We analyse the nonlinear dynamics of large scale flow in Rayleigh-B\'enard convection a two-dimensional, rectangular geometry aspect ratio $\Gamma$. impose periodic and free-slip boundary conditions streamwise spanwise directions, respectively. As Rayleigh number Ra increases, zonal dominates moderate Prandtl fluid. At high Ra, turbulent regime, transitions are seen probability density function...

The radiation impedance is an essential parameter in analyzing the vibroacoustic response of planar source. In order to calculate acoustic rectangular plate with arbitrary boundary conditions, a unified approximate approach proposed this study. displacement function expressed form supplemented two-dimensional Fourier cosine series, which can be solved by Rayleigh–Ritz method. radiated field fro...

In the present study, natural convective heat transfer in a partitioned square cavity utilizing nanofluids is studied. The vertical left and right walls are considered as the hot and cold walls, respectively and the partitions assumed to be adiabatic. The nanofluid used in this study is Al2O3 with the volume fraction of 20%. It is assumed that nanofluid is a single phase f...

A numerical study of the natural convection of the laminar heat transfers in the stationary state was developed in a horizontal ring and compared between a heated trapezoidal internal cylinder and a cold elliptical outer cylinder. This annular space is traversed by a Newtonian and incompressible fluid. The Prandtl number is set to 0.7 (air case) for different Rayleigh numbers. The system of equ...

Rayleigh-Bénard convection with internal heat sources and a variable gravity field is treated with no-slip boundary conditions. It is proved that the principle of exchange of stabilities holds at all Prandtl numbers, as long as the gravity field and the integral of the heat sources both have the same sign. The proof is based on the idea of a positive operator, and uses the positivity properties...

Some difficulties are pointed out in the methods for identification of obstacles based on the numerical verification of the inclusion of a function in the range of an operator. Numerical examples are given to illustrate theoretical conclusions. Alternative methods of identification of obstacles are mentioned: the Support Function Method (SFM) and the Modified Rayleigh Conjecture (MRC) method. 1...

Abstract The main purpose of this study is to determine the radii starlikeness and convexity generalized k -Bessel functions for three different kinds normalization in such a way that resulting are analytic unit disk complex plane. characterization entire from Laguerre–Pólya class plays significant role paper. Moreover, interlacing properties zeros function its derivative also useful proof resu...