Transport in Porous Media

, Volume 70, Issue 3, pp 407–425

Free convection from one thermal and solute source in a confined porous medium

OriginalPaper

DOI: 10.1007/s11242-007-9106-7

Cite this article as:
Zhao, FY., Liu, D. & Tang, GF. Transp Porous Med (2007) 70: 407. doi:10.1007/s11242-007-9106-7

Abstract

This paper reports a numerical study of double diffusive natural convection in a vertical porous enclosure with localized heating and salting from one side. The physical model for the momentum conservation equation makes use of the Darcy equation, and the set of coupled equations is solved using the finite-volume methodology together with the deferred central difference scheme. An extensive series of numerical simulations is conducted in the range of −10 ⩽ N ⩽ + 10, 0 ⩽ Rt ⩽ 200, 10−2Le ⩽ 200, and 0.125 ⩽ L ⩽ 0.875, where N, Rt, Le, and L are the buoyancy ratio, Darcy-modified thermal Rayleigh number, Lewis number, and the segment location. Streamlines, heatlines, masslines, isotherms, and iso-concentrations are produced for several segment locations to illustrate the flow structure transition from solutal-dominated opposing to thermal dominated and solutal-dominated aiding flows, respectively. The segment location combining with thermal Rayleigh number and Lewis number is found to influence the buoyancy ratio at which flow transition and flow reversal occurs. The computed average Nusselt and Sherwood numbers provide guidance for locating the heating and salting segment.

Keywords

Free convectionPorous mediumNumerical solutionHeatlinesDiscrete source

Nomenclature

AR

aspect ratio

B

Dimensionless length of segment

c

Specific heat at constant pressure

D

Mass diffusivity

Ex

total dimensionless exit length

g

Gravitational acceleration

H

Height of the enclosure

K

Permeability of the porous medium

k

Thermal conductivity

L

Dimensionless position of segment

Le

Lewis number

N

Buoyancy ratio

Nu

Average Nusselt number

p, P

Pressure and dimensionless pressure

Rt

Thermal Darcy–Rayleigh number

s, S

Concentration and dimensionless concentration

Sh

Average Sherwood number

t, T

Temperature and dimensionless temperature

u, v

Velocity components in x, y directions

U, V

Dimensionless velocity components in X, Y

U0

Velocity scale

W

Thickness of the enclosure

x, y

Cartesian coordinates

X, Y

Dimensionless Cartesian coordinates

Greek Symbols

α

Thermal diffusivity k/(ρ c)f

β

Volumetric expansion coefficient

ɛ

Normalized porosity of the porous medium

Δ

Difference value

ν

Kinematic viscosity

μ

Dynamic viscosity of fluid

ρ

Density

σ

Heat capacity ratio (ρ c)p/(ρ c)f

τ

Dimensionless time

ϕ

Porosity

Φ

Generic variable

Ψ

Streamfunction

ξ

Heatfunction

η

Massfunction

Subscripts

max

Maximum

min

Minimum

o

Reference value or location

Superscripts

*

Dimensional variable

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.College of Civil EngineeringHunan University ChangshaHunanP. R. China