Background: The heat transfer and fluid flow within a lid-driven, inclined, square cavity
containing three circular heat sources are investigated. The enclosure is filled with DWCNT-water
nanofluid. The effects of some important parameters, such as Richardson number, inclination angle,
solid volume concentration and aspect ratio, are studied based on streamline, temperature field and
average Nusselt number. The study is performed for Richardson numbers ranging from 0.01 to 100,
inclination angles ranging from 0 to 60°, aspect ratios ranging from 0.05 to 0.15 and solid volume
fractions up to 0.004.
Method: The finite volume method and the SIMPLER algorithm are employed to solve the governing
mass, momentum and energy equations numerically. The first step in discretizing the governing
equations is to generate a finite difference mesh in the computational domain. A control volume is
generated around each node of the mesh afterwards. The governing equations are then integrated
over each control volume. In order to obtaine a stable solutions the diffusion terms are replaced using
from the second-order central difference scheme, with a hybrid scheme for the convective terms for
Results: According to the results, as the Richardson number increases, the average Nusselt number
decreases. Furthermore, at a constant solid volume fraction for R/L=0.05 and R/L=0.1, as the
inclination angle increases from 0 to 30o at Ri = 0.01, the average Nusselt number enhances. The
maximum and minimum enhancements of the average Nusselt number for this case are 2.35% and
0.79%, occurring to φ=0.004 and 0, respectively.
Conclusion: The general behavior of the streamlines and isotherms for nanofluid and pure fluid is
similar, but there are differences in terms of the lines. One of the differences is the formation of an
inner vortex inside the larger vortex, which occurred for nanofluids at all Richardson numbers while
was not observed for pure fluid. For all Richardson numbers, inclination angles and aspect ratios, as
the solid volume fraction increases, the average Nusselt number is enhanced. For all the considered
cases, as the Richardson number increases, the average Nusselt number decreases.