The free conv ection boundary layer flow of a Darcy-Brinkman fluid that is induced by a constant-temperature horizontal semi-infinite surface embedded in a fluid-saturated porous medium is inv estigated in this work. It is shown that both the Darcy and Rayleigh numbers may be scaled out of the boundary layer equations, leav ing a parabolic system of equations with no parameters to vary. The equ...

We investigate the dynamics of a thermally convecting fluid as it interacts with freely moving solid objects. This is a previously unexplored paradigm of interactions between many free bodies mediated by thermal convection, which gives rise to surprising robust oscillations between different large-scale circulations. Once begun, this process repeats cyclically, with the collection of objects (s...

The source of increased water vapor mixing raregions of convective outflow. These studies dealt with varitios over the central and eastern tropical Pacific region during ations in relative humidity over a broad region of the tropthe 1992 E1 Nifio event is examined using measurements of ical upper troposphere (i.e., 200-500 hPa). Presently, it is upper tropospheric water vapor provided by the Mi...

In this paper, free convection flow and heat transfer of nanofluids of differently-shaped nano-sized particles over a vertical plate at very low and high Prandtl numbers are analyzed.  The governing systems of nonlinear partial differential equations of the flow and heat transfer processes are converted to systems of nonlinear ordinary differential equation through similarity transformations. T...

We consider the Galerkin nite element method for partial diiferential equations in two dimensions, where the nite-dimensional space used consists of piecewise (isoparametric) polynomials enriched with bubble functions. Writing L for the diierential operator, we show that for elliptic convection-diiusion problems, the component of the bubble enrichment that stabilizes the method is equivalent to...

We examine the nature of the thermosolutal convection with or without rotation in the infinite Prandtl number regime, which is applicable to magma chambers. The onset of bifurcation and the structure of the bifurcated solutions in this double diffusion problem are analyzed. The stress-free boundary condition is imposed at the top and bottom plates confining the fluid. For the rotation free case...

A new upper bound on the rate of vertical heat transport is established in 3 dimensions for stress-free velocity boundary conditions on horizontally periodic plates. For large (but finite) Prandtl numbers this bound is an improvement over the ‘ultimate’ Ra scaling and in the limit of infinite Pr, agrees with the bound of Ra recently derived in that limit. keywords: Rayleigh-Bénard convection, B...