A generalized form of Wien’s displacement law and the blackbody radiation laws of (a) Rayleigh and Jeans, (b) Rayleigh, (c) Wien and Paschen, (d) Thiesen and (e) Planck are derived using principles of dimensional analysis. This kind of scaling is expressed in a strictly mathematical manner employing dimensional π-invariants analysis sometimes called Buckingham’s π-theorem. It is shown that in t...

In present paper, a numerical analysis for a rectangular cavity filled with a anisotropic porous media has been studied. It is assumed that the horizontal walls are adiabatic and impermeable, while the side walls of the cavity are maintained at constant temperatures and concentrations. The buoyancy force that induced the fluid motion are assumed to be cooperative. In the two extreme cases o...

Abstract The paper represents an analysis of convective instability in a vertical cylindrical porous microchannel performed using the Galerkin method. dependence critical Rayleigh number on Darcy, Knudsen, and Prandtl numbers, as well ratio thermal conductivities fluid wall, was obtained. It shown that decrease permeability medium (in other words, increase its porosity) causes flow stability. T...

Direct numerical simulations of turbulent convection at high Rayleigh numbers in large aspect ratio cells are challenging because the prohibitive computational resources required. One can achieve affordable costs for low ratios, but effect small remains to be understood fully. In this work, we explore integral quantities a cell with 0.1 by varying both and Prandtl systematically. We find that h...

In this article, entropy generation due to natural convection in entrapped trapezoidal cavities filled with nanofluid under the influence of magnetic field was numerically investigated. The upper (lower) enclosure is filled with CuO-water (Al2O3-water) nanofluid. The top and bottom horizontal walls of the trapezoidal enclosures are maintained at constant hot temperature while other inclined wal...

We present a class of a high-resolution Godunov-type algorithms for solving flow problems governed by the incompressible Navier-Stokes equations. The algorithms use high-resolution finite volume methods developed in SIAM J. Numer. Anal., 33, (1996) 627-665 for the advective terms and finite difference methods for the diffusion and the Poisson pressure equation. The high-resolution algorithm adv...

We study the fine-scale statistics of temperature and its derivatives in turbulent RayleighBénard convection. Direct numerical simulations are carried out in a cylindrical cell with unit aspect ratio filled with a fluid with Prandtl number equal to 0.7 for Rayleigh numbers between 10 and 10. The probability density function of the temperature or its fluctuations is found to be always non-Gaussi...

We describe experiments on Bénard-Marangoni convection which permit an useful understanding on the main concepts involved in this phenomenon as, for example, Bénard cells, aspect ratio, Rayleigh and Marangoni numbers, crispation number and critical conditions. In spite of the complexity of the convection theory, this work carries out a simple and introductory analysis of it which has the additi...

The effects of weak breaking of the midplane reflection symmetry on the 1:2 steady state mode interaction in Rayleigh–Bénard convection are discussed in a PDE setting. Effects of this type arise from the inclusion of non-Boussinesq terms or due to small differences in the boundary conditions at the top and bottom of the convecting layer. The latter provides the simplest realization, and capture...

We consider 2n× 2n symplectic difference systems together with associated discrete quadratic functionals and eigenvalue problems. We establish Sturmian type comparison theorems for the numbers of focal points of conjoined bases of a pair of symplectic systems. Then, using this comparison result, we show that the numbers of focal points of two conjoined bases of one symplectic system differ by a...