Thermal Convection of a Non-Fourier Fluid in a Vertical Slot

Abstract

The instability of steady natural convection of a non-Fourier fluid of the single-phase lagging (SPL) type between two vertical surfaces maintained at different temperatures is studied. SPL fluids possess a relaxation time, which reflects the delay in the response of the heat flux and the temperature gradient. The SPL model is particularly relevant to low-temperature liquids, ultrafast processes, and nanofluids (with a retardation time added in this case). Linear stability analysis is employed to obtain the critical state parameters, such as critical Grashof numbers. For intermediate Prandtl numbers (Pr = 7.5), when non-Fourier level exceeds a certain value, the neutral stability curve comprises a Fourier branch and an oscillatory branch. In this case, oscillatory convection increasingly becomes the mode of preference, compared to both conduction and stationary convection. Critical Grashof number decreases for fluids with higher non-Fourier levels.

Causal Heat Conduction Contravening the Fading Memory Paradigm

“…In the past, different hyperbolic transport equations have been used to study convection processes [28,29,30,31,32,33,34], and in general a variety of different interesting physical phenomena [35,36,37,38,39].…”