Turbulent superstructures in horizontally extended three-dimensional Rayleigh-B\'enard convection flows are investigated controlled laboratory experiments water at Prandtl number $Pr = 7$. A cell with square cross-section, aspect ratio $\Gamma l/h 25$, side length $l$ and height $h$ is used. Three different Rayleigh numbers the range $10^5 < Ra 10^6$ considered. The accessible optically, such t...

The objective of the present chapter is to analyze the radiation and mass transfer effects on an unsteady two-dimensional laminar mixed convective boundary layer flow of a viscous, incompressible, electrically conducting chemically reacting fluid, along a vertical moving semi-infinite permeable plate with suction, embedded in a uniform porous medium, in the presence of transverse magnetic field...

We report on some recent existence and uniqueness results for elliptic equations subject to Dirichlet boundary condition and involving a singular nonlinearity. We take into account the following types of problems: (i) singular problems with sublinear nonlinearity and two parameters; (ii) combined effects of asymptotically linear and singular nonlinearities in bifurcation problems; (iii) bifurca...

the fluid flow and heat transfer in lid-driven enclosures filled with cu-water nanofluid is numerically investigated. the moving vertical walls of the enclosure  are maintained in a constant temperature, while the horizontal walls are insulated. the hybrid scheme is used to discretize the convection terms and simpler algorithm is adopted to couple the velocity field and pressure in the momentum...

We present an explicit sixth order compact finite difference scheme for fast high accuracy numerical solutions of the two dimensional convection diffusion equation with variable coefficients. The sixth order scheme is based on the well-known fourth order compact scheme, the Richardson extrapolation technique, and an operator interpolation scheme. For a particular implementation, we use multisca...