901 publications from this institution
It is shown that the phenomenon of natural convection driven in a porous medium by a cold plate facing upward or by a warm plate facing downward consists of a finite-length boundary layer flow chopped off by the sharp edges of the plate. The heat and fluid flow features of the boundary layer are determined analytically employing scale analysis and integral analysis. The overall heat transfer rate between porous medium and plate is found to vary as Nu/Ra1/3 = 0(1), where Ra is the Darcy-modified Rayleigh number based on plate half-length. The boundary layer features of the flow and the heat transfer effected by it are confirmed in the Ra range 100–700 by numerical solutions of the complete partial differential equations.
The cerebral vascular network has evolved in such a way so as to minimize transport time and energy expenditure. This is accomplished by a subtle combination of the optimal arrangement of arteries, arterioles and capillaries and the transport mechanisms of convection and diffusion. Elucidating the interaction between cerebral vascular architectonics and the latter physical mechanisms can catalyse progress in treating cerebral pathologies such as stroke, brain tumours, dementia and targeted drug delivery. Here, we show that brain microvascular organization is predicated on commensurate intracapillary oxygen convection and parenchymal diffusion times. Cross-species grey matter results for the rat, cat, rabbit and human reveal very good correlation between the cerebral capillary and tissue mean axial oxygen convective and diffusion time intervals. These findings agree with the constructal principle.
