# A comparative study of two-dimensional natural convection in an isotropic porous medium

Research output: Contribution to journalArticle

4 Citations (Scopus)

### Abstract

One of the most commonly used models describing flow through porous media is the Brinkman-extended Darcy model, often called the Brinkman model. This model has been modified in the literature by including the usual inertia terms of the Navier-Stokes equations. In some other works, the basic Brinkman model has been modified by introducing the Forchheimer model. This latter model enables one to account for certain other nonlinear features of the flow. It is thus desirable to investigate the relative merits of employing the Brinkman model with inertia terms and the Forchheimer model, in porous media flows. In the present work, we have considered steady, two-dimensional natural convection taking place entirely in a rectangular porous cavity using both models. Assuming that the upper and lower walls of the cavity are adiabatic while the side walls are isothermal, we have solved the governing partial differential equations numerically. The effects of these models have been analyzed and compared based on the results obtained for the physical quantities of interest. A number of plots illustrating the effects of Darcy number and Rayleigh number on the streamlines and isotherms, have been shown. We have also computed the maximum absolute value of stream function and the average Nusselt number. It is seen from these results that the two models are more sensitive to Darcy number.

Original language English 60-74 15 International Journal of Applied Mathematics and Statistics 21 J11 Published - 2011

### Fingerprint

Natural Convection
Natural convection
Comparative Study
Porous Media
Porous materials
Model
Inertia
Cavity
Flow in Porous Media
Stream Function
Nusselt number
Rayleigh number
Term
Streamlines
Absolute value
Navier Stokes equations
Partial differential equations
Isotherms
Navier-Stokes Equations
Partial differential equation

### Keywords

• Brinkman model
• Forchheimer model
• Natural convection
• Numerical solution
• Rectangular cavity

### ASJC Scopus subject areas

• Applied Mathematics

### Cite this

In: International Journal of Applied Mathematics and Statistics, Vol. 21, No. J11, 2011, p. 60-74.

Research output: Contribution to journalArticle

@article{4c75635de3474c48948ba28af210a55d,
title = "A comparative study of two-dimensional natural convection in an isotropic porous medium",
abstract = "One of the most commonly used models describing flow through porous media is the Brinkman-extended Darcy model, often called the Brinkman model. This model has been modified in the literature by including the usual inertia terms of the Navier-Stokes equations. In some other works, the basic Brinkman model has been modified by introducing the Forchheimer model. This latter model enables one to account for certain other nonlinear features of the flow. It is thus desirable to investigate the relative merits of employing the Brinkman model with inertia terms and the Forchheimer model, in porous media flows. In the present work, we have considered steady, two-dimensional natural convection taking place entirely in a rectangular porous cavity using both models. Assuming that the upper and lower walls of the cavity are adiabatic while the side walls are isothermal, we have solved the governing partial differential equations numerically. The effects of these models have been analyzed and compared based on the results obtained for the physical quantities of interest. A number of plots illustrating the effects of Darcy number and Rayleigh number on the streamlines and isotherms, have been shown. We have also computed the maximum absolute value of stream function and the average Nusselt number. It is seen from these results that the two models are more sensitive to Darcy number.",
keywords = "Brinkman model, Forchheimer model, Natural convection, Numerical solution, Rectangular cavity",
author = "Pallath Chandran and Sacheti, {Nirmal C.} and Singh, {Ashok K.}",
year = "2011",
language = "English",
volume = "21",
pages = "60--74",
journal = "International Journal of Applied Mathematics and Statistics",
issn = "0973-1377",
publisher = "Centre for Environment Social and Economic Research",
number = "J11",

}

TY - JOUR

T1 - A comparative study of two-dimensional natural convection in an isotropic porous medium

AU - Chandran, Pallath

AU - Sacheti, Nirmal C.

AU - Singh, Ashok K.

PY - 2011

Y1 - 2011

N2 - One of the most commonly used models describing flow through porous media is the Brinkman-extended Darcy model, often called the Brinkman model. This model has been modified in the literature by including the usual inertia terms of the Navier-Stokes equations. In some other works, the basic Brinkman model has been modified by introducing the Forchheimer model. This latter model enables one to account for certain other nonlinear features of the flow. It is thus desirable to investigate the relative merits of employing the Brinkman model with inertia terms and the Forchheimer model, in porous media flows. In the present work, we have considered steady, two-dimensional natural convection taking place entirely in a rectangular porous cavity using both models. Assuming that the upper and lower walls of the cavity are adiabatic while the side walls are isothermal, we have solved the governing partial differential equations numerically. The effects of these models have been analyzed and compared based on the results obtained for the physical quantities of interest. A number of plots illustrating the effects of Darcy number and Rayleigh number on the streamlines and isotherms, have been shown. We have also computed the maximum absolute value of stream function and the average Nusselt number. It is seen from these results that the two models are more sensitive to Darcy number.

AB - One of the most commonly used models describing flow through porous media is the Brinkman-extended Darcy model, often called the Brinkman model. This model has been modified in the literature by including the usual inertia terms of the Navier-Stokes equations. In some other works, the basic Brinkman model has been modified by introducing the Forchheimer model. This latter model enables one to account for certain other nonlinear features of the flow. It is thus desirable to investigate the relative merits of employing the Brinkman model with inertia terms and the Forchheimer model, in porous media flows. In the present work, we have considered steady, two-dimensional natural convection taking place entirely in a rectangular porous cavity using both models. Assuming that the upper and lower walls of the cavity are adiabatic while the side walls are isothermal, we have solved the governing partial differential equations numerically. The effects of these models have been analyzed and compared based on the results obtained for the physical quantities of interest. A number of plots illustrating the effects of Darcy number and Rayleigh number on the streamlines and isotherms, have been shown. We have also computed the maximum absolute value of stream function and the average Nusselt number. It is seen from these results that the two models are more sensitive to Darcy number.

KW - Brinkman model

KW - Forchheimer model

KW - Natural convection

KW - Numerical solution

KW - Rectangular cavity

UR - http://www.scopus.com/inward/record.url?scp=79954997489&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79954997489&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:79954997489

VL - 21

SP - 60

EP - 74

JO - International Journal of Applied Mathematics and Statistics

JF - International Journal of Applied Mathematics and Statistics

SN - 0973-1377

IS - J11

ER -