Page 269 - Fundamentals of The Finite Element Method for Heat and Fluid Flow

CONVECTION IN POROUS MEDIA
T = 1
r i Insulated T = 0 261
r o

z

r

Figure 8.10 Natural convection in a fluid-saturated constant porosity medium. Problem
definition

Average Nusselt number 10

Present, Pr = 5.0
Exp., 3 mm
Exp., 6 mm
1
10 100 1000
Darcy−Grashof number
Figure 8.11 Natural convection in a fluid-saturated constant porosity medium within an
annular enclosure. Comparison of hot wall steady state Nusselt number with the experi-
mental and numerical data (Prasad et al. 1985)

results. As seen, the results are in excellent agreement with the reported results. In Table 8.2,
the analytical solution has been obtained from reference (Walker and Homsy 1978), ‘Numer-
ical1’ and ‘Numerical2’ have been obtained from references (Lauriat and Prasad 1989) and
(Trevisan and Bejan 1985) respectively.
It should be noted that the results by Walker and Homsy (Walker and Homsy 1978)
are analytical. The numerical results presented by Trevisan and Bejan (Trevisan and Bejan
1985) over-predict the results, which may be due to the coarse mesh employed.
In order to compare the present numerical results with experimental data, an axisymmet-
ric model was developed and a buoyancy-driven flow problem was studied. The boundary
and initial conditions are the same as for the previous problem, the main difference being
in the definition of the geometry. In this case, the geometry is an annulus with a radius