Thermal instability of the buoyant flow in a vertical cylindrical porous layer with a uniform internal heat source

TL;DR

This paper investigates the onset of thermal convection instability in a vertical cylindrical porous layer with uniform internal heat generation, identifying critical parameters and the most unstable modes through numerical analysis.

Contribution

It provides a detailed linear stability analysis of buoyant flow in a porous cylinder with internal heat sources, highlighting the dominant axisymmetric instability mode.

Findings

Critical Rayleigh numbers for instability are identified.

Axisymmetric modes are the most unstable.

Neutral stability curves are numerically computed.

Abstract

The buoyancy-induced parallel flow in a vertical cylindrical porous layer is analysed. A radial thermal gradient caused by a uniformly distributed heat source is assumed to induce the buoyant flow. The layer boundaries are modelled as isothermal and permeable to an external fluid reservoir. The onset of the convective instability is analysed by linearising the governing equations for the perturbations. The governing parameters driving the instability are the heat-source Rayleigh number and the ratio between the internal radius and the external radius. Neutral stability curves and the critical values of the Rayleigh number, the perturbation wave number and the angular frequency are computed numerically. It is shown that axisymmetric modes form the most dangerous mode of instability.