Abstract:
Laminar natural convection in Bingham plastic fluids has been investigated from two differentially heated cylinders arranged either one above the other or along the diagonal of
the square enclosure. The coupled momentum and energy equations have been solved to
elucidate the effect of Rayleigh number (104
–106
), Prandtl number (10–100), Bingham
number (0.01 to Bnmax), and the gap between the two cylinders in terms of the geometric
parameters (0 to −0.25 for vertical alignment and 0.15 to 0.35 for diagonal alignment)
on the detailed structure of the flow field and the overall heat transfer characteristics of
the system. New extensive results are visualized in terms of streamlines, isotherm contours,
and variation of the local Nusselt number along various surfaces. Additional insights are
developed by examining the shear-rate contours and the yield surfaces delineating the
fluid-like and solid-like regions in the flow domain. At high values of the Bingham
number, the average Nusselt number reaches its asymptotic value corresponding to the conduction limit. The increasing Rayleigh number promotes fluid-like behavior which promotes
heat transfer. The augmentation in heat transfer depends on the volume of fluid participating in the buoyancy-induced flow. For the vertical arrangement, the average Nusselt
number (for the heated cylinder) decreases a little as these are moved slightly away from
the center of the enclosure, followed by an increase as the two cylinders approach one of
the sidewalls; this is so even in the conduction limit. In contrast, when the two cylinders
are arranged along the diagonal, the Nusselt number progressively decreases as the gap
between the two cylinders increases. Finally, predictive correlations have been developed
for the average Nusselt number and the limiting Bingham number thereby enabling their
estimation in a new application
