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dissipation in the fluid is negligible and assuming constant thermophysical proper-
ties (Hartnett and Kostic
1989
; Peterson and Ortega
1990
), while only relatively few
studies that assess the effect of variable properties and viscous dissipation are avail-
able. Barletta (
1998
) studied analytically the laminar mixed convection with viscous
dissipation in a vertical channel and showed that the latter enhances the buoyancy
forces. Barletta and Nield (
2009
) studied numerically the mixed convection in a lid-
driven square enclosure by taking into account the effects of viscous dissipation and
pressure work and showed that their effects are not negligible. Costa (
2006
) pointed
out that erroneous conclusions about flow and temperature fields and heat trans-
fer results are obtained in convection heat transfer problems if viscous dissipation
effects are neglected with respect to the First Law of Thermodynamics. Zamora and
Hernández (
1997
) studied numerically the influence of variable property effects on
natural convection flows in asymmetrically heated vertical channels and found that
variable property effects have a strong influence on the Nusselt number. Hernández
and Zamora (
2005
) assessed the effects of variable properties and non-uniform heat-
ing on natural convection flows in vertical channels and pointed out that variable
property effects are significant and cannot be neglected.
The above literature review reveals that there are relatively few studies that deal
with the investigation of temperature dependent viscosity effects and viscous dissipa-
tion during mixed convection heat transfer. The aim of the present study is to perform
a numerical investigation for opposing laminar mixed convection in a rectangular
enclosure subjected to isothermal side walls that are kept at different temperatures,
while the top and bottom walls are assumed to be adiabatic. Emphasis on the effect
of the Richardson and Brinkman numbers on the overall flow and heat transfer is
presented.
2 Problem Formulation
A schematic diagram of the enclosure configuration studied is shown in Fig.
1
.The
height and width of the enclosure are
L
and
W
, respectively, with
W
1.5
L
.
The top and bottom walls are assumed to be adiabatic, while the left (hot) and
right (cold) walls have uniform surface temperatures
T
H
and
T
C
, respectively. The
flow enters through the upper left inlet with uniform velocity
u
0
and temperature
T
0
=
(
=
T
H
+
T
C
)/
2. The density variations in the buoyancy term are treated according
Fig. 1
Schematic diagram
of the flow and heat transfer
problem
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