability

The natural convection of non-Fourier fluids is examined. These fluids possess a relaxation time that reflects the delay in the response of the heat flux with respect to the temperature gradient. Non-Fourier fluids span a wide range of applications, including low-temperature liquids, nanofluids, convection in nano-devices, and fluids subjected to fast heat transfer processes. The constitutive equation for heat flux is frame invariant. For small relaxation time, the neutral stability curve comprises a Fourier branch and an oscillatory branch, intersecting at some wavenumber. Both stationary and oscillatory convection become equally probable as the relaxation time increases, suggesting the existence of a bistable mode. With increasing relaxation time, oscillatory convection becomes increasingly the mode of preference, at the expense of both conduction and stationary convection, with increasing roll size. Although the oscillation frequency decreases monotonically with roll size, it exhibits a maximum against the relaxation time. Finally, the parallels between non-Fourier and non-Newtonian effects are emphasized at the formulation and phenomenological levels.