Onset of darcy-brinkman convection in a rotating porous layer induced by purely internal heating

Dhananjay Yadav, Junye Wang, Jinho Lee

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

The influence of rotation and Darcy number on the criterion for the onset of convection induced by purely internal heating in a porous layer is investigated. The boundaries are considered to be free-free, rigid-rigid, lower-rigid, and upper-free boundaries and subjected to two sets of thermal boundary conditions, namely, case (i) both boundaries isothermal and case (ii) lower insulated and upper isothermal. The Darcy-Brinkman model, with fluid viscosity differ-ent from effective viscosity, is used to characterize the fluid motion in porous medium. The coupled governing partial differential equations are transformed into ordinary differential equations by use of linear stability analysis and solved numerically using the higher order Galerkin method with the internal Darcy-Rayleigh number as the eigenvalue. Re-sults indicate that the nature of boundaries, Darcy number, and speed of rotation significantly influence the stability characteristics of the system. Convection, when it occurs for case (i) where both boundaries are isothermal, is concen-trated in the upper portion of the layer; whereas for case (ii) with lower insulated and upper isothermal boundaries, it is concentrated in the whole layer. The effect of increasing rotation parameter inhibits the onset of convection, while Darcy number shows dual behavior on the criterion for the onset of convection in the presence of rotation. Some known results are also recovered as special cases of the present study.

Original languageEnglish
Pages (from-to)691-706
Number of pages16
JournalJournal of Porous Media
Volume20
Issue number8
DOIs
Publication statusPublished - 2017 Jan 1

Fingerprint

Convection
Heating
Rotating
convection
Internal
heating
Viscosity
Linear stability analysis
Fluids
viscosity
Galerkin methods
Fluid
Ordinary differential equations
High-order Methods
free boundaries
Partial differential equations
fluids
Galerkin method
Linear Stability Analysis
Rayleigh number

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Biomedical Engineering
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

@article{57daf96c0f6e4a18a99a61519c2f573b,
title = "Onset of darcy-brinkman convection in a rotating porous layer induced by purely internal heating",
abstract = "The influence of rotation and Darcy number on the criterion for the onset of convection induced by purely internal heating in a porous layer is investigated. The boundaries are considered to be free-free, rigid-rigid, lower-rigid, and upper-free boundaries and subjected to two sets of thermal boundary conditions, namely, case (i) both boundaries isothermal and case (ii) lower insulated and upper isothermal. The Darcy-Brinkman model, with fluid viscosity differ-ent from effective viscosity, is used to characterize the fluid motion in porous medium. The coupled governing partial differential equations are transformed into ordinary differential equations by use of linear stability analysis and solved numerically using the higher order Galerkin method with the internal Darcy-Rayleigh number as the eigenvalue. Re-sults indicate that the nature of boundaries, Darcy number, and speed of rotation significantly influence the stability characteristics of the system. Convection, when it occurs for case (i) where both boundaries are isothermal, is concen-trated in the upper portion of the layer; whereas for case (ii) with lower insulated and upper isothermal boundaries, it is concentrated in the whole layer. The effect of increasing rotation parameter inhibits the onset of convection, while Darcy number shows dual behavior on the criterion for the onset of convection in the presence of rotation. Some known results are also recovered as special cases of the present study.",
author = "Dhananjay Yadav and Junye Wang and Jinho Lee",
year = "2017",
month = "1",
day = "1",
doi = "10.1615/JPorMedia.v20.i8.20",
language = "English",
volume = "20",
pages = "691--706",
journal = "Journal of Porous Media",
issn = "1091-028X",
publisher = "Begell House Inc.",
number = "8",

}

Onset of darcy-brinkman convection in a rotating porous layer induced by purely internal heating. / Yadav, Dhananjay; Wang, Junye; Lee, Jinho.

In: Journal of Porous Media, Vol. 20, No. 8, 01.01.2017, p. 691-706.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Onset of darcy-brinkman convection in a rotating porous layer induced by purely internal heating

AU - Yadav, Dhananjay

AU - Wang, Junye

AU - Lee, Jinho

PY - 2017/1/1

Y1 - 2017/1/1

N2 - The influence of rotation and Darcy number on the criterion for the onset of convection induced by purely internal heating in a porous layer is investigated. The boundaries are considered to be free-free, rigid-rigid, lower-rigid, and upper-free boundaries and subjected to two sets of thermal boundary conditions, namely, case (i) both boundaries isothermal and case (ii) lower insulated and upper isothermal. The Darcy-Brinkman model, with fluid viscosity differ-ent from effective viscosity, is used to characterize the fluid motion in porous medium. The coupled governing partial differential equations are transformed into ordinary differential equations by use of linear stability analysis and solved numerically using the higher order Galerkin method with the internal Darcy-Rayleigh number as the eigenvalue. Re-sults indicate that the nature of boundaries, Darcy number, and speed of rotation significantly influence the stability characteristics of the system. Convection, when it occurs for case (i) where both boundaries are isothermal, is concen-trated in the upper portion of the layer; whereas for case (ii) with lower insulated and upper isothermal boundaries, it is concentrated in the whole layer. The effect of increasing rotation parameter inhibits the onset of convection, while Darcy number shows dual behavior on the criterion for the onset of convection in the presence of rotation. Some known results are also recovered as special cases of the present study.

AB - The influence of rotation and Darcy number on the criterion for the onset of convection induced by purely internal heating in a porous layer is investigated. The boundaries are considered to be free-free, rigid-rigid, lower-rigid, and upper-free boundaries and subjected to two sets of thermal boundary conditions, namely, case (i) both boundaries isothermal and case (ii) lower insulated and upper isothermal. The Darcy-Brinkman model, with fluid viscosity differ-ent from effective viscosity, is used to characterize the fluid motion in porous medium. The coupled governing partial differential equations are transformed into ordinary differential equations by use of linear stability analysis and solved numerically using the higher order Galerkin method with the internal Darcy-Rayleigh number as the eigenvalue. Re-sults indicate that the nature of boundaries, Darcy number, and speed of rotation significantly influence the stability characteristics of the system. Convection, when it occurs for case (i) where both boundaries are isothermal, is concen-trated in the upper portion of the layer; whereas for case (ii) with lower insulated and upper isothermal boundaries, it is concentrated in the whole layer. The effect of increasing rotation parameter inhibits the onset of convection, while Darcy number shows dual behavior on the criterion for the onset of convection in the presence of rotation. Some known results are also recovered as special cases of the present study.

UR - http://www.scopus.com/inward/record.url?scp=85034239804&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85034239804&partnerID=8YFLogxK

U2 - 10.1615/JPorMedia.v20.i8.20

DO - 10.1615/JPorMedia.v20.i8.20

M3 - Article

AN - SCOPUS:85034239804

VL - 20

SP - 691

EP - 706

JO - Journal of Porous Media

JF - Journal of Porous Media

SN - 1091-028X

IS - 8

ER -