Energy growth of disturbances in a non-Fourier fluid

Non-Fourier effects in macro- and micro-scale non-isothermal flow of liquids and gases. Review

“…This effect has been predicted theoretically by including non-Fourier effects in a linear stability analysis of thermal convection [58,75]. These authors showed that if C becomes of order 10 À2 , which is a plausible value in a small enough system, then the conduction state becomes unstable at a smaller value of Ra than for a Fourier fluid.…”

“…In other words, both the steady and oscillatory branches exhibit a minimum at the same (critical) Rayleigh number but corresponding to two different wavenumber. For C > C H , only oscillatory convection is predicted, at a critical Rayleigh number decreasing with C [58,75]. Experimentally, oscillatory convection in liquid metals has indeed been observed, and the predicted non-Fourier character of the liquid may be responsible for this behaviour [96].…”

“…The reference heat flux is taken as À kDT. With these scalings, the dimensionless equations for conservation of linear momentum and energy for a general read, respectively [58,75]:…”

“…Similarly, conduction in a non-Fourier fluid is lost to convection once a critical value of the Rayleigh number is exceeded. However, unlike a Fourier fluid, but similar to a viscoelastic fluid [49], nonFourier conduction can be lost to either steady or oscillatory convection, depending on the flow parameters [58,75]. For small Table 1 Thermal relaxation time t for water, mercury and molten gallium.…”

“…For thermal convection, much of existing work pertains only to thermal instability [20,46,58,75,76]. This is rapidly changing, however, with the growing importance of fast processes, micro-and nano-fluidics, and the flow and convection of nanofluids, which are suspensions of nanoparticles in a normal (base) liquid.…”