Thermal Instability of a Power-Law Fluid Flowing in a Horizontal Porous Layer with an Open Boundary: A Two-Dimensional Analysis

Abstract

A two-dimensional analysis of the onset of thermal convective instability in a horizontal porous layer with open upper boundary is carried out. The saturating fluid is non-Newtonian of power-law behaviour, and its flow is represented through a suitable extension of Darcy’s law. A model of temperature-dependent viscosity is employed where the consistency index is considered as variable, while the power-law index is assumed to be constant. Numerical data for the neutral stability and for the critical values of a modified Darcy–Rayleigh number have been obtained. The feasibility of an experimental validation of the theoretical results predicted by the stability analysis is discussed in detail. An experimental set-up based on a Hele-Shaw cell is described, and preliminary results relative to the onset of convective cells are described. Observed hysteretic effects and deviations from the rheological model are identified as potential sources of uncertainty.