A Numerical study is carried out to investigate the effect of RAYLEIGH NUMBER with rotation on the flow and heat transfer characteristics in a differentially heated enclosure rotating about the horizontal axis. A Fortran Code developed based on FVM is used to discretize governing equations. Upwind difference scheme for convective terms and fully implicit scheme for transient terms are used. The SIMPLE algorithm is employed to couple pressure and velocities on staggered grid arrangement. The results were obtained for a Taylor NUMBER(10􀬷 ≤ 􀜶 􀜽 ≤ 10􀬹 ), rotation (10 􀝎 􀝌 􀝉 ≤ Ω ≤ 25 􀝎 􀝌 􀝉 ), and Rotational RAYLEIGH NUMBER (10􀬵 ≤ 􀜴 􀜽 􀯪 ≤ 10􀬷 ) for two different RAYLEIGH NUMBER (1. 3 × 10􀬸 & 1. 1 × 10􀬹 ) with fixed Prandtl NUMBER (􀜲 􀝎 = 0. 71). The results showed that the Coriolis force first tends to decrease heat transfer to a minimum and then starts to increase it with increase RAYLEIGH NUMBER and rotation. Minimum depends on RAYLEIGH NUMBER and corresponds to the balanced effects of interacting forces at the point of transition. At rotations, below minimum in average heat transfer, the circulations are counter clockwise. The direction of coriolis force is from core region, so both flow and heat transfer is reduced. When coriolis force is much larger than thermal buoyancy, motion is clockwise, and transition is prevented. coriolis force now tends to promote flow circulation and therefore increases the heat transfer. The frequency content of flow pattern reveals the structural changes in the flow and temperature fields with increasing RAYLEIGH NUMBER and rotation. The existence of different flow regimes dominated by these body forces complicates the time average heat transfer characteristics with a different behaviour in each of the regimes.

Double diffusive convection (DDC) flows are widely seen in many industrial processes where the thermo-solutal buoyancy forces generates vorticity and initiates convective heat and mass transfer. In this paper numerical computations are conducted on this behaviour inside cavities of different aspect ratio at nominal RAYLEIGH NUMBER using a finite element based code. Velocity – vorticity form of Navier-Stokes equations are solved along with energy and solutal concentration conservation equations simultaneously using Galerkin’ s weighted residual method. Bottom wall is assumed hot and salted while top wall is maintained as sink, both side walls of the cavity are assumed to be adiabatic to heat and mass flow. Generally cavities with the present boundary conditions exhibit weak vorticity and convection characteristic especially at low RAYLEIGH NUMBER. In this numerical work an attempt is made to explore the role of variation in relative strength of thermal and solutal buoyancy forces on flow characteristics and mode of heat and mass transfer in such conditions. Simulation results have been reported for different buoyancy ratios in the range-2≤ N≤ 2, RAYLEIGH NUMBER varying from 1. 0e5 to 1. 0e3, for cavities of aspect ratios, 0. 5(shallow), 1 (square) and 2 (deep). Flow contours are well validated with the results in the literature. The fluid rotation patterns are captured and reported under different operating conditions chosen, the vorticity generation is observed relatively low for deep cavity when compared to other two. Investigations revealed that fluid convection gets greatly hampered when operated in negative buoyancy ratio regime and require relatively higher RAYLEIGH NUMBER to change the mode of heat transfer from diffusion to convection.

In this paper, we study a three-parameter bivariate distribution obtained by taking Geometric minimum of RAYLEIGH distributions. Some important properties of this bivariate distribution have been investigated. It is observed that the maximum likelihood estimators of the parameters cannot be obtained in closed forms. We propose to use the EM algorithm to compute the maximum likelihood estimates of the parameters, and it is computationally quite tractable. Based on an extensive simulated study, the effectiveness of the proposed algorithm is confirmed. We also analyze one real data set for illustrative purposes. Finally, we conclude the paper.

RAYLEIGH-Taylor (RT) instability has a growing importance in many fields including aircraft industry and astrophysics. The development and the growth of RT instability were investigated using sinusoidal disturbances with different wavelength at the interface of the two fluids. Numerical simulations were performed by solving Navier-Stokes unsteady equations with the VOF formulation. Results of the 2D simulation are compared with experimental results.It is shown that beyond a critical time, not captured experimentally, the mushroom shape of RT instability turns into a helical path or breaks down into a patchy shape depending on the shape of disturbance. Nonlinear instabilities responsible for such behavior are apparent when the wavelength exceeds 10 times the length scale introduced in this study.

RAYLEIGH waves are surface waves which are dispersive in layered media. In order to study RAYLEIGH wave dispersion, there are several methods. Among these methods the application of matrix methods for elastic layered media is preferred to other methods. In the matrix method for a layered medium, boundary conditions for different interfaces are satisfied to obtain a relation for calculating RAYLEIGH wave dispersion which should be resolved by numerical methods. A program for the computing of RAYLEIGH waves dispersion was developed. The resulted dispersion curves from this program werecompared to similar methods which showed good agreement. According to the resulted graphs, wherever the earth structure is complex the dispersion curves also will be complex and different models will be moved oscillatory. Phase and group velocity curves tend to lower values when there is a surface sedimentary layer in the earth model. Thus, synthesis of these curves leads to clarification of different seismic phases, history of waves propagation from source to receiver and consequently imaging of earth structure.

In this study, natural convection of a viscous nanofluid-casson model with a yield stress in a square enclosure with differentially heated side walls has been studied. The system of coupled nonlinear differential equations for flow, heat transfer and mass transfer were solved by using the finite element method. The effects of yield NUMBER (0≤Y≤Y_max), RAYLEIGH NUMBER (〖10〗^3≤Ra≤〖10〗^6 ), Lewis NUMBER (2.5≤Le≤7.5) and Buoyancy ratio NUMBER (0.1≤N_r≤1), on the flow, heat and mass transfer have been investigated and the yielded and unyielded regions are specified. The results show that the mass distribution in the enclosure is strongly influenced by the Lewis NUMBER, but this parameter does not have a significant effect on the flow and temperature fields. The combined effect of Lewis NUMBER and yield stress on fluid flow is negligible and as a result, this parameter has no significant effect on unyielded regions. On the other hand, increasing the buoyancy parameter suppressed the convective flow and heat transfer rate in the cavity. It was observed that increasing the buoyancy parameter enhances the effect of viscous force and as a result, the unyielded regions expand in the enclosure and the critical yield stress decreases.

This paper investigates the distributed controllability of nonlocal RAYLEIGH beam. The mathematical problem is formulated as an abstract di, erential equation. It is shown that a sequence of eigenfunction of nonlocal RAYLEIGH beam forms Riesz basis. Based on Riesz basis properties and theory of abstract di, erential equation, it is proved that a vibrating nonlocal RAYLEIGH beam is approximately controllable under suitable distributed control force while it is not exponentially stable.