Long-Wave Instability of Advective Flows in Inclined Layer with Solid Heat Conductive Boundaries

TL;DR

This paper analyzes the long-wave stability of steady convective flows in inclined layers with solid boundaries under a longitudinal temperature gradient, identifying critical parameters for instability.

Contribution

It provides an analytical determination of the stability boundary and critical Grashof number for long-wave perturbations in inclined convective flows.

Findings

Identified the stability boundary for long-wave perturbations.

Calculated the critical Grashof number for the most unstable spiral perturbations.

Analyzed the influence of inclination and boundary conditions on flow stability.

Abstract

We investigate the stability of the steady convective flow in a plane tilted layer with ideal thermal conductivity of solid boundaries in the presence of uniform longitudinal temperature gradient. Analytically found the stability boundary with respect to the long-wave perturbations, find the critical Grashof number for the most dangerous among them of even spiral perturbation.