This paper examines the formation and characteristics of Rayleigh–Bénard convection in ethanol–water mixtures a rectangular container with large aspect ratio 100. Using high-accuracy numerical method, governing hydrodynamic equations were solved, revealing three distinct convective states: double localized traveling waves (DLTWs), source defect undulation (SDU), spatiotemporal grain boundary (SGB). The processes, influencing factors, flow these states are explored, along effects varying...

ABSTRACT This study investigates the solution of an ill‐posed time‐fractional order Schrödinger equation using a mollification regularization technique Dirichlet kernel. The regularized is obtained through convolution kernel with real measured data. Estimations convergence are derived based on parameter selection criteria priori and posteriori. efficiency methodology was successfully verified by simulation tests.

Double-diffusive convection under an external magnetic field has several industrial applications, and how the affects flow heat mass transfer is a research focus. This paper studies dynamical behavior of two-dimensional double-diffusive in uniform investigated using high-accuracy numerical method. The effects strength on are analyzed, process transition presence studied. results show that, as increases, gradually inhibited, most occurs through conduction. For fixed strength,...

In this paper, the dynamical behavior of two-dimensional double-diffusive convection is numerically investigated using a high-accuracy numerical method. The process flow transition in presence buoyancy studied detail, and effects fluid properties geometric parameters on characteristics heat mass transfer are discussed. results show that, as ratio increases from 0 to 2, undergoes complex series transitions, steady, temperature-dominated state periodic motion, then chaotic back finally...

By using a high-order compact finite difference method to solve the full hydrodynamic field equations, convection in binary fluid mixtures with weak negative separation ratio of −0.1 rectangular containers heated from below is numerically investigated. We consider problem Prandtl number Pr ranging 0.01 10 and Lewis Le 0.0005 1. Several convective structures such as traveling wave, localized undulation wave well stationary overturning (SOC) are obtained. For considered, state exists range...

We study the inverse issues for heat equations with spatial‐dependent source and time‐dependent source, respectively. In this work, identification are ill‐posed, numerical solutions (if they exist) not continuously dependent on data. A mollification regularization method Dirichlet kernel is proposed to tackle presented problems. Convergence analyses carried out via two parameter selection rules (a priori a posteriori), Ultimately, series of experiments verify our theoretical results.

Light-emitting diodes (LEDs) have been widely used in road lighting. This study investigates the optical design of a high-mast luminaire based on four chips-on-board LED light source modules and applies it to The model is built with Solidworks, then simulations are analysed by Tracepro Dialux. We also make physical prototype test its performance practice. illuminance distribution area nearly rectangular. interior rectangle forms smaller highlighted rectangular illumination uniform...

This paper studied the Rayleigh-Bénard convection in binary fluid mixtures with a strong Soret effect (separation ratio ψ = - 0.6 ) rectangular container heated uniformly from below. We used high-accuracy compact finite difference method to solve hydrodynamic equations describe convection. A stable traveling-wave convective state periodic source defects (PSD-TW) is obtained and its properties are discussed detail. Our numerical results show that novel PSD-TW maintained by Eckhaus instability...

<sec>Thermal convection in conducting fluids under the influence of a magnetic field is hot research topic. In this study, high-precision and high-resolution numerical method used to directly simulate double-diffusive liquid metal two-dimensional cavity. The study covers effects strength (<i>Ha</i>), Prandtl number (<i>Pr</i>), Lewis (<i>Le</i>), aspect ratio on dynamics flow heat/mass transfer both horizontal vertical field. considers intensities...

In this paper, the dynamics of an axially translating functionally graded cantilever beam (FGCB) with time-varying length are studied under environmental temperature variations. Firstly, governing partial differential equation for FGCB different temperatures is established based on Euler–Bernoulli theory. Secondly, Galerkin discretization and assumed mode method (AMM) employed to derive vibration equations each mode. Then, coupling effects axial translation motion bending deformation...

In this paper, we study the backward stochastic differential equations driven by G-Brownian motion under condition that generator is time-varying Lipschitz continuous with respect to y and uniformly z. With help of linearization method G-stochastic analysis techniques, construct approximating sequences G-BSDE obtain some precise a priori estimates. By combining approximation method, prove existence uniqueness solution conditions, as well comparison theorem.