Free Convection in Porous Media
Introduction
• This model exemplifies the use of COMSOL Multiphysics for
modeling of free convection in porous media.
• It shows the following COMSOL Multiphysics features:
– Porous media flow
– Multiphysics between fluid flow and heat transfer
– Results that are in excellent agreement with published models in the research
journals in the field
• The model has applications mainly in the fields of:
– Geophysics
– Chemical engineering
Geometry, Heating and Cooling Surfaces
Tc
Th-(Th-Tc)*s
Th
•
Enclosed domain with porous
material
•
The walls of the domain are
impervious to flow
•
The walls are either heating or
cooling surfaces with linear
temperature profiles uniting the
cool and hot surfaces
•
The arc length s goes from zero to
1 along a boundary segment.
Tc
Th-(Th-Tc)*s
Domain Equations
Momentum and mass balances


   u  u  
u  0
T

k
u  p  gT T  Tc 
Boussinesq buoyant lifting
term links flow and heat
Heat balance
   kT  c p  T u   0
Brinkman equations for porous media flow





   u  u  u  p  g 
k
T
u  0
p
u

k

g
T
T
Tc
T
T  Tc 
Solution technique:
Parametric solver to
increase T from zero to
problem- specific value
= pressure
= vector of directional velocities
= dynamic viscosity
= permeability
= fluid density
= gravity
= thermal expansion coefficient
= temperature from heat transfer application
= initial temperature
Convection and conduction
   K eT  CL T u   0
T
Ke
CL
cp
u
= temperature
= effective thermal conductivity of fluid and solid medium
= fluid volumetric heat capacity… CL= cp 
= fluid specific heat capacity
= vector of directional fluid velocities from flow application
Boundary Conditions
• Brinkman equations
u0
no slip so velocity drops to zero at wall
p  pref
for unique solution fix pressure at a point
• Convection and conduction
T  Tc
T  Th
T  Th  s Th  Tc 
Results
• Dimensionless temperature
• Velocity field
Concluding Remarks
•
•
The model is simple to define and solve in COMSOL Multiphysics
The results give excellent agreement with published scientific papers, see
M. Anwar Hossain and Mike Wilson, Natural convection flow in a fluidsaturated porous medium enclosed by non-isothermal walls with heat
generation, International Journal of Thermal Sciences, Int. J. Therm. Sci. 41
(2002) 447–454.