This paper concerns the two-dimensional NavierStokes equations in a Lipschitz domain Ω with nonhomogeneous boundary condition u = φ on ∂Ω. Assuming φ ∈ L∞(∂Ω), we establish the existence of the universal attractor, and show that its dimension is bounded by c1G + c2Re, where G is the Grashof number and Re the Reynolds number.

A new characteristic-based method is developed and used for solving the mixed and forced convection problems. The nano-fluid flow with heat transfer is simulated with a novel characteristic-based scheme in closed domains with different aspect ratios. For this purpose, a FORTRAN code has been written and developed. Water as a pure fluid and water-titanium dioxide as a nano-fluid were considered....

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...

Mixed convection fluid flow and heat transfer of water-Al2O3 nanofluid inside a lid-driven square cavity has been examined numerically in order to find the optimal distribution of discrete heat sources on the wall of a cavity. The effects of different heat source length, Richardson number and Grashof number on optimal heat source location has been investigated. Moreover, the average Nusselt num...

In this paper, we investigate the effects of slip condition, transverse magnetic field and radiative heat transfer to unsteady flow of a conducting optically thin fluid through a channel filled with porous medium. Exact solution of the governing equations for fully developed flow is obtained in closed form. Detailed computations of the influence of the Grashof number, Hartmann number, slip para...

flow field and heat transfer of a nanofluid, whose non-newtonian behavior has been demonstrated in the laboratory, in a square enclosure have been numerically modeled and investigated. to estimate the viscosity of nanofluid, experimental data of hong and kim, 2012 have been used, and a new model has been proposed. finally, the obtained results have been compared to those of newtonian behavior. ...

An analytical study was performed to study effects of thermo-diffusion and chemical reactions on a three-dimensional MHD mixed convective flow of dissipative fluid along an infinite vertical porous plate with transverse sinusoidal suction velocity. The parabolic partial differential equations governing the fluid flow, heat transfer, and mass transfer were solved using perturbation technique and...

The boundary layer fluid flow in a channel with heat source, soret effects and slip condition was studied. The governing equations were solved using perturbation technique. The effects of different parameters such Prandtl number Pr , Hartmann number M, Schmidt number Sc, suction parameter  , soret number Sr and the heat source s on velocity, temperature and concentration were studied. Numerica...