Effect of anisotropy on the onset of convection in rotating bi-disperse Brinkman porous media

Florinda Capone,Giuliana Massa,Roberta De Luca

doi:10.1007/s00707-021-03002-8

Florinda Capone, Giuliana Massa + Show 1 more

Open Access

https://doi.org/10.1007/s00707-021-03002-8

Copy DOI

Journal: Acta Mechanica	Publication Date: Jun 23, 2021
Citations: 10	License type: open-access

Affiliation: University of Naples Federico II

Abstract

Thermal convection in a horizontally isotropic bi-disperse porous medium (BDPM) uniformly heated from below is analysed. The combined effects of uniform vertical rotation and Brinkman law on the stability of the steady state of the momentum equations in a BDPM are investigated. Linear and nonlinear stability analysis of the conduction solution is performed, and the coincidence between linear instability and nonlinear stability thresholds in the L^2-norm is obtained.

Highlights

Thermal convection in single porous layers has attracted—in the past as nowadays—the interest of many authors due to its numerous applications in industrial processes, in geophysics and in astronomy, for instance
The attention of researchers has turned to the onset of thermal convection in bi-disperse porous media (BDPM)
Double porosity materials are employed in engineering, medicine, chemistry, since brain, bones or heat pipes can be modelled as bi-disperse porous media

Summary

Introduction

Thermal convection in single porous layers has attracted—in the past as nowadays—the interest of many authors due to its numerous applications in industrial processes, in geophysics and in astronomy, for instance. In [2] mixed convection flow has been numerically studied; in [4,11], the effect of an external magnetic field induced in an electrically conducting fluid has been investigated; in [17] doublediffusive convection is analysed, while [24] deals with double-diffusive convection according to the Brinkman model. In [6], Capone et al analyse the influence of vertical rotation on the onset of convection in a single temperature BDPM, according to Darcy’s law, while in [8], the authors investigate the onset of convection in a horizontal, vertical rotating, anisotropic porous layer assuming a local thermal non-equilibrium. The goal of the present paper is to study the onset of thermal convection in an anisotropic bi-disperse porous medium uniformly rotating about a vertical axis, assuming the validity of the Brinkman law both for the micropores and the macropores. The paper ends with a concluding section (Sect. 6), in which all the obtained results are collected

Mathematical model

Onset of convection

Nonlinear stability

Numerical results

Conclusions